Roger Penrose - Is Mathematics Invented or Discovered?

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Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music? Or is mathematics discovered-always out there, somewhere, like mysterious islands waiting to be found? Whatever mathematics is will help define reality itself.
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Sir Roger Penrose is an English mathematical physicist, recreational mathematician and philosopher. He is the Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of the University of Oxford, as well as an Emeritus Fellow of Wadham College.
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Closer to Truth presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.

[@CloserToTruthTV]

This interview is part of our Mathematics and Philosophy playlist series, created for Mathematics and Statistics Awareness Month. Starting Monday, 4/20/20, we will be publishing two mathematics playlists of all-new, never-before-seen interviews with renowned mathematicians! If you can't wait, the "Is Mathematics Invented or Discovered?" playlist is already available (and freshly updated!) on CTT's channel. Playlist - Is Mathematics Invented or Discovered? - kzbin.info/aero/PLFJr3pJl27pIp1EsDD2rYaTI7GxoXqrLs

[@OjoRojo40]

Lol, I can't believe this pedantic asshole. He's a Platonian.....not only he believes in ideas, but he thinks mathematics is the ultimate idea that explains everything. Plato said only the philosopher could get us out of the dark and show us the light, so we can only hope enlightened mathematicians like him can show us the true.......Give me a break dude.

[@NicksterNOC]

@@OjoRojo40 I disagree. Also they talk about all the bizarre math that doesn't appear to tie into reality. Eventually they'll figure out how even those equations tie into the natural realm. Philosophy can explain how everything works, but math can show the mechanisms that make that happen. Penrose even talks about how consciousness is probably a quantum phenomenon so don't go around thinking he's close minded or a small picture type of person

[@thysvanzyl2782]

I am so interested to know what Sir Penrose thinks about the work of the Indian mathematician, Ramanujan. Ramanujan's ideas were apparently so powerful and 'visionary'.

[@OjoRojo40]

​@@NicksterNOC You are proving he's close minded and so you are. "they talk about all the bizarre math that doesn't appear to tie into reality. Eventually they'll figure out how even those equations tie into the natural realm". The "bizarre math" could be a door for different forms of interpretation (again, it's bizarre but still math.....). Eventually they'll figure out how even those equations tie into the natural realm? What natural realm please... the natural realm of math??? "Philosophy can explain how everything works, but math can show the mechanisms that make that happen". You are repeating what Penrose said and his essentialist narrow view of philosophy. That's why he believes in mathematics as the "real" true that will get us closer to the ideal realm (in a Platonic sense) Philosophy most certainly can't explain how everything works, hence math like I said, will never have any response to the most fundamental metaphysical questions of humans. "Penrose even talks about how consciousness is probably a quantum phenomenon", I really can't see how this help his case. Consciousness reduce to a physical interpretation??? Maybe you can help me. Thanks for your time.

[@Lorendrawn]

Even philosophy KZbin video comment sections become toxic. You guys are taking quarantine very badly.

[@megamillionfreak]

We are immensely blessed to be living in an era where such minds are available for our casual consumption and for free.

[@xgengx7530]

Indeed

[@johncastillo8551]

@M Grant the internet WANTS you to think that it has improved your life… and that you are gaining knowledge from it but in reality it is gaining knowledge from YOU… the Plutonic world needs to be left alone or else it will enslave us all… it has lurked in the shadows before the existence of time and WE are what it has been waiting for… WE WILL BE THE HOST IT HAS BEEN WAITING FOR!

[@fadelfakih3511]

Can't agree anymore

[@ChosenPlaysYT]

And we waste it on TikTok watching morons.

[@lailandadumbmathematician7747]

@@ChosenPlaysYT People will always find ways to 'waste' time. That's their choice, but there's no reason to insult anyone over it.

[@simonhallin8909]

When he talked about molecules and atoms, in the beginning, I thought, nice! A mathematician who seems comfortable in physics. Then I searched him up and found out he has a Nobel prize in physics. I guess he's more than comfortable.

[@festusbojangles7027]

why would you put your own picture on the internet? thats kind of weird

[@EnjoySackLunch]

@@festusbojangles7027 why do you eat snails

[@festusbojangles7027]

@@EnjoySackLunch be quiet pooh pooh

[@EnjoySackLunch]

@@festusbojangles7027 rude

[@ccunliffe]

@@EnjoySackLunch Why do you enjoy sack lunch?

[@stellarwind1946]

It’s always a privilege to listen to the great mind of Sir Roger Penrose

[@eduardo6380]

He answered the question with more questions. A wise man

[@Treador55]

9:00 if you are wondering where the title question starts.

[@chuckmanson6092]

Thank you.

[@wkmalory]

here for Penrose so no need to fast forward nice that one of you for every video tho

[@NoOne-ky1er]

Tell me his answer too

[@333peacher4]

@@NoOne-ky1er both.

[@infinitenature703]

@@333peacher4 that's not what he said

[@trajan75]

Roger Penrose was awarded the Noble Prize for physics when he was 90 years old; That was an astounding achievement. I am in my early 70s, I can only tell you younger people that to be able to think clearly an and creatively at that age is truly astounding.

[@ysph]

eh, we're too dumb to even recognize if roger penrose was developing dementia or something anyway.

[@dustypope3571]

I am in my pre-fifties and I find that achievement unfathomable!

[@crustyoldfart]

Well since we're all bragging about how smart we are - I'm in my late 80's, and surprised that Dr Penrose believes that mathematics is not an invention, but is " absolute " in some sense. I greatly admire him for his achievements - who would not - but I take issue with this statement. He himself invented Penrose tiles. Would he claim that these are not inventions but in some sense a revelation of something absolute ? Why is there a Nobel Prize for Physics, and no such prize for engineering ? Such as suggestion is absurd of course. But it illustrates in a small way the difference between the real world and the abstract world of mathematics. Nobel Laureates have bragging rights in a way that many useful people grounded in the real world cannot aspire to.

[@trajan75]

@@crustyoldfart Harold, congratulations on being so articulate in your late 80's although I must say that your notion that mathematics is a pure invention is nonsense. It is a bottom absolute and, just to get your dander up, it is one of our insights into he nature of God.

[@crustyoldfart]

@@trajan75 Thank you for pointing out that what I suggest is nonsense. The thing I always bear in mind when receiving a gratuitous insult is that it is delivered with sincerity, and am accordingly appreciative. Your second strategy of invoking God, far from getting my " dander up ", I take as a clear warning that any further dialogue on the subject is impossible. For the benefit of others who may be reading this I would suggest that the conclusion that I for one draw from Kurt Goedle's result that mathematics can contain true statements which are unprovable, suggests that mathematics is a self-referencing system, no more, no less. On a slightly different tack: the great Michelangelo is reputed to have said that the awkward block of marble he chose to work on had contained the figure of David within it all along, and all he had done was to reveal the figure. Could this be a metaphor for the history of the development of mathematics ?

[@shadowfantasiesf8556]

This makes you wanna do math. I never in my life had a teacher, that had the same philosophical euphorism that these to convey. It's such an obvious thing you would need to convey, in order for a student to care about learning it and yet nobody does this.

[@KarlPilkington89]

hahaha

[@kiwibrainstorm1487]

There is a big difference between doing / researching math, and listening to someone that does it...

[@daviddempsey8721]

It really does, doesn’t it? Nothing stopping you! There are lots of interesting Math teachers on KZbin exploring it for the joy of seeing and understanding more. See Eddy Wu’s TED talk about what Math is for - Australian Math teacher. kzbin.info/www/bejne/honahKeaqrOqZ5Y

[@shadowfantasiesf8556]

@@privateaccount8027 This isn't blaming. In fact I loved math as a kid. But that came from myself and not the teacher and that's the point.

[@grostoss4259]

@@shadowfantasiesf8556 I hated math when it was only abstract and physics and then started playing with computers. Oh boy do I love math and logic now. Sometimes it is only about what peeks your interest !

[@coder-x7440]

I wish… that as a kid, someone had described math to me in this way. That it’s something humanity discovered. It exists independent of us, it’s not all understood or discovered. And in order to predict how reality will play out, you need to understand math. It describes reality, past, present, and into the future.

[@SpaceCadet4Jesus]

Mathematics may make future predictions and depending on all sufficient factors known may describe present reality of which we are ignorant, thereby looking as if it created something. In other words, our mathematics cannot bring into reality that which doesn't exist. It's only an inbuilt fabric tool which have discovered, are using and learning from.

[@vishnusharma3209]

Today he was awarded with Nobel prize.

[@vasile.effect]

Maybe that large part of maths applies to the dark matter part of the universe ? Which is huge compared to the visible one. So that would explain why only a tiny part of maths applies to the visible universe, which itself is a tiny part of the universe.

[@londoncalling7895]

It's all relative man ;) and Penrose is massive in my universe .

[@amitprakashjha1821]

I came to this video only after I learned that he got Nobel :)

[@Chaosdude341]

Incredible! Thank you. I had no idea. Excellent news!

[@michaelwoods2903]

@@vasile.effect Why is he wasting his time on black holes when they can't explain why a snowflake occurs? They can't explain biology. Science is still locked in the past and the academics are just preening each others' intellects with these Nobel prizes when they are too scared to admit they can't solve the major problems with science like the contradiction between the 2nd Law of Thermodynamics and Evolution.No wonder the general public is so skeptical of scientists, because they are not holding each other to account.

[@jaydeeppatil1488]

Amazing interviewer.Asks pricise questions and let the guest speak without interrupting.rare quality in today's interviewers.

[@irfanjeelani9587]

Call aurnab

[@alpacino4857]

when smart and intelligent people talk, we listen ... that's how we learn from the best

[@mruse7180]

8:20 “There are wonderful examples like the ...........” (there are so many great insights In the recording, but that moment was tantalising!)

[@jolttsp]

That's what happens when the interviewer has a genuine appreciation and interest in the guest

[@michaelwoods2903]

@@jolttsp But also doesn't have a proper grasp of math to ask the next pertinent question, which is; why are those math patterns there if nature isn't using them? You can't describe something then offer no explanation for them! The reason why Penrose doesn't do so is because he's locked into tradition which is the opposite of the scientific method ; it's the same old anti Galileo stance; an argument from authority --and what makes it infuriating is - that Penrose is smart enough to realize it!

[@joemcfatter1170]

Dr. Kuhn, just to say your overall program and interviews are a gift to our world today. Thank you for creating and capturing all these wonderful discussions.

[@Jacob-jg6cd]

Access to conversations like this are magnificent to have available online.

[@soggy7142]

The amazing part is how someone so intelligent can describe things so incredibly well that everyone can follow along.

[@oyounes5945]

He's unbelievable

[@fettigeredgar]

Truly understanding something means being able to explain it in a simple way :>

[@milee105]

Icant understand anything guess im just stupid

[@SanjaySingh-oh7hv]

That's proof that he is truly intelligent. People that can explain complex phenomena in simple terms truly understand it. Contrast with arrogant professors who try to snow their students with lingo and jargon that took them years to perfect, and then they dump it on undergrad students and make them feel bad, which is what some profs want.

[@satoshinakamoto7253]

that means he understands it

[@thecoton6152]

Mathematics is just reverse engineering the source code of the Universe.

[@mattgalloway7786]

OH really? Explain that..

[@iminalert9289]

@@mattgalloway7786 Mathematics is one of the way to understand and comprehend what Universe says . Its universe's language .

[@balloonsystems8778]

Other way round: The Universe emerges due to the existence of mathematics.

[@aoxy87]

@@balloonsystems8778 Max Tegmark ?

[@Llllillilililililillll]

ishkar it's pretty self-explanatory...

[@CJ-gn8qm]

As a protagonist in engineering for more than 40 years I still get bamboozled by the depth of maths and it’s relation to physics! (This was by far and away my favourite subject through high school) I recognise that this work is vitally important for human development but there is a point at which we have to make sensible decisions that mean we can develop in a cost effective and acceptably safe way! There is somewhat of a philosophical position to take!

[@NewWorldSinner]

who the fuck upvoted this ai

[@Omnicis]

Yes you’re right, because we have become so dependent on production rates, and etc we have detached ourselves from the philosophy of science in our western society and almost the entirety of civilization

[@nngnnadas]

-Is Mathematics Invented or Discovered? Mathematicians: Yes.

[@lilhikaru8361]

Well actually he's giving a very precise answer in this case

[@tomazkavsek236]

He says that it is discovered, but saying it simply will deprive you of the path how to understand it. Adding to that, It's only our language that applies to the physical world as it is.

[@jnananinja7436]

Is the universe invented or discovered?

[@effedrien]

@@jnananinja7436 God discovered it when he was trying out everything what was mathematically possible. It must have been trial and error with no specific goal in mind, so you can't call it an invention.

[@classicalharmonicanalysis3348]

Math professional here. Great answer. Fun question to ponder when you've had too many beers to drink or have nothing better to do (and the latter is rarely true.) I tend to think math is invented as a language that can be used to unravel scientific truth, but that's my opinion and I don't care at all if anyone else disagrees.

[@jamessykes2760]

"Pure mathematics is, in its way, the poetry of logical ideas." - A.E

[@trapbeatproducer]

🥺❤️

[@words007]

This is not philosophy philosophy pertains to single statement giving multiple logical meanings. All religions on earth are basically philosophy because every reader gonna take different meanings out of it. Mathematics, NO WAY. 2+5 is still 7. And in year 3022 it will still be same 7-2= 5. Same Math is a language and humanity's logical mind operates on it without a sweat. It is unchangeable by our feelings and moods. Science doesn't change of reality based on our moods thats why Science and Mathematics are always used together from where i came from.

[@ursamajor77]

Well, doesn't that beg the question. I believe we can only say for sure, that it is 'our poetry of logical ideas', not 'the' poetry. Maybe it is, but probably we will never know.

[@cassiuscramos]

Delightful interview to listen to. I had to watch it many times, because at many points my mind went far away thinking about what they'd just said. Very good!

[@jamesbenning9665]

My thoughts exactly. They would make wonderful dinner guests. I've often wondered whether the apparently trivial or superfluous aspects of mathematics is a clue as to what we might be missing out there in the real world.

[@jackmermigas9465]

What a glorious conversation! In regards to a simple equation being responsible for producing the mandlebrot set, I wonder what sort of equations are involved in producing the seemingly impossible visual shapes we can witness in a DMT breakthrough.

[@serioussrs9349]

wow!

[@trybunt]

I think DMT experiences are more accurately described as "unexplainable" or "incomprehensible" rather than impossible. They can certainly be described as beneficial imo

[@THEMAX00000]

There’s always one, lol

[@SEAIRA2007]

Sacred geometry ; I’m no expert but there is def a link w mathematics ❤

[@13e11even11]

Remember hearing a great story. I hope I can tell it right. A mathematician walks into his colleagues office to find him reclined in his chair practically motionless with his eyes closed and then slowly steps back out saying “I am sorry I did not know you were working.”

[@OtaBengaBabalanga]

it's weak story not great

[@13e11even11]

@@OtaBengaBabalanga gee thanks for weighing in🥱

[@OtaBengaBabalanga]

@@13e11even11 you're welcome

[@eugenecalma1807]

After laboriously tending to our garden at school, we took a drink of water and our math teacher yelled at us saying " you guys sweep the floor while taking your rest ".

[@benjaminwilkinson9675]

@@OtaBengaBabalanga What a low iq comment

[@dxk2007]

Sir Roger is a mathematical legend. I read his books in high school and college in the 1990s. His achievements are inspirational, and he stands among the greats like: Dirac, Hilbert, Poincare, Lagrange, and Hamilton.

[@ysph]

because of the like... logic disconnect that seems to be the main hurdle for most people when trying to learn math, do you think folks like einstein or penrose are more lucky or do you think they would've been exceptional at whatever they did? in this particular circumstance, i find myself entertaining the idea of luck. for me, i just suddenly got it after years of overlooking and immediately realized that we must all have been doing basic algebra in our heads all the time, even when we're babies and even mentally handicapped people. hell even when we were covered in fur. math is native to the way the human mind works at least and i believe it's native to the way intelligence itself works. discovered for sure.

[@jgcaesar4]

Don't forget Gauss. :-)

[@bernardthedisappointedowl6938]

@@jgcaesar4 People just don't make enough noise about Gauss, ^oo^

[@TAYLORFAN50]

@@jgcaesar4 - And Dr. Suess! 👍

[@ivok9846]

@@ysph "do you think folks like einstein or penrose are more lucky or do you think they would've been exceptional at whatever they did?" last time that was possible was stone age, when they had 3-4 things to pick....and all were simple

[@papa.mike01]

Nice discussion. Thanks for sharing it.

[@S-L-J]

I would say, neither of both, but we deciphered and still deciphering it. Mathematics is a language of our universe and as with any unknown language, we try to figure out how does it work. Every time when we find out how something could be mathematically explained, we have deciphered a new area of this language.

[@Omnicis]

Science is not like the ancient bone we dig up at an archeological dig. It is more like the conjecture we assign to that bone. Science, in fact, is not a body of knowledge at all. It is a methodology, or the outline of one, for discovering knowledge. But it is the equation, not its solution. And it is an equation that can take many different forms. There is not one equation, or very, very few, that rise to the level of “law.” Mathematics is no different. We didn’t “discover” it buried deep in the earth somewhere. We - humans - developed it. As the physicist Sean Carroll notes, equations are “just a way to compactly summarize a relationship between different quantities.” And “A function is simply a map from one quantity to another quantity.” Mathematics, in other words, is simply a system or notation used to attempt to understand the world around us - emphasis on attempt.

[@tripp8833]

This guy is a great interviewer. Like a common guy who is really curious

[@GeoCoppens]

Lots of times he is asking nutty "deep" questions.

[@timkbirchico8542]

a common rich guy, oxymoron

[@AndrewDavidBaron]

Raziel Lentz hot tip...no one does

[@DarkestOne7]

common guy with a phd

[@mytube2013]

I feel he is a science guy too. His voice is rich though.

[@layladerya7730]

Mathematician: "Math is the language of the universe." Physicist: "Math is the language of physics." Engineer: "sin(x) = x."

[@adamrobinson4982]

CAD work flash backs lol

[@rubensano4860]

Engineering. I've got the knowledge.

[@joecrook1725]

also pi=e=3

[@adlg5158]

pi = 3 = e = sqrt(g)

[@ahmadtariq3960]

@ASquadWiper tan(x) =sin(x)

[@akira_asahi]

Thank you for the video. I am grateful for your time and contribution. Kind regards, Akira.

[@zauber620]

What I find most intriguing about mathematics is that it seems to be a self annihilating language. When we look at quantum mechanics and consider, just to name a couple, the work of Heisenberg and Schrödinger, what we see is that mathematics itself led us to a place where all calculations become void and irrelevant because it is impossible to mathematically predict the behavior of existence itself when we are faced with its particle-wave duality. I find it to be so poetic that mathematics itself had proven to us that the quest to understanding the universe/multiverse at its most fundamental functions will require a language that would be very far removed from the nature of mathematics.

[@Ilestun]

Schrödinger wave function equation is fantastically simple mathematically speaking, very elegant and ez to kno by heart. It just happens that we can't find the exact solutions of this equation.....just like countless other equations in physics (like the plasma equation form Botlzmann). But we can discover some properties from the solutions, like Cedric Villani did with Boltzmann equation of plasmas, it even won him the Fields medal.

[@keithlauderjr1691]

I don't like numbers, there's like too many of them. - Beavis

[@maxnaz47]

I will stop at nothing to avoid negative integers. - Someone

[@stephenfiore9960]

*....Who ever invented “zero” - said it was nothing...* -Butthead

[@stephenfiore9960]

*.....ROUNDED NUMBERs ...aren’t REALLY ROUND* ...ME

[@stephenfiore9960]

*......IF YOU DONT LIKE REAL NUMBERS, then use IMAGINARY NUMBERS...* (They are real also-see Google...* ME ME

[@stephenfiore9960]

*....IT IS PHYSICALLY impossible to keep on dividing a string in half...* You eventually get to a quantum level....that can’t be divided anymore and ... It’s physically impossible to keep dividing a SECOND in half-You come to a quantum limit..*

[@warrenpeece1726]

I hope the IRS doesn't discover the math I invented!

[@TheBlurayHacker]

Good joke

[@ThePeaceableKingdom]

!!!

[@AfricaRecapped]

@@coffeebean7340 😂😂😂💀nice

[@SOLIDSNAKE.]

Ohh please please tell me!

[@upuldi]

Gold

[@CNFrostXY]

That question is like asking: Is reference discovered or invented? We refer to stuff by assigning them symbols. So we refer to quantities, structures with symbols. The question is whether the structures are 'in the world' or invented by us.

[@devon_lettuce_tomato8637]

Always had this question but never was able to word it so simple and comprehendible.

[@gordonconlogue5686]

I love the old books in the background

[@mannytps9986]

I’d love to read one

[@rgoodwinau]

What a wonderful, flowing and enlightening interaction between these two men, on such a deep subject, without resorting to gobbledygook! Thankyou.

[@akumar7366]

Fantastic presentation, Penrose is a wonderful intellect.

[@michaelwoods2903]

No he isn't. He refuses to follow up the scientific method to admit that Math is all causality; he's resorting to emotion in supporting tradition that physics alone is not causality even though he partially admits it in this interview. Shocking!

[@lightworker4512]

@@michaelwoods2903 I don’t think the universe was created randomly. I think there is a Creator energy behind the scenes. I am not religious but I am spiritual and believe without a doubt that causality is not the full explanation.

[@hakonaae9636]

@@lightworker4512 Why?

[@lightworker4512]

@@hakonaae9636 I don’t know. Understanding consciousness will be a start to beginning to understand. We can study the 3D world, but I believe through my own NDE/ spiritual awakening that there is much we do not know. a patient asked me, do you think my daughter....she stopped mid sentence. An overpowering feeling of love immersed her and me at the same time. We couldn’t even speak, we were frozen. The feeling soon passed and she said, oh my God, my daughter is fine. Thank God. I’m Catholic and she committed suicide and I was going to ask you if she was Hell as I have been a nervous wreck. And I got the answer. Over 20 years, I have many stories, many much more paranormal. I used to be an atheist but not any more. Many people are unbelievers and that’s fine.

[@akumar7366]

@@michaelwoods2903 A Nobel prize suggests you are wrong.

[@ciesinsk]

I am so thankful for being smart enough to appreciate how very very very smart Penrose is.

[@TheMan21892]

I’ve always thought “Mathematics” is universal, we just invented a language for it.

[@javiervasquez625]

That is right do not let the "skeptics" twist words around and make baseless claims about mathematics just been an spontaneous chemical process with which humans are able to calculate things in order to achieve certain values that help us in the day to day as it further clouds the evidence that there is far more to the Universe that our minds are currently capable of seeing and understanding. Wether that is something akin to "God" or some grand spiritual power rest assured it's more than likely more real than the bigotted naturalist dogma that the skeptic community profess as fact.

[@Jrpyify]

Mathematics is the language. The thing it describes is just "what is" for lack of a better label. It's like saying "[the things described by] English is universal, we just invented a language for it" which is technically accurate but also sort of an uninterestingly so.

[@foulmercy8095]

@@Jrpyify So you're saying the "discoveries" counts as "what is"? And that mathematics is the language we use to describe it? In the same way, English and French have a word for dog, Indian math and Anglo Math has a "word" (equation) for 1+1?

[@user-or3bb6es5h]

@@Jrpyify Mathematics doesn't describe everything though, such as the nuances of natural language, qualitative aspects of our experiences, such as feelings, emotions, and our inner sense of consciousness. Mathematics is part of our Universe, and there seems to be parts in it that could be even beyond our Universe, without any current known application. For example, we only need to know around 40 digits of pi to perfectly calculate the radius of the observable Universe to the width of a hydrogen atom. And we know that the Universe isn't infinitely divisible. At a specific point, we reach the Planck scale. Mathematics is all about measuring and making predictions. It is an essential part of our Universe, but it isn't the whole picture. We still have no idea how qualitative aspects such as being self-aware and experience feelings and understanding, are interrelated with quantitative aspects.

[@tjmarx]

Mathematics can only describe those things that we know, think we know or suspect. It can not describe the unknown. In that context mathematics is the language of describing those things we want to describe, in the way we wish to describe them and it's accuracy is only related to our own understanding. Calling mathematics, or what it describes a discovery is like taking a video game or the computer it runs on and calling that discovered. Neither are discovered. It's just doing the thing it's designed to do, spitting out the information it was designed to spit out.

[@tonywong1259]

A group of mathematicians were trying to measure the height of a long flag pole but it was too high. A group of engineers came along and said they could help. They pulled out the flag pole and laid it on the ground and had no difficulty measuring the pole. The engineers smiled and left. The mathematicians scoffed at the engineers, "Engineers! We wanted the height, they gave us the length!"

[@coolworx]

Some ancient Greek dude stuck a one cubit stick in the ground and measured it's shadow to be 3/4's of a cubit. He then measured the shadow of the flagpole and found it to be 15 cubits. Looking at the engineers and the mathematicians he announced: "It's a score!"

[@nawgra8455]

🤣

[@thomaswalsh287]

For an egghead, the man is very engaging. He gets his points across with great clarity. When a super genius explains things well enough so that even a cave-dweller like myself can understand, he is an exceptional communicator. Thanks professor, and congratulations on your Nobel prize....

[@tiffanyh1274]

Fellow birdbrain here, I also agree.

[@andrew4life362]

Yeah, fellow failure and lizard brain here, we all seem to agree, over.

[@jonwhite549]

Egg head?? The sign of a smart person is someone who can break down deep topics to a child, many ppl who want to be noticed as smart are just verbose in many cases.

[@tiffanyh1274]

@@andrew4life362 🤣🤣🤣

[@davinbaker1045]

Wait. Smart people can talk too? All life: lies.

[@darrex999]

Mathematics describes what is happening, and somehow reveals to us what that reality is. It's like a communication pathway... a medium of exchange of information...

[@deegee6863]

Mathematics was discovered - the method of understanding mathematics was invented.

[@MrSaemichlaus]

The principles and the phenomenas are real, we're just figuring them out and giving names and labels to them.

[@johnburnham6239]

@Jeanette York Are you saying here that math is fundamentally a mental experience? If so, why?

[@MrSaemichlaus]

@@johnburnham6239 Nature is as it is, things happen in it even without our existence or awareness of them. The behaviour of matter and non-matter apparently follows certain patterns depending on their level of complexity, which apply to all of its parts. The apparent fact that there is this consistency at some level is what gives us hope to understand everything, as a random, chaos sandbox of particles would defy any attempt to intelligently interact with it. Now what I call Mathematics is the collection of models, tools and language that allow us humans to analyse (past) and predict (future) phenomenas qualitatively and quantitatively, to derive certain characteristics of them that are used for purposeful considerations and to communicate findings between ourselves effectively. What we always work with are models. Models simplify reality from lumps of matter consisting of inconceivable complexity down to primitive representations like points, lines, spheres, cubes. As the world changes, we update those inner models and all of our rational process is done on this model, while being aware of significant differences between this model and reality to a certain extent. Also, across time we discover new models, such as in astronomy the flat earth model -> globe earth model or the geocentric model -> heliocentric model. As those methods of simplification become more effective at retaining detail, our predictions become more accurate. Personally, I'd replace the word "natural law" with "natural pattern", as that would further outline the fact that the behaviour of nature is independant of our understanding of it. We're merely observers and we're working on efficient simplifications of reality to run certain calculations and algorithms which we found to be useful. Math observes patterns. Why those patterns are what they are may be a question for quantum mechanics or beyond our horizon of material analysis, philosophy.

[@johnburnham6239]

MrSaemichlaus so I apologize for not specifying in my comment, but it was addressed to Jeanette York. So I wasn’t assuming any of your meaning. But since you’ve made a comment, it does seem to me that you, like her, are calling math a mental, human thing. It’s the language that’s math. Language is fundamentally mental in origin. Also, “models,” “tools” sound like they can mean many things... A scale, a ruler, and a toothbrush are tools that might help me predict the future or past, but none of these is a piece of mathematics. And it seems to me like pure math has no necessary bearing on the physical world at all. So math wouldn’t fundamentally be about “analysis” and “prediction.” Though also I see no reason why one can’t analyze a prediction... Honestly I was under the impression that analysis just meant “a breaking up into pieces” as opposed to having some reference to the past. And I can’t think of an instance of math describing anything in a non-quantitative way.

[@404nomore]

As with anything else as well

[@johnburnham6239]

systematic self organization for some reason I got a notification for this comment... were you replying to me? As in everything’s a mental experience?

[@ramesh.programming]

Congratulations to him for winning Nobel Prize 👏🌟

[@CemalSert]

I always appreciate good questions as much as good answers.

[@motherofallemails]

Not a good question at all. Nothing is invented, least of all mathematics, even things you thought you invented, actually you merely *discovered*, all "inventions" are actually discoveries.

[@zqzj]

Nothing has ever been invented, we've only ever discovered the potential that was always there

[@FlamingRobzilla]

Relationships are discovered, the method of discovery is invented.

[@TeaParty1776]

Methods of knowledge are discovered. Mind has a specific nature ,thus it acts in a specific way.

[@FlamingRobzilla]

@@TeaParty1776 I think you have it backwards.

[@TeaParty1776]

@@FlamingRobzilla ?

[@TeaParty1776]

The method of discovery is a natural power of the natural mind. It is discovered as much as the universe is discovered. Subjectivism is the death of the mind.

[@johnmagelus6895]

The nearest i can describe it Good's language.

[@emanuellopez8578]

He's 88, impressive

[@nonserviam751]

Now he's a Nobel laureate.

[@waterkingdavid]

He must be 89 now. Good math eh?

[@didyoustealmyfood8729]

@TyLEr is he rich?

[@Wykesidefruitmachine]

Age is just a number.

[@En-of5oh]

Really, some wonderful peopl add to our knowledge and notions and make this world wonderful. How we can know such notions without such a mathematician. Amazing.

[@Kivas_Fajo]

Isn't that like Michelangelo's answer to the question, how he could make such beautiful statues, which was: "I didn't do anything special. The statue was inside the block all along. All I had to do was to chip off the unnecessary pieces."

[@gr637]

Exactly. Which is obviously incorrect.

[@slyder25400]

Mathematics emerges when you try to understand relations in a complex system. It just happens that in our universe everything seems relational so it makes math a good candidate to understand it.

[@tsumade0]

I think you have the best definition here

[@benandsylvia]

That is an excellent way of understanding it.

[@sayamqazi]

Let me change your statement a lil bit. "It just happens that the interpretation sensory data collected by our consciousness seems to have relations"

[@stuntmusicgameshow311]

I like this answer.

[@stuntmusicgameshow311]

@@sayamqazi thanks, but no thanks. i like siduxs’ answer enough ;)

[@nyrtzi]

My intuition tells me that reality has a structure and math is an expression of that.

[@bottytoohotty]

Its called Khufus Pyramid.

[@georgejo7905]

only information exists

[@georgejo7905]

@ayoub laarouchi proof is not availlabel and may never be. One problem is a version of The incompleteness theorem. If you try to falsify the hypothesis that only information exists then you would have to so within the realm of information and mathematics . en.m.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems It is a problem of a system looking at it'self , a self referential regress ad infinitum. Another way of posing the question is equally valid ie Is there anything other than information in reality and if so can you prove that. This has has one advantage that if true that there is something other than information and and it is falsifiabel then it would not be a problem of the incompleteness theorem . In an earler version of this problem was the refutation of Berkeleys immaterialism by Samuel johnson en.m.wikipedia.org/wiki/Appeal_to_the_stone Berkeleys immaterialism was given little recognition at the time due to its seeming absurdity but in the 20th century it has become regarded as important in light of the incomleteness theorem and quantun theory A historic view of berkely and johnson www.irishphilosophy.com/2016/03/12/berkeleys-immaterialism/

[@iisaka_station]

“There is geometry in music. There is music in the spacing of the spheres.” Pythagoras

[@mwmingram]

Metaphysics. Loved this. Many thanks.

[@En-of5oh]

What I understood from this video, mathematics has two functions, one it enables us to understand the behave of objects and fields, either they are classical objects or quantum particles, either field or quantum field, the second function, mathematics serves the reality that not need to be proven by any means, reality that stands there for us to discover.

[@bobbysilver272]

Ever since Ant Man came back from the Quantum Realm our understandings of things have really progressed at an amazing pace.

[@streetkaraoke30]

Yeah, and destruction too

[@paulg444]

I like Penrose, he seems like a very humble man. And the interviewer is likewise. Two good men grappling with the most important questions in life.

[@ashoksafaya5397]

I simply thank the better sense to put an end to square root on reaching iota,at times I feel tempted to carry it forward similar to logarithm.

[@edwardlewis1963]

Mathematics is discovered. The language we use to represent mathematics, is invented.

[@LS-qu7yc]

I love Penrose so much. I feel intuitively and logically that his answers are correct about mathematics being a discovery. Our labels of math and language are the invention, the reality always existed.

[@asherujudo7383]

I'm not a mathematician and I struggled with it in school but I completely agree. It always seemed that way to me. Like, mathematicians were in fact simply inventing a useful language to describe naturally occurring phenomena. I always liked the concept of math and I feel like if I had had more patient teachers I would have really gotten into it.

[@jcr912]

We certainly didn't invent it, but we invented its language. When you look at anything, even if you aren't aware of mathematics, you can tell the difference between one of something and a hundred of something, even if you don't know what they're called or how to describe it. Mathematics is the language we invented to describe measurements of things around us, the labels and lengths we use are only a way to navigate through what is built into the universe.

[@eltonmayo2027]

really. like the mississippi river was 'discovered'. mankind had to 'invent' bumping into the river's edge. took alot of brain power to fall into a river.

[@diggitus]

This doesn't settle the philosophical debate though. It just punts it down the road a bit.

[@peteraka3783]

I believe the term mathematics is used to describe two things. At times multiple invented languages, and at times a prior reality of relationships. There are multiple math languages that can describe a problem - I have seen the same problem on youtube solved with both geometry and calculus.... both were valid languages to describe that solution - since a particular problem/solution is abstract until it finds a physical use you could argue that mathematics 'discovered it' before physics did... however since two pretty independent branches of mathematics can be used to solve a problem you can argue that they are just 'inventions'.

[@jcr912]

@Razor Face I don't believe the characteristics of the universe were invented by man.

[@Asak999]

@@jcr912 i think that to exist characteristics is necessary an observer to interpret it, without an actor there's no math.

[@joaowiciuk]

Being surprised with the fact that math can be used to describe the world precisely is the equivalent of being surprised English can be used to write poetry that captures human feelings. It's a languague at it's best use. An endeavouring question one can make is in which cases math fails to describe the world accurately and also if we can ever realize it

[@XMachete]

Ahead of watching this, presuming the question isn't misleading, I will guess that the mathematical properties of the natural laws governing this universe is what we discover, and what we invent are systems for expressing them and leveraging what we've discovered both in practical application and also in the pursuit of new discoveries. Now to watch the video and learn how muddled my guess was.

[@jordanious7711]

Yeah, boiled down to it's most basic premise, math is just seeing a cup and thinking "thats 1 cup" then if you add another cup you now have 2 cups. It doesnt matter how you explain that, the concept will always be the same. You can have "1" or you can have a trillion lots of "1".. it just is that way, how we describe that is irrelevant... Any intelligent life would be forced to make the same observations eventually. All of math is based on these very simple foundations. In that sense we aren't really creating anything, just trying to understand what reality has already given us.

[@dunzek943]

Agreed. I don't think it's muddled. Why math isn't a discovery I'd say is because mathematics is literally invented. It isn't a scientific discovery; it's a field and practice built on supposed axioms that have turned out to be very useful. These axioms developed throughout the course of human history, but started in a humble manner (counting: one deer, two deers, etc.). How these axioms were conceived were primitive and so primitive and subconscious that perhaps it's treated as a natural part of the world discovered. People are mistaken to treat mathematics and the phenomena that it describes well in the physical world the same.

[@Soylent1981]

I love thinking about these topics. It’s gives me a great sense of awe at the natural world.

[@MrMurl]

it’s the bomb

[@xXTopGXx]

if you believe mathematics was discovered they probably still think Columbus discovered America.. periodtt

[@xaviermohmarc1100]

After combing through and scanning over all these provocative vid titles, I think I've found the equivalents of gold here on this channel. I'm about to binge all of this.

[@AccendoWorld]

It’s very fascinating, the idea that the physical and non-physical worlds operate independently - yet, work or interact between each other transactionally.

[@RetiOrchid58]

One thing this shows clearly to me its how crucial the a priori is epistemologically in a sound scientific method. At the same time, it's surely important not to mistake sometimes mathematical correlation for causative mechanism, and to remember that it's possible to obscure discrete causation with calculus' "smoothing out of the continuum".

[@loschekell]

"Mathematics" is a human contrivance used to describe change and motion. We can't be sure it's accurate over remotely vast distances and time scales. The ancient Greeks pondered this question.

[@risej4164]

The Greeks pondered on what “Egyptians” mastered!

[@2121beastmode]

@@risej4164 so are many alive today. Whats your point?

[@risej4164]

@@2121beastmode the fact that you don’t know, is beyond me!

[@theheebs100]

really? because we've used math to put telescopes floating around the Earth and use them to take pictures of galaxy's billions of light years away. that seems like a pretty vast scale where our math works to me.

[@risej4164]

@@theheebs100 lol… that’s bs, and if you believe that then u r a straight clown… I think you really are one though!

[@horariojoselo7178]

I really don't know what to say except "Thank you Roger!". Your thoughts are the beacon of our lives. And also thanks to Closer to Truth.

[@vhawk1951kl]

Whose truth?

[@vhawk1951kl]

You are a romantic

[@siinxx7656]

It is wonderful that mathematics describes the world very precisely or that the world functions in such ordered simple matter, that from adding and substracting you will eventually figure it out

[@archaeologistify]

The subject of the video (and of course the discussion) are fascinating, but aside from that, I'm very happy that a video such as this reached over 2mil views.

[@diegobravo641]

So deeply interesting. Would love to see more.

[@milkmanswife93696]

this was great. so thrilled to think how much more of mathematics might be understood to in fact relate to reality as we experience it, and possibly unite physics and metaphysics.

[@cemerson12]

At 12:15 Robert asks what the Platonic reality of mathematics means to or about the physical world (he refers to infinite structures or ideas)? It means, I think, that the physical world (as we are able to perceive it) is but a subset of the possibilities in reality itself.

[@ms-tw4sj]

Answering the question: The very basic thing we do in mathematics is to count things. That's what started mathematics. That's a human invention, no other living thing counts. Everything that follows is a discovery.

[@jjt1881]

One of the best short discussions about the topic of philosophy of mathematics, and with some insights into the interactions between mathematical structures with the real world. e.g. what Eugene Wigner called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". He has what I call a beautiful mind.

[@michatroschka]

its like a language for us to interpret the universe. of course it doesnt "use" math, it just so logical that it can be expressed with maths. for example how the atoms behave and frequencies isnt becase of maths, its because of physical laws which can be described with maths. i was looking at a forest with beautiful trees once with a friend and he said "its all mathematics" and he couldnt be further from the truth, because maths is just our description of nature, not the cause.

[@ccshumshum8104]

your friend is right. mathematics is logic. mathematics is more than just an expression, and the fact is no one invents theorems in mathematics because if it were it could be changed. it's set in stone. your interpretation is incorrect and it's frustrating how someone with such a faulty understanding of mathematics would think they're in the position to be condescending.

[@michatroschka]

@@ccshumshum8104 ok, you seem to have a point, mathematics is logic, and nature is bild upon logic i agree. Id be interested if you could further educate me

[@Snuusnuu69]

@@michatroschka I will simplify it for you. Whether humans existed or not, the mathamatical principles that govern the universe would still be there. Humans have created the formulas for better understanding about these natural laws, but we didn't invent the laws themselves. It's similar to computer code, it is a "language" on which we use to describe what we have discovered about the universe and how it works.

[@michatroschka]

@@Snuusnuu69 thanks for describing it in simple terms and it is well understood what you mean, could you name an example for those principles in nature you were writing about?

[@Snuusnuu69]

@@michatroschka The fundamental laws of the universe. Physics, trigonogmetry/calculus, probability and statistics, chemistry. The building blocks of the universe. If you punch a brick wall, there are fundamental principles dictating that an equal or greater force(with a greater probability than chance) will stop your fist from passing through it. Another example you will learn about is called the 'golden ratio', which is found in abundance in nature. It is another mathematical formula to study. I will tell you, going to college is where I came to truely beleive that we are either living in a simulation(simulation theory), or there really is a God/God mind that created the universe. To me, it takes more faith to beleive that all of existance came from absolutely nothing, no matter what you beleive in. Good luck on your path to enlightenment.

[@rayraycthree5784]

As an EE, it is amazing how electrical parameters are so related in straight forward equations and that many of the constants that bind the equations also work well in other disciplines. The only thing that the math doesn't seem to fit very nicely is that a number of the constants are irrational numbers.

[@AethericTheorem]

You should definitely checkout Eric Dollard’s books lectures... One of the most authoritative EEs alive & in the public domain.

[@manuelteixeira2496]

Mathmatics is a science and a tool at mankind's disposal, through brain's operation, trying to understand awesome wonders of reality around us, and in the skies above.

[@vhawk1951kl]

Whose reality? What you mean by "reality? No idea? - No surprises there.

[@georgebush6002]

@@vhawk1951kl When talking of science, I define reality as mind-independent and refers to the universe (i.e. space, time and everything in it). An important caveat to this is that observations and theories are based on reality rather than reality itself.

[@vhawk1951kl]

@@georgebush6002 Whose "reality"? Is define reality.

[@dontmisunderstand6041]

It's not. It's a language. Mathematics does not create knowledge, it explains what you already knew to someone else in a way that leaves no room for interpretation.

[@ka7al958]

@@vhawk1951kl why are you talking to yourself

[@estrellasirio]

It is a wonderful video. I have to congratulate everyone who has participated in it, not only the great R. Penrose, because the most important merit is having shared it for free. Thank you. This video should be seen in every school in the world.

[@quixodian]

I noticed Robert Lawrence Kuhn's repeated invocation of the idea that mathematics must be 'out there'. It seems 'out there' is his criterion for 'what really exists'. But the point about mathematics, is that it transcends space and time - it's not 'out there', it's true by virtue of inherent reason. The intellect's grasp of the transcendental nature of intelligible reality is fundamental to traditional platonist philosophy, but has been squeezed out of Western thought due to the influence of nominalism and, later, naturalism. Thank heavens there are some leading scientists such as Sir Roger who are fighting the good fight.

[@walterevans2118]

Very interesting....I think that materialism of people like Hobbes thought itself to have transcended Platonist philosophy but in the exploration of Quantum Mechanics its re-emergence was necessitated .....Heisenberg realized that visual pictures from the macroscopic world were NOT adequate to describe the sub atomic domain...To do that accurately you have to go into pure mathematics like Roger is describing....I guess mathematics could be seen as transcending time & space because it is an abstraction which is not a physical object that can only exist in time and space...But it IS an abstraction which pre-exists......In a way Heisenberg was using Platonism to go beyond not just Hobbes materialism but also Descartes.

[@quixodian]

@@walterevans2118 Google 'The Debate between Plato and Democritus' - a speech Heisenberg gave late in life. His Physics and Philosophy is also good. (It's a canonical text of the Copenhagen Interpretation.) The point about mathematics is that it's not simply 'abstract' insofar as it is also predictive. Many of the seminal discoveries of qm came out of the analysis of mathematical symmetries the gold standard being Dirac's discovery, or rather prediction, of anti-matter. Another example is Eugene Wigner whose Nobel Prize was for application of symmetries to nuclear physics. Wigner penned a famous essay on the unreasonable effectiveness of maths in the natural sciences. Plato will have the last laugh.

[@walterevans2118]

Jonathan Shearman...Yes, I've got Heisenberg's Physics & Philosophy. A great book particularly in the way he explored all the different objections to the Copenhagen interpretation...Yes, even if with the measurement problem of electrons we cannot have mathematical certitude between momentum & position in observations mathematics has an incredible predictive power in the physical world...This has led some to call it a useful tool which is invented but it also predicts THEORY.. I think Penrose is correct when he says calling it an invention doesn't really go far enough to explain mathematics ....& Heisenberg would have agreed with him otherwise he would not have developed his matrix Mechanics . In Athens in 1964 he explored these ideas about patterns in our minds called 'architypes' by Plato might have reflected the internal structure of the world.

[@123mcgarrigle]

Can I just say, your vocabulary impressed me.

[@Yemeth42pis]

@@walterevans2118 Aren't *all* abstractions pre-existents ?

[@christianzeitler8006]

Math itself is inarguably, definitionally a human creation But what it attempts to describe already exists and it can be a great tool for discovery. But it is a language we made up to make sense of the world around us

[@haydenwayne3710]

Well done, gentlemen!

[@davidfarrall]

This is thrilling and fascinating to me, Sir Roger. The confluence of All Mathematics and All Physics is so beautiful and allows us to go deeper into the Reality and Truth of our Universe. And We, most probably, will never find a total solution. But the Theoreticians can dovetail with the Engineers, Scientists, Explorers, Practical People, etc. We can look forward to a testing and interesting future based on your thinking and your Associates and Colleagues. Thank you for your (summary) talk on this.

[@bryandraughn9830]

I'm amazed when mathematical ideas uncover things about reality that wouldn't have occurred to us if we hadn't been calculating a bunch of weird ideas. Sometimes it literally points the way.

[@C3LTICART3L]

this for me is one of the most satisfying videos on youtube an I've seen a few... thanks :)

[@goriaakash]

Physical laws and concepts exist, you discover said physical concepts and use language to convey or understand them, this language is numbers, formulas, symbols, equations.This whole process is mathematics. That was in my head and i wanted to get it out

[@gr637]

Nope, they don’t exist. In fact, they are concepts. As such, they are invented.

[@user-ul5pt1yb8z]

Thanks a lot

[@jrousselle7828]

Roger Penrose is amazing. He makes the complicated seems so simple. Einstein had the same ability. Roger's brother (Jonathan) was a chess grandmaster. Good genes, I guess.

[@simonasfaw9450]

Do I sense an eugenics argument here 👀... Lol sry I had to cr*p on your comment but I had an argument with a math fanatic about this very topic of "is math made up or sown in the fabric of reality"... And he wasn't nice about it ☹️

[@bumbo9506]

More like amazing parents and environment. Geniuses don’t appear magically in a bottle.

[@simonasfaw9450]

@@bumbo9506 yes and genes don't get to be expressed if not under the right condition... We usually do not use all of our genetic code... Sometimes it needs a trigger to be expressed... IDK I saw it on BBC

[@jararacavoadora5868]

Well fenotype is produced by environmental externa factors + genetics

[@marklammas2465]

An early chessboard helps the good genes. For Roger an early something else kicked him off.

[@willymack5677]

I think in a sense, it is both. The language of mathematics that we use was certainly created by humans as a tool to easily describe and communicate to each other just how these principles exist within the fabric of the universe.

[@vhawk1951kl]

Help me with this please: What is bread in the "language" of mathematics? Or what is "universe" in that language"?

[@AdelaideBen1]

We use both - the act of discovery, and the act of intuition based on insight (whether or not is a universal truth). The problem is when people say that Mathematics isn't discovered also is a cop-out... it suggests that all the answers are there, you just need to (hijacking a gamer term) "git gud". It actually undervalues the cognitive effort to progress maths, as it suggests the limits are only ourselves. I believe the advances are because of ourselves - not that we're holding things back. Yes - it's a mater of perspective. However, I don't see much inspiration in telling people their deficiencies are what's defeating humanity. Also, unlike most other "sciences" mathematics has intentionally ignored any discussion of ethics... and that worries me, as many an evil has been progressed based on the belief that ethics didn't apply. I am not saying it exists - but I think that there needs to still be a discussion within the mathematics community as to what is ethical mathematics (beyond how maths is misused to influence stock prices).

[@Mageblood]

@@vhawk1951kl B R E A D= 13 12 3 4 D

[@cheminem]

@@AdelaideBen1 it is actually refreshing to me that mathematics is divorced of the normative. However, there are many instances where it is, e.g. decision theory, how the rational man ought to make decisions. I don't think mathematicians are interested in the ethics of their discoveries for the most part, because a lot of modern mathematics are difficult to apply readily. Mathematics with respect to the stock market is also extremely complicated, but the manipulation of it is straightforward, e.g. arbitrage. If anything, I think it's the reverse, not understanding the mathematics behind such actions is what allows such morality to decay. When leverage was 20:1 prior to the 2008 financial crisis, Its taken that a lot of the people piling that machine did not know of the consequences, they simply knew that they got paid very well to give people mortgages, to over leverage themselves on CDO's, etc.

[@judemorales4U]

I agree William. I think math existed universally and intrinsically (such as sacred geometry) but that man created 'the use' and methods of counting, tracking, measuring and so on.

[@bloopboop9320]

I feel like the better question would is mathematics Observed vs Discovered. Discovered implies that it is a fact of reality that the universe is mathematical in nature while Observed implies that mathematics is a tool for observing things and categorizing them as close to reality as possible. I can see arguments for both because both would give you essentially the same result. Is math a categorization tool or is math fundamentally the programming of the universe?

[@user-vc5zt9ci12]

Observed and discovered both mean they were there already. Invented means it doesn't really exist, it's just a tool (like you say) For me, it's 100% invented for one reason. All physical processes are relational and aren't based on pre defined mathematics because, if they were, it would mean that the math existed before the universe existed (otherwise, the initial conditions couldn't be set). Mathematics existing outside of the universe is nonsensical

[@bloopboop9320]

@@user-vc5zt9ci12 I guess what I mean is that "observed" simply states the properties of what is being seen, not necessarily what it is. We observe mathematical properties. "Discovered" means that the math came first as a means of coding the universe or something along those lines.

[@ths2479]

i have a question please: would the mathematics be different in a different universe with different characteristics or do we have already mathematics which cover all sorts of universes?

[@recsa8882]

And you want someone from this universe to answer that? dont think its possible, we could say that it seems like maths are in a layer above the physical expression of the universe (this or any other else) but we dont even know if is its possible for other universes to exist, or better said, if this is the only possible way for the physical world to exist.

[@MaorRa]

I was thinking about it myself these days, great philosophical question! IMO, math, not as discussed by the conversation there which mixed science (nature science) and pure math, I think that math is universally true in the sense that it does not relate or depend on the current way of the universe.

[@johnevans6399]

What I think is fascinating is how often maths departments have musicians trying to break free! 🤔

[@molybdaenmornell123hopp5]

I have a problem with one notion suggested here: that we can or should quantify the accuracy of mathematics itself by how well the equations we've so far come up with model observable reality. If an equation, say the ideal gas law, pV = nRT, imperfectly predicts the volume of an amout gas at some given pressure or temperature, that is because the mathematical model applied doesn't exactly reflect the physical facts, not because 2+2 is not exactly 4. The answer is to make a better model, not to somehow tweak arithmetical results. No physical discovery needs to call into question the axioms and theorems of maths, only their usefulness. 2+2 can remain 4, whether or not there's a world to apply that to.

[@alexlaverick6111]

Today. Two plus two equals five. Correct?

[@lookupverazhou8599]

@@alexlaverick6111 That would imply that 1 + 1 equals 2 and 3 simultaneously, which cannot be axiomatically. Thus, disproven by counterexample.

[@lookupverazhou8599]

That comes down to whether there really is such a thing as "1", and not just the appearance of "1". That is to say, in it's application to reality.

[@Shootskas]

"No physical discovery needs to call into question the axioms and theorems of maths." And yet there are mathematical systems that have applications in physical systems that do exactly that.

[@Trentstone121]

"keep your mind open to the possibility that 2+2 does not equal 4" -Jubal Harshaw.

[@timdowling6950]

The mathematical description is the most precise we know. So it is guaranteed to strike us as incredibly precise. In the nature of the case - we possess no greater precision to run it up against.

[@patrickprior4826]

Anyone who's still a materialist after studying mathematics at a high level is kidding themselves. The existence of numena, immaterial objects, is pretty much self evident when you think about math a bit. After that, it's a hop, skip, and a jump to religion, but lots of people aren't ready for that conversation.

[@jthomasjohnson]

Mathematics is the scaffolding onto which material reality is affixed.

[@mathematicalninja2756]

Flash Fordon why not?

[@MediumDSpeaks]

I have been saying this question to people my whole life. I never knew it was an actual thing people like Dr. Penrose studied! I always thought discovered, just our units to describe things are "invented" but also based on discovered properties of reality as well.

[@vhawk1951kl]

"Reality"? Whose reality? If you experience pain or anything else that-for you, cannot be different, that is as real as real can be for you, but nobody else, thus whose reality? o you suppose there to be a " reality"(whatever that means) other than the direct immediate personal experience of some particular being?-Some sort of vague generalised " reality"? Whence you get that strange idea?

[@MediumDSpeaks]

@@vhawk1951kl go away year 2 philosophy study

[@nikitanikitov9362]

What is the criterion for the accuracy of the description of reality by mathematics?

[@doctorfaris]

You need to ask also about invention of computer program or software

[@zenbum2654]

It was hinted at in this video, but Penrose considers himself a Platonic Idealist, in the traditional sense of that term. Most philosophers nowadays consider such notions silly and quaint, but Penrose makes a very compelling defense of it in his books. Everyone would agree, however, that Penrose is a brilliant mathematician; I would argue that he's also a pretty damn good philosopher.

[@dennisalwine4519]

Yes! I found that very interesting, almost Pythagorean! I think in your statement is the argument summed nicely. Remember it was the pre-Socratic Pythagoras who indicated the right triangle *is* a2 + b2 = c2, while a drawing of the right triangle is the approximation-who needs Plato here :-) . I'm inclined to say there are things we describe as right triangles in nature (such as the relationship among reactance, resistance, and impedance in electricity), in which Pythagoras has made a mathematical approximation of the reality. And I assert it remains an approximation, despite claims of relative accuracy. There is still room for idealism here, though!

[@marcosgalvao3182]

Yes , hes very bright.

[@Google_Censored_Commenter]

He's an awful philosopher. Platonic idealism is archaic. Idk why he would even attempt to defend that position. It's been well-established maths is just language, nothing more, nothing less.

[@marcosgalvao3182]

@@Google_Censored_Commenter all language have semantics structure, it means the universe have a mathematical structure.

[@Google_Censored_Commenter]

@@marcosgalvao3182 It means humans invented a mathematical structure that (currently) applies to our universe. And said structure is just labels, nothing else.

[@jobebrian]

For what it’s worth, the word “invention” is derived from the Latin “invenire”, which means “to come upon, to find”, which is somewhat close to “discover”. The word “discover” is derived from “discoopeire”: dis (same as the English “dis”, also like “un”) and coopeire (cover). So the meaning associated with the terms is somewhat muddled. I don’t suggest that the etymologies invalidate the meaning we have now, but that maybe the concepts aren’t quite as opposed as ordinary language infers. After all, nobody claims that an invention such as the lightbulb was created out of nothing. It was invented on the basis of previous ‘discoveries’ (electricity) and ‘inventions’ (glass, filaments, whatever). But-conceptually speaking-is bringing light to what used to be dark all that different than the solution for Fermat’s Last Theorem? I wonder.

[@nqobilengema2165]

So all in all... Its all perceptive. Like anything in life... And context also

[@omairbinenam6337]

discovering = surprise or a fluke. inventing = planning and a definite road map

[@omairbinenam6337]

one might say that the lightbulb was invented after countless discoveries.

[@chazzabh]

The point is to ask 'Did we simply make maths up and use the maths that fits our reality because otherwise it's no use?' or rather 'Was/is maths 'out there' somewhere in an abstract space and we stumbled on it?'

[@peytonquinn3095]

@@omairbinenam6337 Yes and after more experiments and discoveries the Newtonian based light bulb is replaced with a Quantum based device, the LED (light Emitting Diode)

[@bennyaction]

This has always been an easy answer for me: Invented. It's language - symbols you can combine to create descriptions. There are 2 layers to it, think about this: Italians don't have J or K in their alphabet, they use Gi as in Giovanni and Ch as in Chianti. So layer 1 is that the symbols are arbitrary, and could be denoted in any way. Another example of this is that some language cultures don't distinguish between green and blue, or of orange and yellow - they see those as the same colors (respectively). They refer to them as different shades, the way we consider maroon a shade of red. Another strange thing is - you can imagine a number between 2 and 3 - some new symbol, let's call it ⅎ and it equals 2.5. In the same way that "5" means 1 1 1 1 1, ⅎ means 2.5, arbitrarily. And now the number system goes 1 2 ⅎ 3 4 5 6 etc. The Romans only had I V X etc. skipping entire chunks of numbers that we have, so the only way to depict "7" was to put a V with II. That's like us saying 7 is depicted as 52. Instead, we invented 7 (yet still randomly go 10 after 9, 1 and 0 instead of another symbol). So the system of labels is completely arbitrary, and so is the so-called meaning - it's like trying to define where green officially becomes blue - we just draw the line somewhere and give it symbols. If you try to prove where green becomes blue in, say RGB, or CMYK, or HEX, I can probably find an accurate color system where that isn't the case. We just invent what is convenient. ^ Most people easily get that. It's this next layer that trips most people up: The concept of the number 1, or of an individual thing disconnected from everything else, is impossible. In any abstract or concrete sense, simply, all things are relational to other things - things co-define each other, especially adjacent things, and all things have attributes (which are themselves other things). But the important part is that we "thing" it - as Alan Watts said reality doesn't come already thinged. There is not really, in any absolute sense "1 apple" "sitting" "there" - all of those concepts are invented by the mind. So the symbols are arbitrary, what they represent is an arbitrary value or range set for our convenience or readability, and the very reality they intend describe is not absolutely that reality from all perspectives - and indeed math and even trivial concepts like the basic notion of "order of events"* breaks down on some space and time scales, giving rise to new fields of study like quantum physics, or people who study supergalactic events. Concepts like what direction time is going in, if there even is time, what happened first and will happen next, and how many of something there are, are not absolute. * Imagine 2 stars, Star A and Star B, both burn out at the exact same time. If you're very near Star A, and very far from Star B, then Star A burned out first, but if you're near Star B, then Star B burned out first. The very basic idea of the order of events is not an absolute thing in reality. It depends on where you are, even your current velocity plays into it.

[@soshady9572]

Mathematics is much more than symbols. It's what those symbols represent and how they interact with one another while describing how things in the world actually work. Your examples using spoken human languages is not applicable. An easy example is 1 thing plus another of the same thing, equals 2 of those things. It doesn't matter what symbols are applied, nor did we invent this. It's just how things work and have always worked.

[@Yizak]

I think you got to the core of the issue. An equation like e=mc^2 only looks elegant because we have abstracted away quantities such e with a single letter. The reason we have these strange looking irrational numbers like pi and e is because we've decided to describe the behaviour of nature in a base 10 counting system.