1. General Overview and the Development of Numbers

[@javiergelatti]

He was my teacher on a Coursera MOOC! I really learned how to think mathematically on his course :D

[@Q_QQ_Q]

link ?

[@dadnoonan]

This should be recorded again with today’s views from the same person. Very well done.

[@johngreydanus2033]

This is worth its weight in gold too kzbin.info/www/bejne/hWKWZKOmnruhjbs

[@ramunasstulga8264]

Sorry I only watch to fall asleep, thanks Stanford ig

[@LanceWinslow]

Wow, you know what, that was a really really great talk. Thank you very much, I am now compelled to watch the rest of these videos, and I feel I've found a gem online here. Awesome, this is what the Internet is for, excellent!

[@thebetterlemonjello]

If you're browsing comments to decide whether you should watch, yes, it's worth your time and you won't regret it.

[@gccg7636]

It happens to every teacher who gets totally, physically, emotionally, psychologically involved in what he is teaching and actually living:-) I told my students that was nature at work. Sweaty teacher, lucky teacher but cannot rhyme in english. He is actually very very good and would pay attention to him even if he happened to be thawing in front of me as longas he has voice and capacity to teach :-)

[@dirobot]

Vasily Davidov lived 10 years longer ))) I'm in the half of this lecture and it is great! Money and real number =) actually I'm learning Math Thinking at Stanford, Coursera, and had to sloow down to understand basements before second lecture. I wanna take more from it, than I can now. Thank you doctor Keithm you are fixing brains in so funny way! Hope to meet you one day in San Diego with Dr Barbara and Dr Terrence, it would be a sweet talk during the Sunset at La Jolla...

[@martianwarlordtv]

There is about 30 min of awesome material scattered in this 9 hour course.

[@robertveith6383]

That sounds like a back-handed compliment.

[@michaelglinsky2614]

Wtf why

[@simonaclutter3138]

i sweat worse than that when i speak in public. props to him.

[@neoepicurean3772]

I'd say it was jogging to get to the lecture that got the juices flowing, as it all dried up during the public speaking bit. Dry as a bone by the end of it.

[@Sheikhmorpheus]

I saw the lecture series and literally thought "jackpot."

[@titanarmy4116]

i thought, nooo, not another rehash of the history of mathematics that has been told 30000 times

[@mechrome7241]

@@titanarmy4116 του Αγίου

[@mechrome7241]

@@titanarmy4116 του Αγίου Βαλεντίνου

[@mechrome7241]

@@titanarmy4116 του

[@mechrome7241]

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[@das250250]

Wow what an amazing lecture and insightful and interesting threads in so many ways . I probably need to listen to this again .

[@johnfoster6412]

Leonardo of Pisa was an accomplished lutenist as well, he has compositions in the standard repertoire for classic guitar

[@LemuelUhuru]

True. Still, your $25,000 education provides you with a tangible degree that you can present upon request. I do look forward to the day where emphasis is place largely on educational sites like Coursera. I'm taking the class as well :)

[@MrPatrickDayKennedy]

Wow! Great information here - fascinating history! I look forward to the following lectures - thank you, Professor Devlin :-D

[@RbtV92]

Good God man! You were incredibly sick during the last lecture! I watched the last lecture first and just thought that was how you sounded but Im listening to you now and I must give my respect for you actually giving that lecture as sick as you were.

[@explorerc607]

Actually, for most of us, caculus is the end of the mathematics because after caculus the maths had evolved into modern style which is quite abstract and difficult to understand.

[@torontosaurusrex4688]

The actual development of mathematics is.. How can anybody sweat that much? Anyway, the actual development of our notions of math is.. Wouldn't he suffer dehydration after 30 minutes or so? In any case I find the evolution of sweat - I mean numbers perspiring - er... evolving.. Surely this is some kind of world record for sweating in a lecture venue.

[@davidshi451]

This brings up an interesting question, that people have debated for a long time: does math exist in the Universe, or just as a human concept?

[@pavel672]

Hey, if somebody did answer this question in a reply to a youtube comment, this would have been so awesome, it would have justified posting the question even though expecting an answer would have been unrealistic to begin with :)

[@thedukeofnuts]

Mathematics exists in the Universe as a human concept (or set of principles). Without sentient beings there wouldn't be mathematics, even though the phenomenon from which mathematics is derived still would.

[@Silly.Old.Sisyphus]

mathematics is a human language; it does not exist outside the human mind. but it is also objective, eg: 1 rock + 1 rock = 2 rocks, whether or not there is anyone to say so.

[@grantperkins368]

Well, we keep discovering new things in mathematics, as opposed to inventing them, so I'd say that yes, it exists in the universe, and the fractal structure of nature proves it, but that's just me :-)

[@grantperkins368]

@@Silly.Old.Sisyphus how do you know it doesn't exist outside the human mind? Oh, I suppose it depends on what "it" is ... If it's only our conception of it then thats one thing, but what if aliens speak the same math?

[@lisaswaboda3127]

I think I would have preferred learning through the Siena Manuscript preferring understanding through language prior to symbolic representation. Thoroughly enjoyed this overview!

[@edgarmatias]

The relations and patterns are discovered. The symbols are invented - e.g., Newton’s vs Leibniz’ formulation of Calculus.

[@torosalvajebcn]

Professor Deblin, you forgot to explain how your Northern English accent opened the doors for your at the library in Florence, I'd love to know the story.

[@bubba1match]

Interesting concept. I never thought about counting and numbers as separate entities. They seem to go hand-in-hand, though I guess that's just because that's how we learned them. I'm wondering now what may have happened if numbers didn't develop as the next step in the mathematical evolution...what might have developed in it's place?

[@kimberlygause]

🎶🎵🎶🎵🎶🎵🎶🎵🎶🎵🎶🎵

[@frankdimeglio8216]

​@@kimberlygause Consider what is the man (AND THE EYE ON BALANCE) who IS standing on what is THE EARTH/ground. Consider TIME AND time dilation ON BALANCE. What is E=MC2 is taken directly from F=ma, AS the stars AND PLANETS are POINTS in the night sky ON BALANCE. This CLEARLY explains and proves the fourth dimension. c squared CLEARLY represents a dimension of SPACE ON BALANCE !!!! Indeed, E=mc2 is taken directly from F=ma; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches it's revolution. Notice the TRANSLUCENT blue sky ON BALANCE. Consider what is THE EYE ON BALANCE, AS c squared CLEARLY represents a dimension of SPACE ON BALANCE. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS what is E=MC2 is taken directly from F=ma; AS GRAVITATIONAL force/ENERGY is proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE. “Mass”/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Accordingly, ON BALANCE, what are OBJECTS may fall at the SAME RATE. By Frank Martin DiMeglio

[@Deuterium2H]

He was using a metaphor. That being that he was taking a large overview of Mathematics to start with (as if looking down on Earth from high altitude).

[@jessmendez4542]

The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC.

[@serdarkacka]

Arabs were not only traders as Mr.Devlin presents. They were also scientists, mathematicians, astronomers etc. Where does the word algebra and algorithm come from? You can look at the first pages of the book The Art of Computer Programming, written by the great computer scientist Donald Knuth. And you see Al-Kwarizmi. As another example you can watch the short video of Terry Moore discussing the origin of the symbol x used for unknowns in mathematics. The title is "Why is 'x' the unknown?"

[@gene546]

Math, is the tool to measure Nature.

[@leandrog2785]

Because it is imprecise and ambiguous

[@Oishi08]

been studying #Mathematics this afternoon, and have been waiting for the #Spring2013Semester to begin to get into this lecture series... So... got my #GreenTea, and #Kush!

[@LydellAaron]

Powerful and inspiring lecture.

[@divakarsnatarajan]

The ancient Hindu fable of The Blind Men And The Elephant en.m.wikipedia.org/wiki/Blind_men_and_an_elephant appears to reflect Prof Devlin's understanding of modern mathematics.

[@JerimiahGentry]

This man needs a pirate shirt. A flowy, billowy, well ventilated pirate shirt.

[@mariannabelmares7116]

Jerimiah Gentry ahahahahahahahAHAHAH

[@R3negadeuk1]

Great lecture

[@madier1000]

thank you very much for such interesting lecture.

[@mohamedaminebenmabrouk]

I'm a software engineer, I was surprised when you mentioned Steve Jobs as iconic CS (computer scientist) figure , this is a myth and you are altering history by telling that , he hasn't any contribution in cs. He was a commercial , manager .... not a CS. I Think comparing him to Leonardo Abbacci is wrong.

[@nodgelyobo1]

Totally agree, Steve Jobs knew as much about computer science as Richard Branson knows about aeronautical engineering

[@dirobot]

but who creates tasks for engineers, controls, combines and engage users?

[@Siriusblck3]

Wait a sec.... didn't Jobs worked at Atari? He was a marketing or manager there too?

[@doNotForceChannel]

Leonardo Psano starts at 58:13

[@abzalabdimanov6395]

Thank you, it's great lecture

[@rostislavsvoboda7013]

The vid is just full of Steve J. and product placements of his company. See examples at: 1:10:12 1:25:30 (watch for 20s) 1:38:59 1:43:03 (watch for 50s) Once I had a lecturer half as bad as this one. The running gag was "Attention! He deals for Microsoft"

[@mrautistic2580]

Thanks for posting this one

[@vectorshift401]

He has the air flow wrong. The air above the wing does go faster. (if it didn't the air would continuously "pile up" at the leading edge. Physically it speeds up because of the lower air pressure above the wing so the normal air pressure in front of the wing pushes it faster as it moves into the lower air pressure region.) Bernoulli' equation does give the correct lift. 2D is adequate to explain lift. The "usual" explanation , as he points out, is also confused , ESPECIALLY in showing parallel air flow departing the wing. The wing pushes air down which is how the lift is generated. Bernoulli's equation gives the upward force on the wing caused by the downward flow of air.

[@xponen]

He already know the correct answer, he just showing one of incorrect theory he found in flight manual. In fact, the correct theory is just too complex to even explain. www.grc.nasa.gov/www/k-12/airplane/wrong1.html www.grc.nasa.gov/www/k-12/airplane/bernnew.html

[@vectorshift401]

+xponen I wasn't referring to his diagrams or the explanations that are in fact incorrect. He himself argues against air speeding up on the top side of a wing. Starting at about 34:20 he criticizes not just the invoking of equal transit but also the conclusion that the air speeds up. "There's no reason to speed up. "There's no reason at all why that should happen and in fact it doesn't." Well it does happen. The air going over the top of the wing speeds up. Clearly the air does have some reason (cause) to speed up. In fact it speeds up even more than the equal transit notion would require. "In reality, the velocity on the upper surface of a lifting wing is much higher than the velocity which produces an equal transit time." The above is a quote from the second to the last paragraph per your reference: www.grc.nasa.gov/WWW/k-12/airplane/wrong1.html He also is way to critical of 2 D models to explain basic lift production. The idea that 2d constructs can't explain lift is also unwarranted. It's not enough to accurately calculate the lift of an entire airplane but it is a good explanation of basic lift production. He correctly identifies lift as being due to pushing air downward by the wings but it would help if he made some mention why wings have their air foil shapes. It's to reduce turbulence, drag. You don't need as powerful of an engine with a wing shape that generates smooth airflow (also it saves fuel). Also in keeping with the idea that lift is due to pushing air down it should have been mentioned in the tennis ball example. He only mentioned the difference in air speed. It is just as crucial there that there is a downward flow of air after the ball as in the case of a wing. I commend his wishes to eliminate such misconceptions and am sorry if my initial post came across as anything more than also wanting to clarify the situation. I was pretty surprised a few years back when I first realized that such a basic thing was being widely misrepresented.

[@WalterAndreeff]

I'm curious. The Mayan's had a system of mathematics-like philosophy. Anyone know if there are lectures on that material anywhere here?

[@lococomrade3488]

It's been 9 years. Did you ever find anything good on this subject?

[@matthewgale1176]

Well the ABC's to it is sometimes you don't shout your way through the room to understand the room you listen ......to the room to understand the room Positions are Nitty Gritty I'm for sure...... So we're not used to taking somebody's word for it...... If you can listen ....... then you acquire a right to speak..... But if you over speak..... You're going to regret what you have to listen

[@carlosalbertocuadros5469]

Good Job Professor

[@WalterAndreeff]

He's very animated. Does he do that to keep the students focused on a moving target subject? I wonder if one can calculate how far he walks through a whole lecture. How many shoes does he go through in a year? Just some thoughts...:-)

[@oldsachem]

What are the mathematics of human relationships and social dynamics? The mathematics of power?

[@grounded9623]

Correction; Newtons 3rd law.

[@charlesdacosta2446]

God i love what this guy is saying

[@JustNow42]

I would have loved a few examples from the book

[@hamnchee]

That shirt soaked in armpit sweat is something else.

[@Mehlsack93]

17:37 Galileo wrote this in ITALIAN not Latin in Il Saggiatore (1623): Philophy is written in that grand book constantly open before our eyes (I say the Universe). Written "in lingua matematica", the characters are triangles and other geometric figures. Without these, it is a vain wandering through an obscure labyrinth. "La filosofia è scritta in questo grandissimo libro.. continuamente ci sta aperto innanzi agli occhi (io dico l'Universo) .. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi ed altre figure geometriche .. senza questi è un aggirarsi vanamente per un oscuro labirinto"

[@andrewchoi5476]

Professor your sweating a lot there. Thank you for your Education! I've learned a lot.

[@aaronbrown200]

*you’re

[@fastballflakes5385]

Did he do his lecture prep in the sauna?

[@TheAhmedMAhmed]

is there a link for downloading slides, lecture notes, hms ...etc ?????!

[@quentinfitzgerald3305]

I have found the explanation for lift as you describe in many books and in some cases I had to stop reading because it did not make sense to me- how could the different particles take two entirely separate paths and yet meet up at the tip of the wing. As you say that is just nonsense. The Newtonian explanation is something I never thought of before. I'm glad it's not just me but finally I now know the explanation is wrong- thanks for that. I came across a different explanation that seems more reasonable. Surely the volume of air travelling under the wing will be greater since it moves at a greater velocity and this would cause lift. Those are the two explanations that I have received to date from 'reputable' sources yet contradictory. One says the curve on the top of the wing causes an increase in flow, and the other says it causes a decrease in flow. I was on the point of giving up on this subject!

[@grrjustletmesignup]

Interesting sentiment, but it has what to do with this video again?

[@nash984954]

I must be just stupid, cuz I was watching number 2 in the series, thinking, damn did he say something from the Number 1 that I missed? I get the Golden Rectangle, and even marvelled at Fibonacci, BEFORE seeing Number 2 video of this dude. My Zeus in the sky, WTF and JFC??!!! He bounced all around the topics, ever spiraling my brain down rabbit through to RABID holes in my brain, and ever more confusing, until thinking back on Physics and Calculus, how on earth did I pass them? I concluded it must've been the 2 books from John Allen Paulos, Innumeracy and Beyond Innumeracy, and I get how some can read and understand, with the most clarity depending on the clarity presented by certain instructors, versus hearing those who as Instructors, they know, but seem to live in the clouds above most of us, or maybe it's just me. Anyway, soon into this video he's still all over the place, maybe I need a sign that tells me from him, that okay I'm digressing for a bit here and introducing another topiv, related but just nothing to do with the subject(s) I began with. Yep, stupid, as I see commenters who revel in that they felt they learned a lot from the Prof here. Asperger's wasn't a problem before I knew I was atypical, but what a disheartening thing to meet yet another Mathematics Instructor that has idea bulbs going off in my brain,but am unable to connect them. Peace and love everybody and much thanks to Stanford for releasing their videos. Perhaps a bad day for me.

[@_N0_0ne]

Thank you kindly ✍️

[@gaussianvector2093]

I define mathematics as study for studies sake, chasing the "light bulb moment" . It happens to involve patterns and abstractions, but only as tools yo get to thier. We make up notation, or the language as a tool to learn, but again mathematics is more than that. Its the only science with no non-optional constraints by design. As long as you can show your logic holds it doesnt matter how you show it, nor what axioms you choose, all that matters it it helps us understand something (again for the pure sake of understanding)

[@gaussianvector2093]

now i get your definition of outside in mathematics is What I call arithmetic (one example is when physicists' use mathematics to understand things with the constraint of reality. ) in general Arithmetic is using math to understand something with non-optional constraints.

[@DebaucherousDaniels]

~47:10 Math may have come before writing, but without shared meaning, effectively communicated, money would be impossible... score for Poli-Sci/Comm majors :P

[@quantumfineartsandfossils2152]

10:45 pause "the science of patterns" there you go... ;}

[@oldsachem]

The first arithmetic primer published in the US was authored by Joe Brandon.

[@BudDubR]

The Science of Patterns....Patterns of Vibrations....It's Vibrations....Vibrations all the way down!

[@illcelebrateyoursuccess8907]

anyone have any advice for someone trying to Get her GED ? math basic math has yet to come easy to me and I want to learn it. thank you to any or all that respond. greatly appreciated!

[@maggiemcgroarty3070]

go to www.khanacademy.org . an excellent site for learning on your own. Good luck!

[@mohamedaminebenmabrouk]

you can enroll in math courses offered by mooc providers like : www.coursera.org www.edx.org www.futurelearn.com/

[@RanBlakePiano]

Wonderful ideas voice not too clear but probably due to my 85 year old ears

[@lukeh2715]

anyone know where I can watch that Chichilnisky video he plays at around 20 mins in?

[@freedomlearner2025]

Life by the Numbers 6 - A New Age - Information Age kzbin.info/www/bejne/bn3En3lom5agldkm45s

[@apm77]

This was a five star lecture up until the Galileo fanboying.

[@GilesMcRiker]

The date he gives for the earliest record of numbers (5000 BC) is not correct-- he probably meant to indicate five thousand years ago, what is a more accurate ballpark figure

[@Quetzalcoatlus_Lawson]

He probably was talking about the stuff he touched on starting at 39:37, the ancient banking system.

[@torosalvajebcn]

So if Fibonacci introduced modern numbers (0,1,2,3,4,,etc), from the Arabs in the 13rth century, what type of number used the Greeks for their calculations?

[@Guitcad1]

This site gives a pretty good overview of ancient Greek numbers. gwydir.demon.co.uk/jo/numbers/greek/

[@bvds]

Guitcad1 Thank you great link!

[@KingSinghaLeo]

Great lecture, but mathematics has been used for more than 10000 years. Just look at ancient structures and cosmic calendars which date before what we are taught to be the time of Greek math. I believe we are just rediscovering math concepts which our ancestors were practicing. Maybe they didn't have the same symbols and numbers as we have today, but it is undoubtably a fact that maths is not modern, its part of our nature.

[@gd34n]

that was a really fast minute :D

[@joshuaguting2782]

Thank you dr!

[@idster7]

If Newton's 3rd law accounts for elevation, then what's the explanation that involves Bernoulli (33:40)?? That's a cliffhanger.

[@PYTHAGORAS101]

Mathematics has been around forever ,there would not have been creation otherwise.

[@zacharycat]

The plane has flaps on the wing to control the air flow, this allows it to fly upside down.

[@boonga585]

So did he ever make the video game

[@simpleman283]

I'm a few snorts under at the moment but I want to say. Everything created was done mathematically. The great I AM is the Great Mathematician

[@Khalidnook]

Good one!

[@MohamedWaheedAtef]

is there any resource that lists all of the branches of mathematics as "the study of pattern of X" as was shown in 16:30 ?

[@amontaval]

At 6:45 I learned Leibniz got fried.

[@frankvanluik5005]

What happend to the sweat marks on the shirt from Steve's armpits?

[@Lilwhitelily]

It’s 4am, I’m doing the math when I have to go to work 😩

[@ThomasHaine]

You better be right about this.

[@Alejandro-Te]

35:30 He means "Newton's THIRD law", I suppose.

[@kukuipupule4415]

One, Two, More than two

[@life42theuniverse]

Interesting, Canadians use animal tokens a beaver, sailboat, elk, loon, bear...

[@zvons]

Where can I find these presentations?

[@trubleSum1]

I have a strong urge to edit these. They're hard for me to watch.

[@erichhitchcock3368]

If there had been a NASA person present, the answer to "What keeps things in the air?"....It's a simple formula: $

[@elmehdifidal4385]

What a jump? from 300 AD to 17th. What about the islamic Math.? did you heard about Algebra and where that comning from? what about number? Waht about zero?.....

[@13Septem13]

Mehdi Fidal You know nothing. Jesus Christ invented algebra.

[@MohamedWaheedAtef]

+Tacticool "Keep beheading people with a smile on your face.." ? :D what are you, nine years old ?! :D

[@MohamedWaheedAtef]

+Tacticool hahaha :D

[@charlieparker5678]

Wasn't that the age of Mohammed's wife?

[@badgerking200]

Indians invented the number system.

[@rostislavsvoboda7013]

Quoting Richard Stallman: Steve Jobs, the pioneer of the computer as a jail made cool, designed to sever fools from their freedom, has died. [..] Nobody deserves to have to die [..] But we all deserve the end of Jobs' malign influence on people's computing. Unfortunately, that influence continues despite his absence. We can only hope his successors, as they attempt to carry on his legacy, will be less effective.

[@AbleLawrence]

Ignorance of the history of mathematics outside of Western world is so glaring,

[@tomdrowry]

He looks just like Graham Nash . He has the same northern English accent too .

[@enragedhedgehog]

It's because your mind is attracted by trivia.

[@quantumfineartsandfossils2152]

when I get sweaty 'its not math' when he gets sweaty its math both are math

[@BudDubR]

All the way down until you reach a Turtle, then.....

[@khajiit92]

no one went back to the flat earth camp, that's a myth. i mean, maybe some peasants who never have to worry about it assumed that, but anyone who would ever have to worry about it (scientists, sailors, mathematicians, astronomers etc.) would know the earth was round.

[@huhghgd]

heatenings

[@Fajoekit]

Quite unlikely

[@civver3]

Wow, I guess some of the commenters don't know what a silk shirt looks like.

[@jeanpietrini]

le sudan feo las alas!

[@latifa6836]

Sous titres français s.v.p. merci

[@BavonWW]

'The Age of a Knowledge'? It's a pity that the ages of Reason and Enlightenment have been shelved. The age of Shoulda Listened To Your Grandparents will follow hard on the heels of Knowledge; although there will be quite a few roads not taken from the table of offerings. This doesn't mean that I don't think that this isn't a great lecture.

[@johnlandis2552]

I would have expected a mathematician to know that"begging the question" is a logical error: it means "using the conclusion to prove itself"; another name for it is "petitio principii"

[@regbhyyu]

i guess you feel good about yourself trying to score points with a stanford professor...you must be lots of fun at family gatherings

[@MetaSynec]

Actually, begging the question/petitio principii is not at all a logical error, since circular reasoning is logically valid (e.g. 'if a, then a'). It is a fallacy for sure, but not one whose fallaciousness is best captured in logical terms.

[@glutinousmaximus]

+john landis Well, you are right. It was our old friend, Aristotle who started it all off (not the romans) His expression was:- " τὸ ἐξ ἀρχῆς"