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There are people who are probably asking why we haven't done any mathematics Crash Course videos. Well, we kinda have, we did an algebra course in partnership with Arizona State University: • Solving Problems: Stud...
But also, it's down to a general frustration we have and a disagreement about what to do about that frustration. The frustration is that, if you teach mathematics in a way that will help students do well on tests, that is a very different course from one that focuses on the beauty and joy of math. Crash Course's goal is to always be both of those things at the same time, but we've had a hard time figuring out how to do that.
I'm not saying it's impossible, just that we've hard a really hard time figuring out how to do it.
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[@mineola_]

Is this Hank's way of telling us he is starting a science cult? Because I'm in.

[@aditi_05]

+

[@rcoatney_maths]

Isn't it called sci show and crash course?

[@OriginalPiMan]

Maybe you've always been in. Maybe hundreds or thousands of years from now, Nerdfighteria will be interpreted as a science and philosophy cult led by the Brothers Green.

[@TheR971]

are irrational numbers forbidden in that club? If so I AM OUT!

[@albertjackinson]

@@OriginalPiMan Hmmm... Maybe not as a cult, but as a very, very, very good organization that figures a lot of math and science and related stuff out. Can I put that idea in my short story set in the 31st century? Because now I want to.

[@hagaikiri3682]

I saw this tiktok on twitter. Somone tweeted it saying "dumbest video ever" or something. A lot of sci/math-comm people (Grant from 3b1b, steven strogatz, Atsro-Toya etc.) I followed than explained that Gracie (that's the name of the girl asking these questions) is brilliant, not dumb. That these are the questions mathematicians ask. Happy Hank can be added to that list!

[@hoosierhiver]

I think there is a knee jerk reaction by many to presume that some young blonde putting on make-up is vapid and doesn't know shit.

[@hagaikiri3682]

@@hoosierhiver someone in tuataria sent this tweet. it's a british man in his 30s reading the same script as grace, checking how different the reaction will be

[@clay3440]

In general the way we as a culture define what is "dumb" and what is "smart" is fascinating and depressing. It's like there's a perception that "smart people" aren't supposed to ask questions, they're just supposed to know things, as if intelligence is about how much you can remember and not about curiosity, creativity, and problem-solving. I think part of it is because we have an education system that rewards memory and punishes anything else, but that may just be a symptom of a larger problem, who am I to say!

[@yoavsnake]

+

[@hagaikiri3682]

@@clay3440 well, in school it's more complicated. Questions are great, they help the entire class learn, and there's no such thing as a bad question. *But* there are badly timed questions (a question too basic or too deep to justify the entire class's time and not personal follow-up). We just need to be better at explaining why questions are out of place, and not turn off the wonderful curiosity that lead to them.

[@lightsquared]

This was actually helpful because I've been so stressed and angry about math lately. Now I kinda appricate math more. Thanks Hank!

[@beatrizcostenaro6759]

i really appreciate math but i still don’t want to learn how calculate the volume of an hexagon

[@vlogbrothers]

Don't worry, you'll hate it again soon! You gotta find joy in the hate though, like doing a puzzle.

[@bikibird]

@@beatrizcostenaro6759 The volume of a hexagon is zero since it is a flat (2-D) object.

[@hagaikiri3682]

In both my job and my academic studies I toe the line between engineering and applied math. You can definitely both hate and appriciate math!

[@beatrizcostenaro6759]

Jennifer Schmidt and i should have known that... just by my comment you can tell that i’m very bad at math

[@jdwebb42]

“A truth so true it is more true than reality is.” “Mathematicians build universes in their minds that are more perfect than the one that we live in.” Thank you for these quotes, Hank, you’ve made this mathematician very happy!

[@lonestarr1490]

And this one as well. Greetings, colleague * performs secret mathematician gesture *

[@kelleenbrx6649]

@@lonestarr1490 Rite of the Protractor I see.

[@AllYouSeeIsHuman]

Please, mathematician, remember the downside of that statement. - you are not actually dealing with reality, you are living in the realm of magic, sorcery and makebelief

[@jdwebb42]

All You See is Human Being a literal wizard doesn’t seem like much of a downside to me ¯\_(ツ)_/¯

[@TheR971]

@@AllYouSeeIsHuman You've got it inverted. The world you call reality is just a play of your senses. Math exists beyond the senses; it would still exist for you without them. Thus the person not studying the abstract is truly the one living in a make-belief world.

[@LikelyToBeEatenByAGrue]

I'm going to start using "visiting a palace" as a euphemism from now on.

[@hagaikiri3682]

+

[@lonestarr1490]

Visiting a palace, sitting down on a throne. Fits quite well.

[@tatianatub]

+1

[@RainaRamsay]

XD

[@IrisGlowingBlue]

++

[@TimTom]

Oh, you interviewed Bill Gates, didja? Just gonna toss that on the end casually, huh?

[@IrisGlowingBlue]

+

[@mrclueuin]

Ya know like ya do in casual conversation. 🤷‍♀️😉😄 ( Well like Hank does really. LOL) 😄

[@janine2957]

There's something very heartwarming about it. Tessa Violet releases an album? Videos, ads, stories, everything for my queen. Bill Gates wanna talk to me? OK if you insist... second channel. I like Hank.

[@deborah3752]

@@janine2957 also, he asked "Bill Gates' people" for more time than they wanted to give him originally... And they said yes.

[@aarons8711]

+

[@KetieSaner]

Phytagoras is wild. I learned about his cult. But not in maths, but in philosophy instead.

[@_mels_]

I learned about it while watching Evan Edinger watching Horrible Histories!

[@lonestarr1490]

Back in the time, that was the same thing. Math and philosophy, I mean. Or science in general.

[@ashp.2460]

I learned about it in a music theory class!

[@DragonFire381]

I learned about it from The Black Tapes podcast 😅

[@DasGanon]

I learned about it in Philosophy too. It was also in context of "what happens to people who break worldviews" and the story of the guy who found √2 is irrational...

[@vonnegut6108]

Imagine getting teased on the Internet and then having the guy who taught you everything about biology in 11th grade come to your defense, Hank is an enigma in the best way possible.

[@Respectable_Username]

That was the most joyous "I don't know" I've ever seen. The sign of a true scientist!

[@4mpersan]

I found that my teachers that explained the “why” behind the theories were the ones that taught me the most: it’s not about the formulas, it’s about a way of looking for knowledge.

[@Bea_Esser]

I always found it easier to memorize the formulas when I knew the whys. Especially what each letter stood for.

[@albertjackinson]

@@Bea_Esser +

[@albertjackinson]

Yes. I think that's why most of my math teachers have been absolutely phenomenal so far.

[@rev.rachel]

Yes! All the best teachers should. I remember my dad telling me he could never memorize the quadratic equation, so he would just re-derive it on every test because he was taught where it came from, so he could.

[@jadenfedorchak8335]

+ My math teacher last year was really good at explaining the "whys" behind everything, and I actually enjoyed that class. My teacher this year is just telling us the formulas and basically just saying "figure it out," so now I'm having a harder time in math again 🙃

[@CMichael2276]

I love how every Hank sentence ends with an exclamation point.

[@aditi_05]

Yes! +

[@KaitlinGaspar]

makes me worry less about my emails! hehe

[@itsPetal]

I spent the morning watching Hank's TikToks on Twitter and that's how I know this is just a very long HankTok (which is incidentally far preferable to most TED Talks)

[@saniyapaliwal1454]

@@MyNontraditionalLife Yup he does! He actually made a video asking people not to download the tiktok as he reposts them on @hankstiktoks on twitter...

[@itsPetal]

@@MyNontraditionalLife yup! @ hanktiktok

[@hagaikiri3682]

Just to clarify, it's not Hank. It's a fan-ran account, and there's often a lag (several go up at once), but they all ended up there!

[@sm92127]

@@MyNontraditionalLife I think someone else reposts them lol not him

[@clairezalla]

Hank Green, folks: the wonderful man who spends four minutes enthusing about strangers on TikTok before casually dropping that he just interviewed Bill Gates.

[@simonmay1671]

The explanation of how pythagoras came up with this has blown my mind... And yeah he was definitely pooping.

[@alexgerweck4507]

Headcanon accepted

[@ariannawright7586]

+

[@IrisGlowingBlue]

+

[@Spicylolipop]

I always thought of math as a language. The first guy to say “water” didn’t necessary discover the word but needed something to describe what he was seeing and decided the word “water” was the best. Same with Pythagorus, he made the theorem to explain what he saw.

[@erinpeterson3202]

i like this explanation a lot. it makes a lot of sense to me

[@janine2957]

+ SAME. The first teacher that taught me algebra said that we could use letters as we could use numbers or any simbols, because it's a language (at least the way we know it).

[@marym361]

Math wasn't my favourite in school but language was. This comparison could have made a world of difference to me!

[@Nashy119]

It's like a game of chess where we don't know the rules, so we write down the patterns and figure stuff out as we go.

[@momotaro1236]

Hank yelling “I think he was pooping!” is amazing

[@hagaikiri3682]

+

[@MsDafiM]

The most Hank thing to say in any given situation.

[@Eazoon]

As a graduate student in mathematics, I really appreciate this video! Seeing Hank do a proof made my toes tingle a lil bit

[@krank23]

You know why I absolutely love you guys? Because of this. Because of how you, Hank, look at this video that has everyone else mocking and jeering and namecalling, and see something interesting and good and wholesome. This made my day, absolutely. Love your perspective. I wish more people were as generous.

[@qzbnyv]

The outpouring of positive vibes for this girl mostly drowned out the negativity. So many people coming to defence of her questioning, like Hank just did. Her follow-ups were pretty funny... she was shocked that “some mathematician that is followed by Barack Obama” was coming to her defence. Hahah loved it

[@krank23]

@@qzbnyv Nice! I'm not on TokTok myself, and I guess my bubble's mostly been showing me the negatives then.

[@beckroberts4537]

If I could have asked these questions without my teachers becoming annoyed I never would have been "bad at math."

[@danieljensen2626]

They were probably just mad they never thought to ask that.

[@TacticusPrime]

I think Common Core math is much better at this sort of thing than the math I learned as a kid. They really want kids to understand why 84 times 6 is 504, not just do the algorithm.

[@bluetoes591]

I really don't think my teachers would have had answers to these questions.

[@lyreparadox]

I suspect the reason so many of us are "terrible at math" - indifferent teaching by people who didn't understand the material themselves. (And who may have been afraid to lose control of the classroom if they ever admitted that they didn't know what they were doing.)

[@EmonEconomist]

I think you're right - I believe part of why I've always been "good at maths" is because, as a child, I was surrounded by people who were willing to answer these questions when I asked. (Which is not to say that I wasn't terribly annoying...)

[@foysalmahmud1936]

I wish my students got this excited when I talk with them about the beauty of math this aggressively.

[@emalinel]

Hello Foysal, keep engaging your students with stories! I'm sure your students will thank you later for keeping them entertained and for becoming willful students who want to learn the subject matter. You can do it!

[@foysalmahmud1936]

@@emalinel Yes, I will keep doing it. Thank You for the words!

[@aronseptianto8142]

trust me, some of them do they are just too shy to geek with you so they just smile internally but have a flat face on the front to not get bullied by the class keep doing what you do!

[@mcjuwono]

I’ve HATED math ever since I was a kid for this EXACT REASON. I would always ask the teacher things like “how did they come up with that” or why does this formula equate this? or why does 1+1=2? because I felt like there always had to be a PURPOSE to things in life and consequently in the things that I was studying!! even in elementary school!! I was just like WHY?? and almost every teacher would brush it off and just say “well that’s the just the way it is” OR “it just is” OR even worse, “just use the formula” !!! and my peers would look at me weird or deem me less intelligent than them simply because I wanted to know the REASONS behind mathematical constructs in order to better understand them!!! ugh okay thank you for coming to my ted talk

[@lyreparadox]

Yeah, I was always bothered by fractions because no one could tell me where one number ended and the next began, and I'd get soooo confused.

[@gnarthdarkanen7464]

@@lyreparadox Your teacher should've started cutting up apples and pies and stuff like we did in school... Cut the thing into 2 equal pieces, and one of them is 1/2 or "1 of 2"... Cut a bunch of fruit in half, and for every 2 pieces, if you take 1, you still get 1/2 of the apples... It works as a proportion that way when you put them back together using toothpicks... and count them up. You get half the fruits... So the top number is the part you "take" and the bottom is the part it was taken "from" or "of"... 3/4 is "3 of 4 pieces"... 7/10 is "7 of 10 pieces"... it always works that way... It looks a little wacky written out like this and sounds a bit nutty at first... BUT that's the best visual aid I've found to work with... Not a lot to get confused with after you've found enough things to hack up into multiple equal pieces... OR count out by so many "portions"... Proportions... Go back to those apples. We could have simplified cutting up a bunch of fruit in half... We COULD have just said, "for every 2 whole fruit, you take 1 whole fruit"... AND when we find ourselves with one "odd fruit" just hack it in half... and there's your "dividend"... A bit of practice, and you'll be able to just "visualize" your answers... It gets a bit arbitrary and abstract when you get into feet, inches, meters, and other measures... but substitute a reasonable facsimile (like a yard-stick) and go through the same processes. The only difference is, you're working on additive distance or whatever you're measuring, and not just fruits and pies and what-not. ...even a bit late... I just hope this might help. I love to "visualize" or "graphically solve" my math problems... It makes the equations make so much more sense. ;o)

[@rekindle7602]

@@lyreparadox the really cool thing is that I don't think there is like, a point at which one number ends and another number begins, they all almost run together... I think ViHart made a video about this a while ago, I'm going to try and find it and edit this comment with a link Edit: so this is actually two links because some of the proofs she shares in the first are flawed, but the basic concept (as I understand it) is that in the kinds of math where you can't use infinity, numbers run together way down in the infinity soup at the end of that 0.99999..... or the math breaks. kzbin.info/www/bejne/inqxl62uiNOhf6c kzbin.info/www/bejne/raSyiamHo5h9q6c

[@purplefire2834]

Yes! Exactly! Like.. why is one, one, and why is two, two? Because that's just the way they are? But why? And why is that the way we've agreed on to build our systems and not some totally different words or concepts?

[@gnarthdarkanen7464]

@@purplefire2834 Setting values to terms was arbitrary in the beginning... AND we "probably" decided on a Log-base 10 numerical system to allow us to count on our fingers... It was simple, cheap, and effective. There's a tribe in the Amazon that only has three numbers and no concept of "zero". They have "one" and "two" and "many"... That's it. They're basically still "preserved" in the stone age. SO log-base 10 math is the easiest unilateral agreement in society for math... There ARE (however) others. Octal is log-base 8. Digital is log-base 2. Hexadecimal is log-base 16... AND the numerical equivalents in those is bordering ridiculous until you get used to it. Math is the language in which we interpret the values of things around us, to measure, count, and take note of their spacial sense to communicate with each other... Since it's original invention, it's gotten VERY VERY complicated. ;o)

[@doublej82]

This is a great video, because my initial reaction to this young woman was "JFC, we have math deniers now?" The social internet has conditioned me to interpret these things as bad faith arguments. But I needed someone like Hank to take these as good faith questions to realize that they are great questions. The history of mathematics is fascinating, and learning some of the history behind it, and playing games with it can really make it click.

[@bittersweetsorrows]

Can we make this video part of common core? Like “must play at the beginning of new school year to get students excited about math”?

[@hagaikiri3682]

+

[@nothingtoseeherefolks6911]

Please.

[@aditi_05]

+

[@IstasPumaNevada]

"How did we go from "go, play!" to "YOU MUST LEARN THIS!"?" Because it benefited economic and religious leaders to put brains on a conveyor belt and have standardized ones come off the other end. You don't end up with good, predictable, exploitable, subservient workers and congregation members if the human brain is allowed to grow and explore and question and experience on its own terms and at its own pace.

[@docnevyn5814]

Have you see the TED Talk where an Indian gentleman (I think he is a computer science professor) talks about the way we learn? The British education system is based around: reading, writing, and arithmetic because they needed clerks for the Dutch East India Company.

[@aronseptianto8142]

but even in this case of making the most out of a workforce to make the economy going it is quite clear that today's school doesn't achieve that goal you want predictable? machines are predictable, way more predictable than human is now how do we maximise the utilisation of those machines, by teaching the students how to use it but they don't, they won't let us use google in exam, they won't let us use calculator in exam, they won't let us do whatever wacky things the student come up with to solve a problem at the time that formal schools are made, they are made to teach the tools at the time the tools have changed, but the school has not one of human's best quality is that we augment ourself with tools to make ourself better in every way possible

[@jamesbrixey8102]

I'm doing a PhD in predictive modelling - (using maths to model the happenings in reality) and I take the stance that maths probably does exist. The fact that this imaginary universe interplays with the real one in ways that can predict things that we had not discovered yet, for example the Dirac equation predicting antimatter or relativity predicting gravitational waves, is too immense to be merely a coincidence.

[@louloureads3953]

Hey, this sounds really interesting and I was wondering if you had any recommended reading about it? I used a little bit of modelling in my PhD, but very much in an “awkwardly using a tool I’m not that great with” way. I’d love to understand more about it!

[@herranton]

She is asking a philosophical question about the universe not questioning whether it works or not. And like you said. It _probably_ does exist. You're smart enough not to take a hard stand in it because just like Hank in this video, you intrinsically understand that the real answer is actually: _We have no idea; and nobody knows._ You like to believe it does because it brings meaning to your work, (which is probably way more complicated than I could ever understand.) But even if math isn't real, and life is a lie in a way we cant fathom now, your math still has meaning to you in the sense that it has brought you joy/frustration/success/whatever in this thing we are all experiencing together. Often times when we look at the very large picture, it seems to work very differently than the very small, in life, and in science. We can question our very existance one minute, but the next understand that it's probably still a good idea to do those dishes before the wife gets home or you're not gunna get your noodle wet for a long time.

[@XxThunderflamexX]

I mean, I take that as a testament to human reasoning, that we can use our pattern-matching abilities to invent models with sophisticated mathematical structure, that not only map onto our known patterns with incredible accuracy, but are generalizable enough to predict new knowledge. I don't know what "math exists" could mean, the whole point is that it's abstract. The premises we found mathematics in were just constructed to be intuitively applicable to our experiences.

[@herranton]

@@XxThunderflamexX She is asking (broadly) that if mathematics is a real construct of the universe or if it is invented by humans to describe their experiences. Edit: poor grammar.

[@rekindle7602]

@@herranton so like, I can describe a chair that I'm sitting on, and that description probably fits other chairs. Chairs are real, but whether or not *my description* is a real thing is kind of a complicated philosophical question, isn't it?

[@MoCassidy]

When I saw the tiktok, I had the gut reaction you described... like, oh this girl is an unfortunate creation of our “fake news” society. But then you took it and went in the complete opposite direction, and then I felt bad for my initial reaction, but then I felt good because you proved to me that I had the power to change my mind about this. You should feel good that you had the power to help me change my mind on something.

[@zoeymathis]

Imagine if math was taught in stories like this. I, an English major, would have been infinitely more interested.

[@ninakay9916]

Days since Hank inspired existential wonder: 0

[@IrisGlowingBlue]

+

[@rafaelah1492]

+

[@qwertyman1511]

Since hank *last* inspired existential wonder*:0 Since hank inspired *any* existential wonder:[too many to count]

[@NintendoCapriSun]

I've been questioning the existence of "logic" itself for a long time now. Obviously it is a system that we can "use" but it's crazy how deep the rabbit hole goes when you look at all the different types of fallacies there are out there. I do remember that a lot of Algebra revolved around proving things, so in essence, logic really is just another kind of math. I guess.

[@GravityUnlimited]

I think most math people would say that math is at its base one of the most widespread applications of formalized logic, but when you start really delving down into certain aspects of mathematics like set theory, the dividing line between formalized logic and mathematics get a little more... iffy. All that said, I would actually state it the other way around actually... Math is really just another kind of logic :)

[@gnarthdarkanen7464]

You'd do well to Scroogle up some free tutorials on C and C++ (mostly because it's relevant and useful code)... You could go for "Bash" of course, as it's also useful, particularly if you're new to code. There's a lot of basic mathematical operations entirely around "logical expression", from the boolean values of "Yes/No" to more statistical sets like "greater or less than"... Math isn't just logic, though. Logic is a facet or sub-set of Mathematics. ;o)

[@emilym9019]

TIM!! Fancy meeting you in the comments section of a vlogbrothers video! Although that's not really all that surprising because I've been a watcher of your channel for years and you always think about the big, abstract concepts. ;) Cheers!❤️

[@dstinnettmusic]

Send hank green videos the Tyler plz. The dude is great but could use some educational content in his life.

[@altrag]

@@gnarthdarkanen7464 Only sort of true. There's two different "types" of logic -- formal logic (the stuff of mathematics) and philosophical logic (which is what non-compsci people are usually referring to.) Formal logic doesn't really have "fallacies." I mean you can do the math wrong, but fundamentally its all proofs and theorems -- an actual subset of mathematics. Philosophical logic on the other hand is a bit of a different beast and while there is some mapping between "fallacies" in philosophical logic and "false statements" in formal logic, its certainly not a full mapping. Something like appealing to authority doesn't really have a correspondence in formal logic because there isn't really a concept of "authority" in math -- there's only true or false statements.

[@ObviouslyBenHughes]

“oh yeah by the way I interviewed Bill Gates” ...is a level of nonchalance I could only wish to attain.

[@TheWolfboy180]

ALL REMAINING LYRICS the world is gonna roll me if you don’t go G̶o̶ ̶p̶l̶a̶y̶ / All that glitters is gold They say it gets colder / how ‘bout yours? / That’s the way G̶o̶ ̶p̶l̶a̶y̶ / All that glitters is gold I said “yep,” If you don’t go G̶o̶ ̶p̶l̶a̶y̶ / All that glitters is gold

[@katherineallen6108]

So close!

[@purcascade]

Wooooooow 😶

[@a.bookmonkey6790]

so close to finishing my full playlist!

[@kurtpleavin]

I remember during my final year of high school back in Australia, we were doing board work in Maths C preparing for exams and there was this I believe algebraic equation where I'd come to the right answer, but the teachers response was "this isn't the right path to the solution though" and no matter how many times I explained the process they simply would not accept it. Current day much older me looks back at this and thinks "why didn't they praise the fact that I thought outside of the mould? Why didn't they test me to use this method on further equations and test it's scalability? Why were they so quick to simply dismiss it as despite the outcome being correct, how I got there wasn't as was expected?" Looking back I think I learnt a lot that day about the education system and regimented society I was about to journey in to.

[@alexgerweck4507]

I would totally join Pythagoras’s cult

[@natepomeroy9756]

Whelp, that does mean no more beans, but if you wanna make that trade-off, go right ahead.

[@LarsCharmerJorgensen]

Alex Gerweck welcome to the Cult of Many toilets.

[@alexgerweck4507]

Nate Pomeroy I know what I’m about, son.

[@neptunepriest]

I'm pretty sure they killed someone for saying sqrt(2) is irrational, so not the safest cult

[@alexgerweck4507]

Neptune Priest ...oof. Well I’ve already committed in writing now. Wish me luck I guess

[@olivermisbach2454]

My most memorable moment in a math class was after I had tried to find the center of a drawn circle without doing any prior research on how it could be done. My best attempt was drawing a square around the circle that had the same length as the diameter of the circle, then bisecting the angles of the corners of the square. The idea was that where the lines crossed, that's the center of the circle. When I asked my teacher about finding the center of a circle, he showed me the method of drawing 2 different lines on the inside of the circle, and then bisecting them with a perpendicular line. Those 2 new lines would cross at the center of the circle. Since I had tried to find a solution on my own, hearing about the method others had already come up with was so much more exciting and engaging. I had a moment where I just thought, "Wow! That's genius!" I'll probably remember how to find the center of a circle for my whole life.

[@d13_a]

what she’s asking is a HUGE question, i’m in a philosophy-heavy class in uni, and we learn that just because something doesn’t have a semantic reference (a real-world reference, like say, how the word “chair” does, because i can /show/ you a chair) doesn’t mean it doesn’t exist or it isn’t true, it’s just an ontological truth. Conventionalism has been fighting verbal realism on this for a while. So, while math may not exist on a real-world basis (as in, i can’t/show/ you math, only it’s process on paper or experiment, the same way i can’t show you time, only a clock) it is a concept that exists in our minds and we can convene on definition and uses. Idk why anyone’s mocking her, she started asking questions on her own that professors beg their students to try and formulate.

[@gameXylinder]

Ah yes, we live in a universe where Hank can add a "oh and also, I interviewed Bill Gates" in the final seconds of a video, making it sound like it's not a big deal. Wild! Or should I say "no edge"?

[@brittanyalvarez439]

I'm glad I stopped studying for my calculus 3 quiz to watch this!

[@hagaikiri3682]

Good luck on your quiz!

[@ericharkleroad7716]

I love that you did this video, when you showed the video of the lady I, now shamefully, thought that she was just another person trying to reject science and reasoning for the sake of it (in mt defense this country has a problem with anti-scientific thinking so I was kind of primed for that). You made me see the beauty and wonder and brilliance of her question. I'd personally been down that road before, but that was a long time ago and I'm much older and so much more cynical and as a result was thinking about her question in the worst context available. Thank you for letting me see the unmitigated beauty that we should all see when we hear such things.

[@cllw325]

During my GCSE Maths exam I spent the time at the end of exams adding "1+2+3" etc. because I had finished early. As the exam was almost over, I got to "+99+100" and realised it was 5050 (split aesthetically 50+50=100) and I noticed it cause I'd also noticed that up to 10 it was 55 (split aesthetically, 5+5=10). If I'd had more time to play with maths, I'd have probably figured out an equation for this pattern eventually - someone else would have probably discovered it first, but I always find it ironic that the day I feel I truly understood why maths exists was also the day I did my last Maths exam, having spent 12+ years being taught it at school. I couldn't tell you a single question on the paper, but I clearly remember the feeling of "getting it" in my heart and not just my head for the first time.

[@Xob_Driesestig]

That feeling when both my intuition and my reasoning 'get' an abstract concept is one of the best feelings in life.

[@hopestreet3452]

Have you heard of the mathematician Gauss? When he was a child, his teacher set the class this exact task to keep them busy, but Gauss worked out the answer immediately by pairing up the numbers to make 100: 1 and 99, 2 and 98, 3 and 97... so fifty hundreds, then he just added the final 50 on at the end. Blew my mind when I read about this. Similarly with what you wrote - you seem really good at seeing patterns, splitting and recombining concepts - really creative :)

[@cllw325]

@@hopestreet3452 I hadn't heard of that! That's super cool!

[@hopestreet3452]

@@cllw325 I'm just gutted so many students have an experience like yours - that the curriculum is so huge, concepts have to be understood with the head only as there isn't time to 'play' with the ideas and understand with the heart. Sorry for rambling - I'm a maths teacher so this is basically all I think about :P

[@cllw325]

@@hopestreet3452 ah no worries! Yeah the curriculum leaves no room for play and freedom to experiment and be creative which is how we came to learn a lot of what we know now. I often wonder just how much we're keeping ourselves back by forcing our kids into a box (governments rather than individual teachers doing this in my experience!)

[@emmyyanchuk3674]

Oh also I interviewed bill gates 😂

[@RainaRamsay]

XD Yep! That's Hank

[@milicangelaa6575]

I wish Hank Green was my math teacher tbh. The only man that can make algebra sound exciting

[@hagaikiri3682]

May I introduce you to kzbin.info/door/YO_jab_esuFRV4b17AJtAw ?

[@milicangelaa6575]

@@hagaikiri3682 wow thank you! I had no idea that learning math could be fun. I've learned more through youtube than my actual teachers lol

[@verayermola5583]

There should be a crash course series about the history of math.

[@hagaikiri3682]

@@verayermola5583 definitely! but at least for now we have a history of science which is pretty similar: kzbin.info/aero/PL8dPuuaLjXtNppY8ZHMPDH5TKK2UpU8Ng

[@Smogget]

I'd really like to see the creation of a class that was just "Does Math Exist?" or "Math wow!" that doesn't involve memorizing formulas or solving equations, but just focuses on math as a concept. I'd like it to explore what math does, how it's relevant in the natural world, and how we apply it to the world around us without even realizing it. Imagine you're trying to catch something being thrown to you, are you mentally calculating its trajectory and velocity without even thinking about it? MATH?!

[@anthonynorman7545]

How can one understand the concepts of mathematics without using formulas?

[@Smogget]

@@anthonynorman7545Formulas should be used to understand the concept, I'm saying there shouldn't just be rote memorization of formulas.

[@erukei_]

2:03 I bet he was taking a bath. For some reason, great thoughts are usually formed in the shower. Also, I like how Hank didn't immediately dismiss the question just because it was posted by a teenage girl sounding like an armchair philosopher on Tiktok. Because I honesty did.

[@booked_by_books]

This is Hank. John is the older brunette one, Hank is the younger blonde one. Another way to tell them apart is john is chill and hank can be hyperactive. As for dave we don't know much about him.

[@PacifyKing]

@@booked_by_books As always: Dave, forgotten through brotherly adventures

[@OrigamiMarie]

@@booked_by_books but I could totally see John having a similar reaction to that TikTok, so I feel like they're not completely wrong either :-) My dad didn't realize there were two brothers for _years_, until I told him (he hadn't watched vlogbrothers, only the Crash Course videos). They just appeared to him to be differently caffeinated versions of the same person.

[@erukei_]

Brain fart!!! I knew he was Hank! I don't know why I typed John. I humbly offer my apologies. I've read AART last year and recently A Beautifully Foolish Endeavor by Hank (not John) and hopefully soon, The Anthropocene Reviewed by John (not Hank).

[@pullingakatherine]

YES THAT KYNE SHOUT OUT sooooooooooo much respect for Kyne for doing Math communications on tiktok!!!

[@ethanrepublic]

I've never thought about that question! my brain can't handle it

[@hagaikiri3682]

Neither can mine, and I do math proffesionally

[@michellerevisited]

This warmed my math teacher heart!! I am happy to report that the graduate program I'm completing on curriculum and teaching mathematics is VERY heavy on exploratory learning and solving fun problems in different ways and sharing that with each other vs. memorizing procedures. Hopefully we can implement more of that style of math teaching so that more people can have an understanding of math as fun tools for patterns and puzzles. :)

[@alisha8201]

One of my favorite things about the Pythagorean Theorem is that there are over 300 ways to prove it!! We have made so much sense of it that it can be proven that many times and yet it is a totally valid question about whether math exists. I love math. And existence

[@c28baby]

I was only taught about Pythagorean’s Theorem, and not about the tiles and his secret society.

[@kima2875]

: A truth so true that it is even more true than reality. : Oh yes here we go..

[@lonestarr1490]

Math is also more than just reality. It's quite easy to postulate universes whose fundamental parameters differ from those of our universe. And then you can perform calculations, since the same math applies (given the right set of axioms). Hence, reality in that sense is just one possibility.

[@RainaRamsay]

+

[@pendlera2959]

I'm so glad I was homeschooled without a curriculum (unschooled). So many people scoff at child-led learning, thinking kids will just spend all day goofing off. They don't realize that only happens if you treat learning as the opposite of play, rather than the natural outgrowth of it.

[@GrantOberhauser]

My Calculus 3 professor was very much about the "go play" attitude towards math. Sometimes our assignments were to just "vibe" on some renderings of graphs he made in mathematica and just sort of think about how it works. He was very much about explaining why things worked in mathematics rather than simply telling us the equations. That was hands down my favorite math class.

[@criticalarts4683]

Hank, you and your brother are a light in these dark times. Thank you for posting as often as you both do. With everything changing and feeling like it is on fire, I appreciate that you both still bring joy, and are unapologetically excited about so many things. I can't thank you both enough for all you do. DFTBA nerd fighters, I hope everyone is holding up okay. Don't forget to be kind to yourself.

[@lilipad90]

Okay I'm in my last semester of my chem degree and I literally only just understood how squaring works. Like I could plug it in my calculator and get the right answers on tests but this video just clicked it in my brain how it works

[@TacticusPrime]

I only really internalized the sin, cos, tan values by watching gifs. Like this one. i.imgur.com/cBzeLOo.gif

[@Norman834]

Literally. I only understood it as more than a concept once it was drawn out in this video

[@waltwhitmansbeard]

my issue with this girl's tiktok was not her questions about "is math real," because those are super interesting for all the ways you discussed in this video. my issue was her attitude that people before, like, the age of the internet didn't need math, and that technology is limited to screens. i can't remember her exact phrasing, and i don't think you included it in this video, but she essentially implied that there would have been no reason for people hundreds or even thousands of years ago to be asking these questions, like the pyramids and the printing press and even the ox cart weren't staggering technological feats that required...math. and i don't think this is her fault, i think this is a failure of our education system to combine our various educational disciplines into a cohesive narrative. there is no math without history and there is no history without math. science is useless without the language skills to describe and talk about science, and language can be talked about in scientific terms. the idea that curiosity about a particular area of study shuts off when the bell rings is ludicrous, but that is the way the american education system is set up. i also think it takes a lot of bravery to be so openly curious on the internet, esp at her age, esp when she had to have known she was gonna get some criticism for it, so good on her for that.

[@itsPetal]

Tangentially related, but I was an English teacher for 5 years and I definitely feel your frustrations about trying to balance helping kids pass their math tests with helping them actually care about academics. Even in English that balance is REALLY hard to strike

[@mexDpeace]

So Hank saw a tiktok and also interviewed bill gates. I mean obviously we know what 95% of this video is about.

[@t.nysted4146]

As a science teacher. This was brilliant. Yes! Question what you are told, and explore the truth yourself. Without scepticism, we are but sheep.

[@angelbeltranabab01]

Great video Hank, see you Tuesday John.

[@mestiarcanus]

I fully expected you to say "The idea that we teach the Pythagorean Theorem without teaching them that mathematicians poop..."

[@GarrettRobinson]

I really loved this TikTok, I was sad to see people hating on the girl. Happy to see she seems to have come out of it well.

[@sarah8978]

I live in Melbourne and our stage 4 lockdown has recently been extended. Listening to this video while i went on my daily walk made me cry

[@jameskeeley5250]

It's interesting... because it's interesting Solid dad logic there

[@Joy-B]

As a mathematics student going into her senior year of college, this video makes my heart so freaking happy. I love learning the history of mathematics as well as proofs and I 100% agree that a lot of how we teach math to younger students takes all the fun out of it lol

[@beatrizcostenaro6759]

my math teacher always says: “back then they didn’t have much to do so they just thought of this things”. i agree with him 100%

[@danieljensen2626]

Yeah, I mean that pretty much explains all greek philosophers. Nothing much to distract them so they just sat around drawing circles in the dirt or staring at the stars.

[@YlvaTheRed]

I'd like to disagree, but I'm not sure that I can adequately substantiate my position succinctly.

[@gnomee9447]

I disagree profoundly, not on the words themselves but on the sentiment. People had lots to do back then. There is a good reason most scientists in the past were men from rich nations. Because the first thing you needed to become a scientist were heaps and heaps of money. No one could afford to spend their time thinking when they had to put their food on their tables themselves even as children. And build these tables to begin with. And noone would have listened to a poor peasant anyway. Almost all of the big names we know today came from rich families, even the first female math professo, Sofya Kovalevskaya, only had the opportunity to get there through the luxury of private tutors and spare time. Did she have to fight all her life? Yes, of course. Did she live in relative poverty as an adult? Also yes. Could she have done that without the privilege she was born with? No. We must fight to make knowledge, education and leisure accessible to anyone. We should make an environment where "people don't have as much to do".

[@beatrizcostenaro6759]

Gnomee i agree. imagine how many brilliant ideas we don’t know of just because someone didn’t have the resources to put them in practice and it’s still happening. but the nobility job was basically going to fancy parties that the peasants paid with their hard work. and they didn’t have all the technology we have today, like the internet, so there’re less distractions and things that you could spend their time doing so they just came up with things (and had affairs).

[@Zablazer7]

We give far too much credit to shower thoughts and not nearly enough to toilet thoughts

[@hotbeefo]

More or Less podcast covered this as well. I'd highly recommend it to anyone into stats in the UK.

[@OrangeYetti]

I found myself always asking this in school! I was given formulas and rules and I struggled to apply any of them, not because I didn't understand how, but because I didn't understand why. Every time I struggled with a question and a teacher asked me what's wrong I always asked "But who made these rules?? and why??? and how??? Why do they get to decide how this works? If they can make rules, why can't I make rules too?" I never got an answer, sometimes a teacher would just laugh away my questions or sometimes they would tell me not to worry, likely because they had the whole class to focus on. Thank you for this video, the more I think about even simple maths the less defined and more mind-blowing it becomes. I also really loved Vsauce's Odd Number Rule video. The why of maths is fascinating and should absolutely be taught in schools.

[@OriginalPiMan]

"Is maths real?" is a philosophical question, and I strongly lean towards yes. Abstract concepts can be real, and maths is one of those. Maths is discovered, not invented, although I would say that maths notations are invented; there is nothing innate and universal about the order we place symbols and numbers, and certainly not about the form of the symbols themselves.

[@tempest_dawn]

Yeah, the symbols are "real" in the way that the language we make to describe the physical world are "real" - its reality comes from a shared understanding of what is being described.

[@altrag]

Is anything real? :D

[@kpbiorlz]

I'm a science teacher. And this video..... is.... perfection. Thank you.

[@ronnedejong7641]

I love the fact that someone had to prove that 1+1=2

[@ronnedejong7641]

en.wikipedia.org/wiki/Principia_Mathematica

[@NoActuallyGo-KCUF-Yourself]

But first, you have to prove that 1=1, and that is even more difficult.

[@johnmcgrath200]

Mathematics -- and even Pythagoras's Theorem -- was around long before Pythagoras himself. Way back to Mesopotamia and the cradle of civilisation. It's also extremely likely that Pythagoras didn't discover it himself but just took credit for the work of one of his students.

[@aislinking5806]

Good morning!

[@Big007Boss]

Top of the morning to ya

[@Tankej0527]

Good 11:30pm ta ya!

[@nothingtoseeherefolks6911]

Good 12:17 pm to you

[@tnorthrup1986]

as someone for whom math beyond Algebra II in high school is inacessible despite all my best efforts and my abilities in other areas, it really heartens me to see someone geek out like this.

[@jdwebb42]

How can math be real if our eyes aren’t real

[@alex0589]

David “jesus take the wheel” -Mark Twain

[@aboz8649]

Nothing is real

[@ShivaniSingh-dl3pe]

Hank and John joining TikTok have definitely helped change the way I see the platform in general, and I like that!

[@juliareste]

i saw you talk about this on tiktok! i just like believing that mathematicians know nothing so i feel better about myself the Pythagorean theorem is a... theory so like does it technically not exist? is math a social construct or is it technically real? i saw a girl on tiktok say that technically 2+2 doesn't equal 4 because that's just an idea. but surely 2+2 *does* equal 4, right? anyway

[@Kimmaline]

Theory means something different in science than it does in lay speak. Einstein has a "theory" of relativity which is roundly accepted. Just because it is called a theory, in science, doesn't mean it isn't fact. This is especially true when you start getting into more advanced physics and stuff. I briefly got the opportunity to study under a professor who had been one of the theoretical physics dudes at UC Berkeley in the 60s and 70s when all this really exciting and new shit was going on - if I could remember half the crap he and I would talk about between classes when we would just chat? Anyway, he had a point that everything gets called a "Theory" because physicists have delicate egos, so if everyone's life work gets called a theory, no one gets their feelings hurt. 😄 I doubt it is true, obviously, but it is pretty funny anyway.

[@Inkinhart]

Well ... 2-ness and 4-ness are just ... concepts. Very useful concepts, and concepts we can apply to real-world physical objects, but like ... on their own, there's nothing that really defines them a pair of 2s as equalling 4. Sure, if you have 2 apples and then you come by another 2, you have 4, but when you write out 2+2=4 you're not talking about apples and the philosophy of maths is *very* mindbending and will make your head hurt if you think about it too long.

[@danieljensen2626]

Theorems are not quite the same thing as theories. Theorems are either absolutely true, absolutely false, or absolutely unprovable. Theories are much more nebulous and you have evidence rather than proof. But also, pure math is basically a set of games. You come up with rules, and then you see what you can do with those rules. Under the rules we usually play with 2+2=4, but you don't have to use those rules. A lot of higher math involves seeing what you can do if you change the rules or add new ones.

[@rosewhipple9923]

@@Inkinhart Yes! 2 doesn't really exist on it's own, it's a metaphor to describe what we see physically. It's like money, the only value it has is the value we all agree it has because of what it represents to us.

[@TacticusPrime]

The Pythagorean Theorem is objectively true about a theoretically perfect right triangle. Math is definitely real, but it exists in an idealized world that we have created in our minds. We can apply that idealized knowledge to real world and get useful knowledge, so in my mind it's as real and real can get.

[@Miss_Myth]

I've never seen anyone so happy to say the phrase "I don't know". 😊 This was beautiful. Thanks for sharing, and teaching, and encouraging play. ❤

[@momotaro1236]

my sister was talking about this

[@TheRexisFern]

Something that I like to tell my friends is that we should ask questions and try to find answers. Not just AN answer, but as many answers as we can that fit into the results you want. If there was a sole way to do things right, the world would have been perfect forever ago!

[@zyaicob]

My thoughts: The universe has a fundamental language that we interpret as maths. If maths is just our name for this universal language, then yes maths is real and fundamental. If maths is just the observing of the phenomenon of the universe's language, then technically maths isn't real. It would be as real as the sunrise.

[@hymnia7]

Speaking as a high school math teacher, I think there's already a great collection of videos out there to fill the niche of math videos that help students do well on tests. But I feel like the world could use more videos about appreciating the beauty and joy of math, especially if they were done in a systematic way to hit the major points of the standard math curriculum, like what Crash Course has done for other disciplines. I would really value such a series in my work as a teacher. I can prep students for tests, but my bigger challenge is always getting students to really connect with the discipline in a way that sparks that intrinsic motivation to learn. (There is, of course, a larger discussion here about what the major points of the standard math curriculum are and why, and whether that deserves some re-thinking or updating...)

[@DefyLov3]

Too Early

[@chelsea6329]

My reaction to the first few seconds was cringe...math is a thing, and we get so much whining from people who are forced to intersect the with it...but another second or two and I realized this was my people speaking... We’ve become defensive because the joy has been squozen from organized learning, and those of us who still find joy there are oddities who invite scorn.

[@metriculous1260]

FIRST

[@sarahsqueeks]

I've never been this early for anything.

[@hambonefakenamington69]

okay Hank I've always had immense respect and admiration for you but that just increased exponentially when you made me and maybe so many others realise that mocking the girl who asked the right questions was incorrect. i didn't mock her because i don't use TikTok but my first impression when you showed the video was to do the same. i just love how you didn't dismiss her as one nerdfighter commented below and you acknowledged her questions and created such a masterpiece of a video out of it! THANK YOU FOR THIS! lately i've been trying to bend myself towards being a fascinated learner rather than a rote one and this was an AMAZING addition to it! i'm going to keep coming back to this video every time i find myself reverting back to my old ways of learning.

[@pancakemaster2482]

Just saying a math based series of crash course courses would be great (not just an algebra either). However I feel like teaching math would be the hardest subject to do on crash course

[@EyeGlassTrainofMind]

Yay Gracie! I thought she was really brave to but herself out there and hate that people weren't seeing her comments and appreciating them. Thanks for appreciating them and her, Hank!

[@nathaneyring4858]

This so relates to me today. I couldn't sleep and at 3 in the morning I found a playlist called imaginary numbers are real, and it goes through the history of imaginary numbers. It is still absolutely blowing my mind. If they had taught me that in junior high or high school I honestly think it would have been life changing.

[@carolh.849]

I was sitting here thinking "oh I saw that tiktok on Kyne's page" AND THEN SHE GOT A SHOUT OUT what an amazing world

[@wmfeagin]

In school, we all hate math. Every middle schooler who has ever struggled with algebra has wanted to know how it would ever be useful in real life. I, for one, HATED trigonometry until I was studying electronics at 30 and learned how it applied to electricity and its principles. Is it real? Yes, in some form. But there is absolutely nothing wrong with asking that question.

[@superplannergirl]

Love y'all and these videos. Thanks!

[@jimsbooksreadingandstuff]

On Spinster's Library channel, they looked at this video too. They had a man in his thirties reading out the same script with a British accent and saying it would be taken more seriously...because of age and gender and because he wasn't applying make up at the time.

[@WolfSeril107]

I've found I can always remember math/science concepts better if I understand how they were created/discovered. That's why Crash Course works so well for me.

[@treetzar1107]

That was such an important day in year7, that I'm pretty sure that no-one else in my class had, that any line I drew on my page was in 3-D, I mean it had to be it was made of pencil lead, but it was being drawn as a model of a one dimensional perfect line. And the tiniest dot I could make was also in 3-D and could not truly do justice to a perfect zero dimension point in space. That drawing a line and a mathematical line were very different things that we spoke of as though they were the same. And also that my terrible drawing skill or my classmates neater writing and drawing were irrelevant, neither came within a million miles of what we were trying to represent. And that it was an act of representation. It was an intentional act of not lying or being wrong but representing something that could not be accurately represented with any technology or skill because it was of only one dimension or even zero dimensions. It was a revelation, and I completely agree that if everyone in the class had had it they'd have been in a much better position to learn math going forward.

[@fiveclub40]

As a history nerd, I personally find the history behind math WAYYYYYY more interesting than actually doing the math itself. Last year in my calculus class, I got so excited when there was a lesson about the stories behind famous mathematicians lol

[@maddie9602]

I know that there has been a revolution in how history is taught between my parents' day and mine: most people in their thirties and older remember history class as being boring and pointless, just dry memorization of names and dates with little context as to why you should care, whereas the history I learned cared little about names and exact dates and instead focused on causes and effects, teaching history as a narrative, a chain of events, this event influenced that event led to that event. I wonder if a similar revolution may come in math. I personally am pretty good at math, certainly good enough to get my Bachelor's of Science in Chemistry, but the math I was taught was nothing but stale formulas learned by rote, or maybe, in geometry and calculus specifically, taking the time to discuss the derivation of the equations, but never was I taught how theoretical mathematicians think, how they come up with ideas for new math. Certainly, math could stand to be made a more engaging subject; even as someone who never particularly struggled with it (or at least not until I was a ways into calculus), I have never enjoyed a math class, never treated math as anything more than a tool I could use to study things that were actually interesting.

[@lobsidedbob]

It's been five days, and I am still thinking about this.

[@MewWolf5]

I don't remember any teachers calling the squares "legs," but I always thought this diagram looked like a funny pair of pants. Your calling them legs was satisfying.

[@jocelynking2421]

Yess!!! I was always scared to ask this because I figured people would think I was dumb...

[@Kamirose.]

As someone who studied language in university, I like to think of math as a language. As humans, it's really hard for us to understand concepts without the language for them, and it can shape the way people view the world. It's easy to forget that the number 0 was revolutionary. Like yeah, people know the concept of having nothing, of course, but being able to represent it in math with a number, was incredible and lead to major advancements in mathematics. "2+2" is language to describe having two things, and then getting two more things. That language, represented by "2+2", didn't always exist, it had to be created to describe an experience in shorthand. The things math decribes may be innate parts of the universe, but the language used to describe it, everything from the hindu-arabic numeral system (and the number 0) to 2+2 to algebra to calculus - had to be created in order to describe the things happening and observed.