He looks like he's in jail for being a mathematical criminal.

Why is understanding why maths is hard, hard?

Why does literarily every 50+ mathematician wear a shirt like that? I'm starting to sense it holds some hidden mathematical super powers

This prison has the smartest inmates

I love when you go deep and I can't understand some of what's being said. Gives me more to go learn about. Please never back down.

"Mathematics is the exploration of the world through a proof trajectory". What a brilliant way to define math.

he uses the word “human mathematics” alot. Alien confirmed. They’re amongst us. He’s trying to computationally irreduce us

I just realised why mathematicians never get invited on podcasts

If he wore a robe and replaced "mathematics" with "life" you'd think he just solved existence

man I can not be more grateful for your interviews. it's like having a direct conversation with brilliant minds. THANKS A LOT , THIS CHEERS ME UP

His answer to "why is math hard?" is itself hard to follow.

You know you're leaving the biosphere when Lex says "is that something that is accessible to someone like me?"

Wolfram is one of those mathematicians that says "is" instead of "modeled by"

Whoa. I'm researching this topic for an essay I'm writing and this is so complex. I love it

Came up the motivation : Finally this would give me some concrete ideas. Leaving : Why the f**k I clicked. I am dumb.

Why is math hard? Because teachers can't teach it. I've found math teachers on KZfaq, that can teach me advanced math.

Historic ground breaking interview... A good clip but the full video is amazing!

LOVE IT. Great work Lex, you have the most interesting guests. Keep it up y que viva tu audiencia de México! :D

I have no idea whats going on but the fact that logic structures can manifest geometrically is really cool, would like to see modeling of that

0:36 Computational Irreducibility

This is refreshingly clear stuff from Wolfram up to 4:00. Great perspective.

Hated math in high school, but after taking a good break and now doing math in my late 20's, math is somewhat ok

Bless this man for creating wolfram alpha, you have made my college life exponentially less painful 😌

I’d love to know Stephen Wolfram’s take on the Yoneda Lemma. Ever since I discovered it I’ve been convinced it is a key to the universe.

I came for an answer, left more confused!

mathematics surpass every other form of knowledge or field for the simply facts that it has and will last time and seem to have no bound

Can’t wait to finish college to understand this. I literally tried to use my brain to the fullest and I understood maybe 20% of the conversation. I feel so so dumb rn. I have to study more 💔💔

Learning math just takes a lot of time in my experience at least i am beginning algebra and it takes myself a lot of time for me to understand a concept.

Remembering the hundreds of algerethems into a specific field is why I'm struggling with math. Instead of years to master, you often times have few weeks to acknowledge every concept. Math in a educational level , moves to fast. In my feeble brain anyways.

I love your podcasts bro

thank you for helping us enlighten our minds..

What he talks about when he mentions paths almost sounds like a neural net, where the weight between nodes corresponds to the distance between elements.

I think effectively the infinity of representation within a domain of mathematics is not wrangled in with effective communication. For example triple integral calculus as Length*Width*Height. It's best to have conversations with people who do not understand so you can grow, more than it is to want to stand out in a group of people who think exactly like you do and want to be delineated from others.

Did u know logirithms have a sister issue. So say your base is 3 then your reverse log is the relation between which root dimension you need when your trying to find your base divided by your rooted base. The questions are 1 is this log as easy to deduce as standard logs and do they add any knowledge/ability to maths and number theory.

The space of possibilities for a “possible” solution granted it exists is the hardest part of math. There is rarely any vantage point towards the end of any proof except one is very experienced in that specific field. The only thing that persists is human persistence to continue building on mathematics despite it’s difficulty. For 1000s of failed attempts, one has got to work, and that one successful attempt nudges us forward just a slight bit.

I realize how hard it is to understand him if you've never tried to construct math from square one yourself

typo, do another pull request :)

When he says that math is hard because it is computationally irreducible, I think he is saying that it is just that, irreducible. It can't be simplified in your head, nor on paper, or else you wouldn't be able to say/think what you were trying to say/think (there is a certain amount of syntax necessary to maintain the semantics). i.e., there is no shortcut to thinking the necessary ideas to get through a mathematical thought process. Also - it is bizarre that after working with a mathematical idea for a bit it suddenly makes sense and we say that it "clicked". With what do we know it clicked? It is not to be taken for granted that we are aware when we finaly get something. Wolfram speaks of this order-2 space which contains the paths that connect the proof paths.. I wonder if we don't have similar levels like this within our own thinking, and that this "clicking" phenomenon is one order of processing confirming another order.

Back to school with conics, directrix, and iterations.

I was listening for a good bit and then I was like wait who is this guy, then I looked at the title and was like :o

Stephen freezes in time for a couple seconds at 2:00 exactly.

What most people understand and use as rational tought is heuristics bound, not actually rational. When you get to math, physics, chemistry, there is only so far you can get following heuristics before you need a complete and actual rational systematic understanding not only in general but also case specific.

This was amazing!!

This all makes me wonder if wolfram physics is just an alternative expression of mathematics, a different but equivalent format for writing down mathematical ideas... so it's not really about physics specifically, it is just able to express the math that we already use to model physics (so it could work just as well for economics or any other highly mathematical field)

"Computational irreducibility" sees a small bump in searches

The lighting in this room is superb.

Stephen Wolfram is such a great guy, I love his enthusiasm for math. I'd very much like to talk to him (meaning sit & stare with blank expression on my face :D)

1:42 actually if one can prove that the Riemann hypothesis is undecidable under the peano axioms, then it must be true because if it was false it would be provable as such using the peano axioms. Fun stuff.

Not the most accessible conversation but somewhat interesting.

I'm always fascinated by Stephen's explanations, despite the fact the I never understand more than 2% of what he's saying.

Computashskkkdhhaggd disability Needed to activate captions to know that that word is irreducibility

Hey buddy can you interview James Woodward and Steve Bassett?

Good luck to all learning the ‘new science’ I haven’t read his foundational text but since the recent academic history of string theory, described in much the same way, an infinite potential space that maps to knowledge we know, let’s not lose ourselves sticking to one tribe. Always be cautious and celebrate new ideas that attempt to further our model of reality.

God i am so fascinated by what theyre talking about and I cant even understand 2% of it

I don’t know how people can mention Eric Weinstein and Wolfram in one sentence. Wolfram has done great things in the past and gets very concrete In his explanation, Eric has neither. Thanks wolfram, this is Just gold!

Everyone's gangsta until shit is computationally irreducible

I understand each and every single word individually, but when he puts those word in that order, i get lost

I would love to watch Mr. Wolfram make all the worlds supercomputers cry, and cry hard.

Lex Fridman having to podcast Wolfram from a living space thats crappy enough to surround him with painted concrete block says something about our world

Why did you have to interrupt him at 10:18? I was dying to hear what he was about to say about relating physics to all that.

These men are clearly far beyond my skills and experience. But as a math/science tutor for 10 years now, I can say that math just isn’t for everyone. Those who get it will always get it with little to no external help-and vice Versa. But I will say, the one thing that my students who struggle HATE when I say, it’s “well, there’s not one sure way to do these problems every time, each one is different.” Some people just know how to do problem solving and utilize ABC 123 logic. People who speak that “language” to them it’s like “well it’s not that hard, you wouldn’t solve it any other way.” And I suppose some people just don’t “speak” that language-which is ok, everyone is just different. Admittedly I’m far from the best mathematician/engineer (BS in Civil), but I know enough to vouch for my experience and work.

Him: Computation irreducibility... Interviewer: Riiiight.... Riiiight... **confused**

Most confusing thing I've watched this year

At 3:46, Maths is not a Battle Royale - woah?!

First time I saw Lex go loco, live: AAhhh WAAOOO

But what can you use this abstract mathematics for ? Like what is it’s use

I suppose, that if you can reduce a problem to a single viable solution, you can then solve for an optimum solution utilising Quantum Computer for exactly what designed for - optimisation problems?

Why is he in a prison cell ?

im sure its been said many times but i have a sneaky suspicion these apparent connections are more of a reflection of the nature of thought and its structural order.

The part before 1:07 means: Math could be infinite, and it's made up by humans. We could measure really complex things sure but that doesn't mean that everything is solvable by simply logic. Logic is limited basically. There might be too many maths to be fully understood by one person. The foundations don't solve everything.

I don't understand his explanation of why mathematics being doable is relevant. He seems to just go off on a tangent saying something along the lines of, "There's an analogue of causal invariance, and there's this thing called homotopic type theory which came out of category theory and its an abstraction of the abstraction of mathematics and there's a thing called the univalence axiom, this axiom is equivalent to causal invariance." And I don't see how that tangent did anything to explain what he was saying.

This is the type of problem we had to solve when I was a kid in elementary school in South Africa back in the 1950s. One cricket bat costs £14-18-9½ . How many cricket bats can you buy for £100 and how much change will you get? £14-18-9 means 14 pounds, 18 shillings and 9.5 pennies. £1 = 20 shillings and 1 shilling = 12 pennies. There were no handy pocket calculators back then. Answer: £100 = 48,000 halfpennies Once cricket bat costs 7,171 halfpennies divide 7,171 into 48,000 gives 6 remainder 4,974. So you can buy 6 bats and have 4,974 halfpennies in change. 4,974 halfpennies works out to £10-7-3 in change. And if you couldn't do that you were a wuss. The smallest coin was a farthing. One farthing was a quarter of a penny.

Here's the real reason. Math is a language, but it's not taught as a language. The way teachers tend to understand math and education in general is backwards. They know that people who comprehend things tend to memorize them, but instead of focusing on memorization by comprehension, they attempt comprehension by memorization. It's like being taught a language in sentences. Imagine you only learn how to translate two sentences: "I would like a coffee" and "your car looks nice". You spend 3 hours memorizing those two sentences with no idea what they really mean, and on the test, your teacher asks you to translate this sentence: "I think you left his coffee in the rental car." You think you didn't learn this in class because you didn't memorize this exact sentence, but your teacher expects you to know how to do it because you memorized things from the language, which (somehow) to them means you know the language. Instead, you have to speak math, and this is what word problems try to teach you to do, but they also suck because once again, you're taught a formula devoid of context. You're given the answer and told to just mindlessly drill it into your head and accept it. If you want math to get easier, give yourself a challenge to work through, something you can't quite solve immediately just by looking at it, but one that can be represented by a physical analog. Once you've found that problem, talk yourself through it. For example, you drill equal sized holes in a plank of wood that are all the same size. The holes are equally spaced from each other and the ends of the wood. Measuring edge to edge (or the material left between the holes, either phrasing works), what is the distance between each hole? Without reading ahead, think about how you'd solve this. Start with what you know- the length of the plank, the diameter of the holes, and the number of holes. If you take the length of the plank and subtract the number of holes times the diameter, you have the total remaining width of material between the holes, but that's all of the little wedge spaces. You're looking for the width of one of them. So, you divide by the number of those spaces, which is always one more than the number of holes. That's your answer. Let's make it a little tougher. You drill holes in a plank of wood, but there's a region of wood at one end that must remain unscathed, and you drill incrementally until your last hole is tangent to the edge of that region. What is the space between your holes now?

But can you give change back from a $20???

Fun fact: the only person that actually saw the bomb exploding was Feynman.

Jeez, I came hoping to get an answer and left with none XD. Honestly though,as someone stated in the comments,maths is difficult because most professors charged with passing the knowledge to us suck at doing it. They might know maths but not able to properly transmit it to a brain that doesn't understand it the same way.

42069 IQ podcast right here

This did not make it any clearer why I was terrible at math in school.

I phrase I coined many years ago, "There is nothing hard, just things you haven't learned yet."

Most difficult undergrad mathematics course you took? Go. For me it was advanced calc or abstract algebra.

The more words you add, the more tedious it gets. Math, if studied systematically from foundation to complexity is pure fun. Doing math whilst listening to music is so much fun and one doesnt get distracted by it. Music and word-heavy subjects dont always work for me.

While I think we can get further in mathematics using computers, I don't think that our brains can keep up. I think I'm quite intelligent, at least I'm good at abstracting and sort of compressing and unifying concepts. However, I think that the specific and the general are at odds, so that I'm merely deleting that which matters. I also think that there's a minimum amount of space needed for complex things which goes beyond my working memory, essentially locking me out of understanding. Similarities, symmetries, morphisms, etc. in mathematics are fairly simple, so it's easy to see that e.g. X relates to Y as Z relates to W, or to stack concepts to make new ones (if math and meta-math exists, then there's an infinite hierarchy of metas). So any person who is sufficiently intelligent should have an intuition for things like group theory before hearing about them, simply because they've already noticed that level of similarity in real life. But what about a concept which forms a more complex structure than just a square, and which doesn't fit in our working memoy? What use is a 200-IQ pattern recognition if the pattern doesn't fit in your mind? And what if math isn't more compressible than this? Space is stronger than time for a reason (complexity theory). In short, aren't we try to navigate a space which is far too large?

the path is a long road, there are no shortcuts, learn the language as you go

Notice that just because something is mathematically consistent, doesn't mean it works in the real world, this guy is on the very edges of what we need to understand to create AI

What did he say, "rulio multiway system"? Its hard to tell?

Professor Edward Frenkel says interesting things on this subject.

Wolfram on point here.

All math in some way can be broken down in percentage i did it once for machining then my note book was Stolen years ago .

Math isn’t hard. It is badly taught though at the higher levels. Also math is easier to start with so there are more people doing it and therefore more competition. This competition just increases the amount and sophistication of today’s mathematics to incredible levels. Back in the 1600s one person could know most about all fields of mathematics. Not even the best mathematicians can know more than 1% of the whole field today.

5:08 "univalence axiom" in homotopic type theory, That's you spell that bloody thing. So we don't collapse google.

Me, a writer but also shit with math: “Shit this is the perfect video, I can finally make my dreams come true of learning math!” Alien Mathematician: 0:36 “Computational Irreducibility” Also me: “What the fuck does that even mean?!?!?”

some prisons do look like that,,.....,but aren't we all in a prison ???

I understand some of these words

what is this "computational aerodusibility"?

0:36 what does he say ?

Yeah i surely understood everything in this video foorr SUREEEE

Thanks spooky algorithm.. I was just trying to remember Wolfram's name 2 days ago. Somehow, youtube knew that.

Wolfram like that one math application?

I love this. :) Beautiful mathematics is part of the mind of God

Mathematics is hard because it requires abstract thinking which humans suck at. Also, like any language, it takes work to learn it and, frankly, most people's struggle with it is not due to Mathematics, itself, but their own laziness.