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Ah, now I understand that maths is founded on Zentucky Fried Chicken

TREE(3) = -1/12

She's so wonderful

If you dont switch you still have the equal chance of losing. Which makes it 50/50. Your same chance of winning is the same chance of losing, by switching or not switching, by winning or losing, the odds are the same. You only show as winning. Which is misleading and deceptive. But you dont show the other side which is losing. I played this same simulation and opted to not switch doors. The results were the same. Even on your own video. So it doesnt matter if you switch or not the results are the same. You equally win as equally lose so it doesnt matter if you switch or stay

Philosophers attempts to make common sense rigourous seems like it makes everything seem illegitimate, but if it keeps you from being bored to death, I am all for it.

Thanks for this entertaining, stimulating video! x

instead of "sums to a square" I tried the relationship "both sum and difference are prime". As with all maths, I can pretty much assume that somebody else has already explored it, but it was fun to play with.

My approach to sleeping better at night has been a regular wind down pattern for everyday and other sleep hygiene methods. But to each their own.

Awesome podcast! I might have misheard, but according to ChatGPT, the integral of 1/sin(x) is not log(tan(x/2)). Are there any references to Landau's comments in hospital? Is it an urban myth? On Wikipedia there is another version with circles and crosses.

we need a system of mathematics that does not involve Infinities of any kind, and that are solvable without infinities of any kind. Infinity doesn't exist anywhere in the universe. Infinity is a concept that does not apply in reality. Until we get past that, we'll continue to struggle with solving the big questions in physics.

The foundation of mathematics is 1+1. Everything referenced in this video sounds like nonsense.

The Yamaha Fazer motorcycle has nothing to do with the Finnish chocolate manufacturer.

Interesting topic, very existential/philosophical

Math is to physics as grammar is to poetry. The vessel, not the contents. There is a deep attraction to mathematics, a beauty that is aesthetic, not rational. That said, all the results of math are analytic, not synthetic as we find in science. Everything in math is already there, inherent in the premises. So math is valid, not true.

The guy is partially right: Watching that video conveys zero information. However he failed making be believe him.

This should be on the main channel. Top tier stuff 👍

Once upon a time circa 1970 computer programmers posed the problem of integral calculus to computers as a demonstration of artificial intelligence. The thinking was that if computers could do symbolic integrals, then they would be artificially. Intelligent. Seemed reasonable back then. Now we have programs like Mathematica and others that do this. No one claims they are intelligent though, excepting maybe Stephen Wolfram. I think the real problem is figuring out exactly what is intelligence, either artificial or natural.

But there is no step whereby the abstract number can be linked with the physical quantity. It's like trying to find the chemical, DNA reason for one's preference for lime Jello.

Is that Fermat? Or Thermals Theorem? 😅

What happened to the menorah that is usually in the top shelf of the bookcase?

I imagine this odel being used for more hgh problems ... on the wider world stage ...35:00

oh thank goodness we can sleep well at night now

As a professional United States based train spotter I feel personally attacked.

Billionaires shouldn't exist. No matter how smart they are.

🤣mostly his @34:03

16:58 I'm still missing something. If he didn't have the proof, how would he be caught cheating? Is it that eventually you would inquire two envelopes and they would have been the same? How do you know he didn't color the map with 1 million colors instead if you're just opening 2?

Mitochondrial DNA has been shown to also be able to be passed from father to son. It is very rare but it happens.

I wonder if anyone knows what the actual theories are

Throwing the needle is just not the same as "choosing a random chord". I think a satisfying empirically true answer to the throwing the needle question should come from presuming not some uniformly infinite set of lines, but a Gaussian representing a drop through air above the center of the circle (resulting in something like Brownian motion I guess). As the drop gets higher, the Gaussian gets more dispersed, and then take the limit of that. I bet you get the same answer as Jaynes, 1/2

And now let the trainee check for printing errors...

It has to be noted that factoring big numbers into their prime factors is not *the* thing that secures the internet today. The current mainstream big thing is elliptic curve cryptography

Best ASMR video ever

4:24 really meased with me 😭😭

13:03 Speaking of LLMs getting maths proofs hilariously wrong, try plugging this into ChatGPT or Gemini or whatever: "For each letter in the alphabet, what is the smallest integer greater than or equal to zero that contains that letter when spelled out?"

I don't have time to hear this whole thing, but to avoid having the house burn down, I would guess that whatever answer is asked for has some relation to pi.

We were short-sheeted in this video, harldly talked about impossible numbers at all. Should clearly explain why 5 is impossible, that's kind of easy I learned in comments. But then talk about many on the list of impossibles being some primes, or squares or primes... I was asking chatgpt about some of this. I think there is enough for at least a little video about the impossibles, which this wasn't

6:16 Chern 陈省身

1/3 is the most natural. I am in the 1/2 camp though. Probably because I dont understand infinities that well but here it goes. If there are infinite chords, then it feels like there should be infinite chords both in and outside the triangle. So now there are 2 different infinites. And if you only get one chord at random, it is either from infinity 1 or 2. So its a 50/50. Like with a coin. If you ask a large amount of people to draw a new line through a circle and then put the triangle in afterwards, I feel like the ratio would be closer to 1/2 than 1/3. probably my 4th time watching this in 2 years btw. always a numberphile i guess

What an interesting person.

Is there a book that explains this all? With the historical context, as well as with formalisms and proofs?

Never understood why it was there, but whet happened to the menorah on the top shelf?

I would love more videos fleshing out some of these topics! A lot of stuff was sort of jumped over that im honestly not very familiar with, but i understood the gist and it intrigued me.

I'd love a video with more details about how mathematicians are using computer-aided proof systems. From what I've heard, one of the advantages is that you can also easily use them to collaborate with other mathematicians by having different people work on different pieces of the final proof. It does seem like a really cool area of maths.

It's pretty obvious why 5 is untouchable. There is no way to obtain 5 as a sum of unique integers that includes all unique divisors of these integers.

That brown paper remained unused, as well as the pen Asaf kept holding in his hand throughout the video. That's not a coincidence when the topic is category theory.

The testable #1 is the foundation of Mathematics and Science. ~Pure Mathematics

I like Asaf Karagila. More of him, please!

You may not be able to write the proof before the death of the universe, but you'll still finish it before the guests get off of Mr. Bones Wild Ride.

Fantastic video! I liked his take on AI too. A great speaker

Disagree