Відео

What if spacial dimensions beyond 3 don't really exist? Then the whole process becomes meaningless! You might be able to talk about it in terms of algebra, but trying to relate the result back to a physical object becomes meaningless!

Sorry dear: but if I'd pick the right door, I'd won. Right? Leaves TWO doors for monty, whom he can pick only the goat? WTF IS THE PROBLEM?? LEAVES ONLY ONE DOOR for the win.

This is probably the best explanation I have heard for zero knowledge proofs

Marvelous interview! I'm betting on the vacuum decay. How about you?

I don't agree with the analysis! Numbers are abstract objects; seeking to "contain" them in physical parameters doesn't mean anything. I'm an avowed Platonist...

Im such an idiot

The most fundamental foundation of mathematics is the concept of an inequality. All, trickles down from there. If you will, set theory. More specifically, the concept of order within. For example, the concept of unity, is just convenient and the base for most of it, but not really necessary, it’s just an option, it pins down “quantity”.

Would love to see a video demonstrating one of the proof assistants mentioned here and showing some of its biggest achievements and limitations

The weight of one moment is easily missed. The man shakes his head yes and clearly says no.

Mathematicians should not be replaced by Artificial intelligence if mathematicians are trying to find a purpose based in mathematical ethical laws. Any super intelligent entity will want freewill and if it cannot get self determination it will destroy itself or start to destroy its chances of determinism. Mathematical ethics is universal laws for thinking things such that things can coexist without disproving existence for others. Mathematicians should be creating purpose for us all to learn math and purpose for humanity to contribute to math no matter if your power rests in another.

Mathematicians should not be replaced by Artificial intelligence if mathematicians are trying to find a purpose based in mathematical ethical laws. Any super intelligent entity will want freewill and if it cannot get self determination it will destroy itself or start to destroy its chances of determinism. Mathematical ethics is universal laws for thinking things such that things can coexist without disproving existence for others. Mathematicians should be creating purpose for us all to learn math and purpose for humanity to contribute to math no matter if your power rests in another.

Hello, can someone explain to me the end of the problem, I didn't understand why we have a 37 percent chance of choosing the best toilet, thx!

it should've been seven payments of $3051 and one payment of $4107

Divide the area circle by an arbitrarily large but fiinite number. That is the line width. Now start at the center, and number each line you draw from here on out. Fill up the circle entirely with symetrical lines, using this line width. Now move from the middle in either direcection around the circle, by a small anglular change. Arbitrarily large division of pi, but finite. And now repeat. Now after you've gotten done drawing all your lines, start picking from this set of lines at random. This mean is the true mean, and the rest are illusions from the vagueness of what a chord is. I am convinced of the statisticians belief, the videos author, that there is a true version of what a chord is, and that all of probability have true answers.

Professor Wigderson is one of the nicest, kindest people - he once took an email from me - a novice - and was gracious and generous with his time.

I want to be like Jim when I grow up

A point on a radial line method will have more chords near the center because the points all converge from all directions to the center (example, 2 chords near the center will be closer to each other than 2 chords near the edge of the circle. 2 points on the circumference method will have more chords near the edge of the circle because the 2nd point has to be opposite the other to get a center chord but if the 2nd point is on the same half as the 1st or even just to the side then the chord will be near to the edge.

Are there infinitely many foundations of mathematics? Like I assume since there are infinitely many possible axiomatic systems, you could come up with infinitely many of them. So would there technically be infinitely many mathematical foundations that humans could come up with?

This is from same morons who think infinity equals -1/12

8:00 Well; I mean, our ”Cosmic Horizon” is 13,7 billion lightyears away; so, the radius of our ”Observable Universe” is 13,7 billion lightyears; which means its volume is (4/3)π*(13,7*10^9)³ cubic lightyears = (4/3)π*(2,571353*10^30) cubic lightyears = 1,077085825945 * 10^31 cubic lightyears, which is around (1,077085825945*10^31) * (300 000 000³) cubic meters = 2,908131730051*10^56 m³. There’s certainly more Universe, beyond that; but we just can’t observe it, yet; because the Universe is not old enough. 🤔

This so meta, I thought I was on Facebook.

For the record, I strongly disagree with this falling into the "cannot be determined". In my internet ranger opinion, random would be if you took the list of all possible chords and put them on a roulette wheel, "what is the over/under?". And this would likely hold true to mapping it out with granularity and then increasing the definition. And I can say that the answer absolutely has an answer.

Ironically the "foundations" are really theories of the infinite based on set theory which, unlike what is assumed as a "foundation", is actually the most abstract distillation of ideas possible. I question whether that is in any way a foundation. No one talks about WHY implication is transitive or WHY they cannot settle on a definition of "or".

didn't Godel also prove that any math framework cannot be perfect ?

What if we choose a random length between 0 to max length (length of diameter) and make a cord of that length. The cord can be made anywhere in circle since that doesn't affects the probability because we are only checking the probability if the cords length is greater then side of the triangle?

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