Very nice :from a didactic point of view. At 16:17 :please use double braces for multisets.

When scientists didn’t advance in Germany because a mad man wanted to utilize them for grim potential- they protected humanity. What the issue with AI and mathematical people in general is they have on the whole, no grasp of sociology, history or consequence & lap up to the private industry incentive no matter how crazed nor ill equipped the one with the turn keys are. Your school is funded by Crypto? No shit. They basically ignore that factor to our peril. This reminds of Oppenheimer being so focused on the advancement of science without the contemplation of what Truman would do with it. While advancement of science and mathematics is important ; without comprehension of the scene & its detractors, it’s like a person running in a dark cave with booby traps they can’t see. Protecting people from the tyrannical & crazy is what is also put to the forefront with this automation & proof rapidity when you ignore the pivot that needs to happen. The people who have always doubted the rigor of math and dismissed it as ghosts ect- are not going to stop their efforts when it is formalized & mechanized -instead they will destroy it as they have always been attempting to do since they burned the Library of Alexandria. This is where rather than hand them the keys, they need to be locked up by the proofs showing what lies they relied on to come to power.

Great lecture! Respect and thank you!

Wasn't it "you can't handle the proof"?

Timestep 28:21. You can't make an infinite list in a finite time!

Jeeesus one guy to intro another guy to intro another guy! Just get to the talk ffs

My take @ 25:46 mapping real line (0,1) to real square (0,1) x (0,1) is this (and its inverse?): (a) the real line (0,1) is a single point continuity that conveniently stretches between zero and one because we wish it to do that (b) the real square is a single point continuity that conveniently stretches between square defined in euclidean space (0,1) x (0,1) because we wish it to do that as well. Why? In the continuum there are no gaps. No measures at all. In those nice graphs of y against x taking y as dependent variable (why) and x as independent variable (why?) they are subliminally imposed upon a single point continuum that fills whole of the graph background. (-∞, ∞) x (-∞, ∞) or even [-∞, ∞] x [-∞, ∞] if you wish. As soon as one describes an axis or two, then applies labels and scales we sort of erringly assume that those lines have somehow partitioned the plane. My take is: those lines are just lines drawn above the plain to given sense to some math that is easier described using vizualizations. The lines and labels give some sense of proportion to the whole. And so it is easy understand why we naively consider a continuum as infinitely many points. A false understanding in my view. It is very good that single point continuums help us to understand things :-) A plain can indeed be a single point stretching to infinity in every direction. We limit that by adding labels and scales to which the continuum meekly condescends. In fact for the tiniest eeny-weeny fraction called p/q where p and q are positive integers the next fraction along from p/q is (p+1)/q. In the land of "divide by q" nothing exists between p/q and (p+1)/q. It is a blank space. We can fill that space with (0,1) continuum, we can also fill that space with quotients of the form 0/100p and 100/100p and we can pretend that the space has been altered. My take: the space has not been altered. It remains the same. The only thing that has happened is some analytical adjustments to show that the labels can be meaningfully manipulated to show some deeper aspects of numbers and measures. Well, that is what i think any way.

The presence of proof is why I love math, however I end up failing at making it mine <3

Calculations are not Mathematics. Calculations work because of Mathematics.

Awesome 🎉❤

11:00

What a moronic comment at 1:07:50 He used "I" because he was the greatest scientist of his era, he's not going to include people like you! What scientific laws have you discovered?

wow woody harrelson really knows his math!!!

Seems like some people in the comments are feeling some kind of way

Legend of mathematics ramanujan

Maths , can't even get your English right .

What a wonderful speaker.

Flatland was parodied as the Russian novel We

Very well made and fun presentation! Question on 49:39 - why is that the case? If the I deleted the unconnected vertex and the "hypotenuse" edge, wouldn't that result in the trace on the bottom left?

So beautiful!

So beautiful!

Great Professor Pomerance!

55:32

A trick for the divisibility by seven: you double the units digit and subtract the result from the remaining number. If the result is divisible by 7, then the original number is also. Example: 252 is divisible by 7 because 25-4= 21. And 383 is not because 38-6=32. Faster than you, professor!

49:04 why Ramanujan is the man who knew infinity ( answer of of to the point question )

His mock theta functions used to find higher dimensions of string theory and behaviour of black holes 😢😢🎉🎉😅😅

Our mathematician Ramanujan is the best in the world 😊🎉

Talk starts at 3:44

Dumb kids in the background talking and screwing around and missing a chance to learn...exactly as I would have done at their age!

Beautiful seminar 👏🏼

Very respectful person.

Can the faulty arithmetic of 9/11 be examined here ? Three thousand missing bodies seemed to totally eliminate any credibility of a building collapses theory given that no other examples exist in world history of such a low rate of recovery. Twenty five years hasn’t given us another example either . Add to that the fact it happened twice on the same day to two identical buildings at the same location and it certainly looks impossible.

Mathematics disproved the official narrative on 9/11. Less than 300 of nearly three thousand bodies were recovered from the debris . These numbers are not plausible as no building collapse in world history had anything close to these statistics

Some fool hasn’t turned off their phone

Newton was not the first to do binomial expansions when r is not a positive integer. Newton was not the first to consider infinite sums that converge. Both were "in the air" in Oxford and Cambridge at the time, some by Isaac Barrow but mostly "the other guy at Oxford" (senior moment -- I can't recall his name). I think Newton's contribution was going from r=1/n (square roots, cube roots, etc) to general fractions, and in finding a neat way to find the formulas: for example, (1+x)^{1/2}*(1+x)^{1/2} = 1+x, so when you multiply out the terms in (1+x)^{1/2} they have to cancel. You can get any rational power, positive or negative, this way. I think Newton also found other surprising identities about binomial coefficients beyond their use in binomial expansions.

super high and I just solved this but I’m not telling anyone

Really Interesting ! !

Leibniz notation in the calculus was superior, and used to this day.

12:40 - Prediction of JSWT application

Bravo!

Bravo!

Thing from Sinatra.

❤❤❤❤❤❤❤❤❤❤❤❤

Excellent speaker 👏🏾👏🏾👏🏾🙌🏾🙌🏾

So sad that now all the universities mentioned are rabidly anti-Semitic and not safe places for Jews - like Erdos - to be.

it amounts to "statistical arithmetics" .

What is it with the shoes? Why does Prof. Tokieda take them off? 2:34

"but we still haven't been able to verify his hypothesis" ... show me someone who refusing to use this hypothesis because it's not been proven. It's as absurd as being concerned that you can't prove two odd integers add to an even.

great talk! ✨ so fun to see the connections between maths and games :)

In Zen there is the exercise to hear the sound of one hand clapping. Here we have seen the sounds of a one handled cup. We have also seen a two handled cup. What are the sounds of a two handled cup?