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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?

"... the list of primes goes on forever ..." According to Edward Fredkin, infinities, infinitesimals, perfectly continuous functions, and local sources of randomness are figments of human imagination and do not occur in nature. I conjecture that the Riemann Hypothesis is true but unprovable in ZFC, but ZFC and Peano Arithmetic are contrary to empirical existence. There is a saying on Wall Street: Trees do not grow to the sky. Do an arbitrarily large number of positive integers occur in nature? Consider some conjectures: (1) There are three fundamental levels of physics: classical field theory, quantum field theory, & string theory, (2) There exist positive integers W, X, Y, & Z - each greater than 1 and less than 10,000 - such that the amount of classical information is < W^X, the amount of quantum information is < Y^ (W^X), and the amount of stringy information is < Z^(Y^(W^X)) , (3) String theory with Fredkin's finite nature hypothesis suggests dark-matter-compensation-constant = (3.9±.5) * 10^-5 . Is Professor MIlgrom of the Weizmann Institute the world's greatest living scientist? Google "pavel kroupa dark matter" & "riccardo scarpa mond arxiv",

282 anyone?

If another aspect of POV is to use Euler's implied symbolically connected inference in the projection-drawing picture-plane, on the Blackboard that is, how effectively the innate "whole message" of logarithmic condensation-coordination vanishing-into-no-thing Singularity-point positioning is exposed to view depends on the assembly of functional abstractions shown us by our Teachers. Eg if we are familiar with the entangled connection of Absolute Zero-infinity reference-framing containment positioning NOW of/by i-reflection Singularity-point, the expectation is that all potential positioning possibilities are contained, recognisable within the holography dimensionality of e-Pi-i 1-0-infinity sync-duration, represented by the Unit Circle of Infinity @.dt instantaneously. But the Mathologer's and 3BLUE 1BROWN Students know how to speak the million dollar language, to qualify.

Proud to be an Indian 😊

Proud to be an indian

I am Indian....🥺🥺🥺proud to be a Indian ❤

Super interesting, thank you.

34:47 dude just shave your head

Hola !, he Tratado de comprar el Libro: Viaje a Través de los Genios!, donde lo puedo Conseguir en español ?... Gracias

MATHS dammit!

This is so tedious. If he cut out all the umms and aahs, it would probably be at least 10% shorter. If you can't present something in a concise and/or interesting manner, stop clogging up the internet!

I came for the puzzles and boom, fractals

Amazing and pleasant lecture. Show this to high school students!

I think the question of who the giants were is the question is begged in too many discussions about Newton's thought. It needs to be discussed and the best discussion is to be found within the pages of Never at Rest, Richard Westfall's monumental biography of Newton. Often people cite portions of Newton's notebooks of the 1660s. But what they neglect is why he turned away from the new Cartesian mathematics after he had mastered it further than anyone living in the West. In his thirties, he gave a second shot at the ancient Greeks. He expressed his regretted his youthful arrogance when dismissing presumptuously the early books of the Elements of Euclid as being too simple. When he wrote the Principia, he wrote it in the style of his new heroes - Euclid, Archimedes, and Apollonius. Contemporary commentators doge the bullet by translating all Newton's proofs in synthetic geometry into modern algebra. Newton had said that the Greeks solved everything Descartes boasted of discovering and had done it more elegantly. Newton also explicitly decried what would happen if the mathematicians of the future neglected the Greeks.

Professor Dunham is one of the best lecturerrs I've ever seen. Totally engaging, knowledgable and informative.

5:00

From every row of Pascal triangle deduce 1-2-1=-2, 1-3-3+1=-4, 1-4-6+4-1=-6, 1-5-10+10-5+1=-8.....etc all trivial zero of zeta function, have such pattern from(x-1)^n of Pascal triangle, flip -,+ sign from 3rd term on.

This is good book and very good information about land we live on it can be submerged. If we can not rewrite the number theory we will be subjected to destiny arranged by some one else but in doing so we may rewrite other destiny too so it it very important and for the pure at heart

I tried hard to focus on the content ... really I did.

I love his version of the 4x4 magic square with a audience member's birthday. Makes it so entertaining and adds a personal touch.

Good at math, but I don't know it.

Great talk! Here are a couple more videos about math and football that analyzes the pursuit of DBs to catch ball carriers. czcams.com/video/5hk5bIEVVe8/video.html czcams.com/video/4D-F2TwC9QU/video.html

People like this person should cease this m.o. of vain joke-attempts and then ‘ok, so, ummm here’s Newton, here now ok ummm’. ‘Ok; so alright, ummm, now…. Huh, hehe, ok, so lemme, ummm ‘ If you really know that much, find a way better way to present it. Great knowledge of a subject doesn’t equal charisma. Modesty; relatability, straightforwardness, and clarity contribute far more.

Shame about the masks. BAA, BAA BAA!

Thoroughly enjoyable. Thank you.

54:08 I thought Bernoulli said, “I recognise the lion by his claw.” Not “paw”. Not that it matters either way as his intended meaning is clear. ADDED 54:24 “dunned” and “teezed”. Just sayin’. 😁

here for the 7 from the web: To determine whether a number is divisible by 7, you have to remove the last digit of the number, double it, and then subtract it from the remaining number. If the remainder is zero or a multiple of 7, then the number is divisible by 7.

Very interesting talk, but the microphone/audio system suffers from inconsistent sound levels and humming noise from poor grounding. Pity and ironic, especially on a talk about sound!

From where did British got mathematical knowledge in the beginning when they did not know how to count.?

A tyre isn't a torus, but yes, I take your point.

Leibniz more or less invented the computer, and wrote its language.

P r o m o S M 💯

Truly amazing! Thank you for sharing ❤👍

Very impressive and detailed info.. thank you.