Math Encounters -- On the Shoulders of Giants: Newton Revealed

Meet the great Sir Isaac Newton, as revealed through a lifetime of collaboration and communication. William Dunham, who delves into both math and its history, uses Newton’s own words to expose the man behind the math. From his earliest known letter, through exchanges with Leibniz, Locke, and others, to his most-quoted passage about standing on the shoulders of giants, Newton comes to life at his best … and his worst.

Math Encounters is a public presentation series celebrating the spectacular world of mathematics and presented by the Simons Foundation and the National Museum of Mathematics.

[CO_]

What a wonderful lecture.... our children should be listening to this, rather than social media

[kevincasson]

What a brilliant lecturer and lovely man! He should never retire!

[randybailin]

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

[ahmedgaafar]

amazing as ever...professor Dunham is a giant himself in giving mathematics that wonderful life.

[TheRebellion-X]

Dunham is a wonderful speaker, i just saw his talk on euler

[robertschlesinger]

Excellent presentation on Issac Newton by distinguished historian of mathematics, William Dunham. Years ago, Prof. Dunham lectured a course comprised of a couple dozen lectures on the history of mathematics. My recollection from Prof. Dunham's lectures is a story that there is only one account of anyone ever witnessing Newton laughing. Newton was at a social event, where a gentleman inquired of Newton, in a rather pompous manner, whether there might be any benefit from reading Euclid's Elements, whereupon Newton is said to have burst out laughing. Being familiar with the broad scope of Euclid's Elements, I must admit it is a rather funny inquiry, especially to the likes of Newton.

[Hythloday]

“I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” - Newton.

[ElectronDust]

wow. Thanks so much for uploading this great speech of Professor Dunham.

I am a big fan of Professor Dunhams books. It was a pleasure to actually hear him talk in his own voice.

[ravichanana]

"Shoulders of giants" statement is a clear example of expressing humility.

[wardelllindsay]

Prof Dunham, you are excellent on Newton ! Newton is the Greatest!

[rossharmonics]

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.

[richardsidler]

Remarkably well balanced audio, with excellent video clarity and direction. Thank you kindly for the outstanding lecture. 🙏

[hiphopdylan]

Wonderful talk and very well presented and organised.. The only blotch is the clearly visible three youths sitting behind Professor Dunham talking to each other the entire time..

[raybeeze]

i would like to thank the camera operator for his or her appreciation of the beauty that can be found in mathematics.

[rosalind]

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

[frenselx]

I'm reading his book "Journey Through Genius: The Great Theorems of Mathematics" for the third times.

[oker]

William Dunham is a great lecturor. I don't feel that he ever equaled his "Journey through Genius". Maybe he's getting ready to write about Isaac Newton? He left plenty out of this great lecture - Newton's classification of cubic curves. He left out the Fermat work on min/max, which he had to admit to in the questions because some in the audience knew about that part(it's well known enough I suppose even today!).

[jongood]

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.

[johngiles]

I like this guy's humor. And I learned something, too.

[MS-cjuw]

Actually I have something to say
It seems that Newton had used the Factorial prenciple (!)  which it comes from Gamma Function in his Binomial Formula before Euler born, means before it had been discovered by Euler...the same thing with Gauss Divergence Theorem,   Newton had used the same prenciple of the Divergence of the Field to apply the inverse square law to discover the Law of Universal Gravitation before Gauss born  ... I think there is something deep going on,   something about Newton's mind and why doesn't he clarified these mathematical principles that he had already used