Richard Feynman invented a whole new way of talking about quantum electrodynamics when writing his PhD thesis at Princeton, which eventually helped him detail some of the properties of weak-force in particle physics in his Nobel prize winning work. Later he invented “Feynman’s diagrams” as an intuitive graphical representation of particle physics, which are still used in theoretical physics to this day.
However, he became famous in part through his maverick and distinctive antics. He was a real character: a very curious character. When at Los Alamos working on the atomic bomb, from picking the locks of his colleagues cabinets which contained top secrets, to playing games with the security personnel; naming a few of his antics which had earned him a well deserved reputation of being a trickster and an iconoclast. Freeman Dyson once wrote that Feynman was “half-genius, half-buffoon”, but later changed this to “all-genius, all-buffoon”. Quickly recognized by the intellectual giants of theoretical physics as a brilliant and quick mind, Feynman was sought out by the innovative thinkers of the day. Contemptous of titles, like all Rationals, when awarded the Nobel Prize in Physics, he tried to figure out a way to get out of accepting it.
… there is something strange going on with Primes
— Paul Erdös
Never mind the mock theta, Ramanujan’s gap, Namagiri dreams.
When Srinivasa Ramanujan wrote to G. H. Hardy in the 16th of January 1913, he had some remarkableformulas in that letter. So remarkable are some of his formulas that mathematicians have been studying Ramanujan’s notebooks of formulas for new mathematical insights to this day, more than a hundred years later.
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras… I have no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling”.
Hardy invited him to England because some of the formulas “had to be true, because no one could have the imagination to make them up”. But there were no proofs. However, when this poor vegetarian Indian Hindu came to England, eventually Hardy showed Ramanujan (thru Littlewood) that his formula on Primes was not EXACTLY correct. So Ramanujan had to bend to Hardy and work on his proofs of some of his formulas, so when they tackled the function of Partitions P(n), Ramanujan with the help of Hardy got to point where they “cracked” Partitions (and could prove it). They developed a direct formula that computed the number of partitions pretty accurately, and at the limit (infinity) it was “perfect” — and, could by truncating the number for high partition number to an integer could guarantee to be exact: since the number of partitions of integers is an whole number (i.e., the real number series “formula” converges with an deceasing error rate). Together they “cracked” the problem where neither man could do it alone. Ramanujan supplied the “intuition” (the finding of the hidden pattern) and Hardy provided the rigor to explain why the pattern is true. The method they created, in this instance, was called the “circle method” — and it has been used ever since by numerous mathematicians for various other results.