Timeline for Proofs that require fundamentally new ways of thinking
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2014 at 20:59 | comment | added | Gottfried William | Arguably Clifford Truesdell invented them in his unified theory of special functions, in 1948. He generalized Euler result at the end as a special case of generating functions. | |
| Dec 1, 2013 at 5:41 | comment | added | Cheyne H | Euler's proof that the number of partitions into odd parts is equal to the number of partitions into distinct parts might be the first useful application of generating functions. Though, you might as well say that the binomial theorem is really just giving the generating function for the binomial coefficients. | |
| Jul 3, 2013 at 9:26 | comment | added | Alexandre Eremenko | By the way, who invented/discovered generating functions? (And thus discovered what is called Fourier analysis now:-) Was this de Moivre? | |
| Dec 17, 2010 at 12:53 | comment | added | fedja | "any technique that has been developed and is now widely used is made to look natural after years of refining and changing the collected perspective, but might it not have seemed quite revolutionary when first introduced?" It surely was, and it is exactly why it is widely used now: it allowed a lot of things that were impossible previously and we are still trying to figure out how much is "a lot". Also note, that shaping an idea and recognizing its power is a long process, so "unexpected" means that 20 years ago nobody would have thought of that, not that it shocked everyone on one day. | |
| Dec 9, 2010 at 17:24 | comment | added | Martin Rubey | I'd like to add to generating functions the idea that you can use singularity analysis to determine the coefficient growth. But I don't know how unexpected this was when first used... | |
| Dec 9, 2010 at 16:58 | history | answered | Gerhard Paseman | CC BY-SA 2.5 |