Timeline for Major mathematical advances past age fifty
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2010 at 3:49 | comment | added | S. Carnahan♦ | I think between "Hendrik was sitting next to me with a calculator." and "I asked him to check the first few terms", Cohen made some remark about calculators being rare and expensive back then. | |
| May 25, 2010 at 3:36 | comment | added | S. Carnahan♦ | The following is my (probably flawed) recollection of part of Cohen's lecture at the Lenstra Truerfeest a little over 7 years ago: "Apéry gave a shameful talk. He explained almost nothing, and many of his formulas didn't make any sense. One of his sums seemed to have zeroes in the denominator of every term. But there was one formula that he wrote that looked interesting and new, and Hendrik was sitting next to me with a calculator. I asked him to check the first few terms on his calculator, and they matched very well. After the talk we were able to use it to reconstruct a proof." | |
| May 24, 2010 at 10:50 | comment | added | Junkie | "Cohen told me that he and Lenstra were in the audience at one of Apery's first public lectures about his proof. He said that they were madly scribbling during the talk, and by the end they were convinced." I heard Lenstra did real-time numerics on his calculator to verify some claims, and gave them greater confidence to delve further. As vdP says, they realised the crux later (despite being "convinced" previously), and was unproved (to them) prior to Zagier. I dont know if Apery stressed where the difficulties were, or if he was asked how it worked. A=B for identities wasnt known widely then | |
| May 24, 2010 at 3:39 | comment | added | Victor Miller | Henri Cohen told me that he and Hendrik Lenstra were in the audience at one of Apery's first public lectures about his proof. He said that they were madly scribbling during the talk, and by the end they were convinced. | |
| May 24, 2010 at 2:43 | comment | added | Junkie | "Upon re-reading it and the article that Wadim linked it became clear that the so-called "community" acted in a worst possible manner. It was only thanks to the determination of a few outstanding mathematicians that he got the recognition that he deserved." I would say this differently. Thru the determination of others Apery's ideas went from a convoluted multi-100 page work to a 3-page note. Has anyone bothered to see if his original manuscript did in fact prove bounded denominators? That's the crux, and vDP's cheeky "utterly compelling" numerically (so is 1.2020569..., no?) is a nip off. | |
| May 24, 2010 at 0:18 | comment | added | Victor Protsak | François Apéry: 2. "The instigators of the Lichnérowicz reform insisted on loyalty to their program and tried to brand any opposition to it as reactionary, which only hardened Apéry’s position and deepened his isolation in the community. It went so far that at the Journées Arithmétiques de Marseille in 1978, his lecture on the irrationality of z (3) was greeted with doubt, disbelief, and then disorder. Its recognition at the Helsinki Congress would finally erase this humiliation." | |
| May 24, 2010 at 0:17 | comment | added | Victor Protsak | François Apéry: 1. "The dominance of Bourbaki meant marginalization for the anti-Bourbakiste. Not being in sympathy even with all the other marginalized, Apéry eventually found himself nearly isolated." | |
| May 24, 2010 at 0:08 | comment | added | Victor Protsak | van der Poorten: 4. "Anyhow, I considered ‘A Proof that Euler Missed’ a racy title. It arose after Cohen’s report at Helsinki, with someone (specifically, an old friend I was sitting next to) sourly commenting ‘A victory for the French peasant...’. To this Nick Katz retorted: ‘No! No! This is marvellous! It is something Euler could have done.’" | |
| May 24, 2010 at 0:07 | comment | added | Victor Protsak | van der Poorten: 1. "Though there had been earlier rumours of his claiming a proof, scepticism was general." 2. "I heard with some incredulity that, for one, Henri Cohen (then Bordeaux, now Grenoble) believed that these claims might well be valid." 3. "We were quite unable to prove that the sequences $(a_n)$ defined above did satisfy the recurrence (1.2) (Apéry rather tartly pointed out to me in Helsinki that he regarded this more a compliment than a criticism of his method)." | |
| May 23, 2010 at 23:59 | comment | added | Victor Protsak | Thank you for the link to van der Poorten's article, Ben! Upon re-reading it and the article that Wadim linked it became clear that the so-called "community" acted in a worst possible manner. It was only thanks to the determination of a few outstanding mathematicians that he got the recognition that he deserved. | |
| May 23, 2010 at 14:08 | comment | added | Ben Webster♦ | Victor, read the article "A proof that Euler missed" maths.mq.edu.au/~alf/45.pdf This provides some historical context around the announcement of Apery's proof. Skepticism toward proofs the prover has not produced the details of is healthy, not snubbing. | |
| May 23, 2010 at 13:48 | history | made wiki | Post Made Community Wiki by Ben Webster♦ | ||
| May 23, 2010 at 10:22 | comment | added | Gerry Myerson | I think disregarded is a bit too strong - more like, met with considerable skepticism, on the grounds that it was not expected that such a venerable problem would be solved by such low-tech methods. The community took the proof seriously enough to go through it in detail and then acknowledged that it was valid. | |
| May 23, 2010 at 10:02 | comment | added | Victor Protsak | I remember reading that Apéry was snubbed by professional mathematical community and his proof was disregarded at first. | |
| May 23, 2010 at 8:37 | comment | added | Wadim Zudilin | +1. And the related link: peccatte.karefil.com/PhiMathsTextes/Apery.html | |
| May 23, 2010 at 7:12 | history | answered | David Hansen | CC BY-SA 2.5 |