| ▲ | impendia an hour ago | |
> The record before this morning was 29 and people suspected that was as high as it got. Exactly this. A fundamental question in the subject is, whether elliptic curve ranks are bounded. Contrast with e.g. prime numbers, of which are known to be infinitely many. If you set a new record for the largest known prime, then that's cool but everyone knew there were plenty out there to discover. This paper, by leading experts, https://arxiv.org/abs/1602.01431 made a significant impact in the field, coming up with a heuristic argument for why ranks of elliptic curves should be bounded. The same heuristic suggests, albeit more loosely, that we should perhaps be a little bit surprised to see a curve with rank at least 30. So it's mild evidence that the heuristic itself could be mistaken. | ||
| ▲ | altairprime 31 minutes ago | parent [-] | |
cc Quanta which has some nice background explainer: https://www.quantamagazine.org/without-a-proof-mathematician... | ||