4 ms·

The relevant journal article is pretty long - great choice by Quanta to cover this article. Here's a link to the pre-print: https://arxiv.org/abs/2201.09445 ht

• artintechni 4y ago
  "Long" but piecemeal. Which is a result of how they approached the problem. They defined every possible curve in infinite dimensions based on 5 characteristics, essentially drawing the problem from an infinite space to an abstracted 5 dimensional space. Think: all black holes can be defined, so far as we understand them today, in an abstracted 3 dimensional space, that is [mass, electric charge, angular momentum](i) Then started proving the theorem for subsets of that 5-d space. Think: proving a theorem for infinitely many integers by first proving for 0, then all even integers, then all odd integers, then proving for a small handful of odd integers that your odd integer proof fail on, then proving that negatives can be modified to the positives you have already proved. It's really great seeing this practical approach laid bare. Also, at the bottom, the paper includes code for "Section 11: Most of the Sporadic Cases", so if you're unfamiliar with the math but are familiar with standard python then you both gain further understanding by seeing the code process, but also by comparing the code to the included corresponding, highlighted as comments, theoretical proofs' propositions. For example, from the paper(ii): def can_induct(d, g, r, l, m): # Proposition 8.4 if d >= g + 2 * r - 1 and good(d - (r - 1), g, r, l, m): return True (i) https://en.wikipedia.org/wiki/No-hair_theorem https://en.wikipedia.org/wiki/No-hair_theorem (ii) https://arxiv.org/pdf/2201.09445.pdf https://arxiv.org/pdf/2201.09445.pdf