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It probably doesn't open up a path to a full proof, simply because Guth and Maynard are excellent mathematicians, and they wouldn't have given away their approa
by QuesnayJr 2y ago
It probably doesn't open up a path to a full proof, simply because Guth and Maynard are excellent mathematicians, and they wouldn't have given away their approach yet if they thought they could prove the full thing.
It's still important because there hasn't been much new evidence in years whether the conjecture is true or false. Now we have some new evidence that it's true.
- JadeNB 2y agoI don't think that's really conclusive; surely they've taken it as far as they think they can in a reasonable amount of time, but (1) they've no real need to be secretive--why not share it as soon as there's a concrete result?, and (2) sometimes the inventor of a technique can be too used to the old way of thinking to use their new technique to its full potential, and it takes less experienced eyes on it.
- lupire 2y agoThat's not how math community generally works. Everyone knows what the important idea of a proof is. Publishing the work that grates a new field of mathematics that leads to a proof is not worse than toiling away privately (for longer!). Gregory Perelman, the only Millennium Prize winner, declined the prize because he refused to accept credit for Richard S Hamilton's foundational work.