points by skew-aberration 18 hours ago

AI has made 'jumps' in demanding fields like leading mathematical research and has made advancements in AI research itself. Is now a good time to start a maths career? Is there a field of research (yours?) which is inherently (more) AI proof?

Btw, I think the discussion of Einstein's career in the paper you link is historically wrong in many respects, particularly the argument about 'weak signal'. Einstein was in fact working on some of the most mainstream and widely discussed problems in physics of the day, he is admired for the creativity of his solutions to those problems, and much of his work built incrementally on ideas and breakthroughs that came (long) before (as all research does).

Article suggests that a central motivation of Einstein's work was resolving action-at-a-distance in Newtonian mechanics - yet Maxwell introduced the same Lagrangian field theories for electromagnetism we use today 50 years earlier to solve the same problem for Farraday's laws of electromagnetism. Similar wave equations existed even earlier. Heaviside in 1893 extended this technique to gravity (matching 'weak field' GR) 20 years earlier. So this is perhaps the one aspect of gravity that had actually already been solved before Einstein. Authors might be conflating his work on action-at-a-distance in QM.

Einstein's GR extended the linear 'weak field' understanding of gravity to include the non-linear self-referential case where masses themselves create gravity. This was mathematically incredibly difficult but was necessary precisely because SR's mass energy equivalence created so many strong signals that were unresolved. For example: if finite energy is mass, then mass changes as objects accelerate past a large mass like a start, and hence their propagation in space could not be explained by linear EM style field equations. Many such considerations were causing very 'strong signals' in SR, and there were analogous problems in QM atomic models being developed at the same time.

SR was also a solution to a problem that was actively being worked by many of the leading physicists of the day. SR actually does match Newtonian mechanics for a single observer - it resolves contradictions in the case of separate observers, by allowing them to assign different values to the speeds, masses, etc of objects such that each object appears to follow Newtonian mechanics for each observer. Again, this was necessary because of a lot of contradictions related to the behavior of light that had been well-known for ~20 years at the time.

Personally, I don't consider this kind of reasoning to be beyond the capabilities of future LLMs (even current LLMs if the task was broken into technical rather than philosophical problems). Personally, I doubt that such problems could stand open for 20+ years waiting for a creative genius to solve them in the modern world.

And don't get me started on the philosophy.