Comment by mattfrommars

I asked Claude how will ETH being solved is a major breakthrough for mankind:

“ Honestly, nothing yet. This is a theoretical result, and it doesn't solve a real-world problem today.

*Why it won't change much in practice:* A running time like 2^(n/√log n) is "subexponential" on paper, but for real inputs it's still astronomically slow. For a few hundred variables it's no better than the brute-force methods we already have. Hidden constants in the exponent could also make it worse in practice. Real-world SAT solvers (the CDCL kind) already handle millions of variables on practical problems using heuristics, and this result doesn't replace them.

*Where SAT shows up in everyday life, indirectly:* - Verifying that chips (like the one in your phone) have no design bugs - Scheduling and logistics, like timetables, delivery routes, and airline crews - Software package dependency resolution - Security analysis and cryptography research

*What it could change over time:* - *Research direction:* Many problems were assumed to be hard because ETH says so. If ETH is false, researchers may find faster algorithms for them, and some of those could eventually matter in practice. - *Cryptography:* It doesn't break encryption, since the algorithm is still far too slow. But it could shift how people think about the hardness assumptions behind some security arguments. - *Theory of math and proof:* The Lean verification is also a notable example of AI-assisted, machine-checked mathematics.

So the "big deal" is mainly for computer scientists: a long-held belief about the limits of computation may be wrong. Any benefit to normal people would be long-term and indirect, and only if it leads to practical algorithms.“