Executive Summary

• Advances in math and computer science are happening at an exponential rate
• Large Language Models are making math proofs more computable
• Some problems remain unsolvable due to computational limitations

The Buzz Score

The Internet’s Verdict: 70% Hyped, 30% Skeptical

Expert Insights

Experts argue that we are on a y=2^x exponential curve, with impressive results being delivered continuously.

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results.

Others note that while Large Language Models have made math proofs more computable, some problems remain unsolvable due to computational limitations.

Any computable problem will eventually fall to computers. LLMs have made math proofs more computable, in the sense that a computer can both generate potential solutions and check the validity of its solutions on its own, with a reasonable chance of converging on something correct.

Challenges Ahead

Despite the advances, some challenges remain, such as simulating the dynamics of a cubic millimeter of water molecules for 1 second.

Unfathomably beyond current capabilities (and LLMs aren’t going to change that).

Additionally, some problems, like the Millennium Prize problems, remain unsolved.

Like the Millenium Prize problems. Haven’t seen a solution to those. So there are limits – but we’re about to learn a lot about the new normal of what constitutes a layup math proof vs the truly difficult.

Focus Keyword: Math Progress