Turing's work on uncomputable numbers and Gödel's incompleteness theorems reveal that not all mathematical truths can be proven, challenging the belief that every mathematical problem is solvable.

The difficulty of proving mathematical problems increases exponentially with the number of steps involved in the proof, making it challenging for AI systems to maintain accuracy.

In mathematics, there are many obstructions to solving problems, and computer scientists have been effective in ruling out certain approaches through no-go theorems, indicating that some problems may be undecidable.

The twin prime conjecture is difficult because while there are infinitely many primes, twin primes become increasingly rare as numbers grow larger, complicating proof strategies.

In undergraduate education, you learn about really hard problems like the Riemann Hypothesis and the Twin Primes Conjecture, but what's interesting are the problems that exist on the boundary between solvable and unsolvable.

To solve a difficult math problem, first find a version that simplifies the problem by turning off most difficulties, focusing on just one at a time.

The Riemann hypothesis, which concerns the distribution of prime numbers, is a fundamental problem in mathematics that remains unsolved, with significant implications for number theory.

The point conjecture, a significant problem in mathematics, involves determining whether a three-dimensional space with certain properties can be continuously deformed into a sphere.

The project involves analyzing 22 million pairs of algebraic laws to determine if one law implies another, providing proofs or counterexamples as necessary. While many problems are solvable by undergraduate students, a few are quite challenging.