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 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.

Mathematics allows you to change the rules of the problem, which is not possible in other fields like engineering, where fixed requirements exist.

Alan Turing and Kurt Gödel are connected through their groundbreaking work in mathematics and computer science, both exploring the limits of what can be proven or computed.

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 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.

The Collatz conjecture, which involves iterating a simple process on natural numbers, is easy to state but remains unsolved, illustrating the complexity of seemingly simple mathematical problems.

If we solve the Riemann hypothesis, it could lead to new mathematics that millions of mathematicians would be eager to understand.