Conformal geometric algebra, which extends to five-dimensional space, allows for the representation of points, lines, planes, and spheres as algebraic objects, simplifying many geometric operations.

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.

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.

Twistor theory originated from my realization that light rays can be represented by points on a five-dimensional boundary, allowing for a global description of space-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 space of all proofs has a shape, and we can rank them based on different axes like elegance and length.

The concept of twistors introduces a new kind of curved twistor, which is essential for understanding complex solutions in physics, but it also leads to inherent confusion in the theory.

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.

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.