Is the Universe a Math Problem? With Terence Tao

What It Covers

Neil deGrasse Tyson and comedian Paul Mercurio speak with UCLA mathematics professor Terence Tao across a 55-minute Cosmic Queries episode covering unsolved problems like the Collatz conjecture, the relationship between pure and applied mathematics, non-Euclidean geometry's role in general relativity, and whether simulation theory can be mathematically tested.

Key Questions Answered

• •Pure vs. Applied Math Spectrum: Pure math is curiosity-driven pattern exploration with no required practical goal, while applied math sits between pure theory and real-world engineering. Tao's collaboration with an electrical engineer and statistician produced MRI algorithms now embedded in all modern machines, delivering scans 10 times faster than previous methods — a direct example of interdisciplinary crossover yielding measurable clinical outcomes.
• •Collatz Conjecture — Unsolved After 100 Years: Take any number: if even, divide by two; if odd, multiply by three and add one. Every tested number below roughly 10-to-the-18th eventually collapses to the 1-4-2 loop, yet no mathematical proof covers all infinite cases. Tao's own partial result showed 99% of very large numbers shrink dramatically, but a complete proof remains out of reach.
• •Non-Euclidean Geometry Predates Its Application by Decades: Mathematicians developed curved-space geometry purely for theoretical reasons, with no expectation of physical relevance. Einstein later needed exactly that framework for general relativity and borrowed Riemannian geometry almost word-for-word. The lesson: mathematical structures developed without practical motivation frequently become the precise language science eventually requires to describe physical reality.
• •Erdős Problem 1026 — Crowdsourced Collaborative Proof: Paul Erdős attached small cash prizes to over a thousand open problems; solvers rarely cashed checks, preferring them framed as credentials. Problem 1026, involving optimal stack-sequencing strategy in a coin game, was recently solved through a decentralized chat room combining pen-and-paper reasoning, computational brute force, and AI-assisted numerical evidence gathered by roughly five to six contributors.
• •Bayesian Framework for Simulation Theory: Testing whether reality is a simulation requires Bayesian probability — assigning prior likelihoods to all possible universe types, then updating those probabilities against observed data. The practical barrier is not mathematical but epistemic: humans cannot enumerate all possible universe configurations or assign unbiased priors, making a definitive probability estimate currently uncomputable regardless of available mathematical tools.