Deep dives into mathematical beauty, research frontiers, and the equations shaping our world.
Showing 1–6 of 18 articles
A rigorous accounting of proven theorems, computational evidence, and 2026's record-breaking bound — not another 'is it finally solved?' piece
What is rigorously proven about the Riemann Hypothesis, what recent record-breaking results actually show, and why the...
A first-principles primer on the function that ties prime numbers to the geometry of the complex plane
Starting from a simple infinite sum, we build up the Riemann zeta function, its analytic continuation, and the critical...
The computational engine behind topological data analysis, built up from geometric intuition
Persistent homology tracks how loops, clusters, and voids in data survive across scales, revealing shape that means and...
Superhuman engines have mastered practical chess. Mathematics has not yet proven what perfect chess is.
Stockfish and AlphaZero have mastered practical chess, but its true value under perfect play remains formally unproven...
When a computer checks every step, what does it mean to know something is true?
Mathematicians are now encoding entire research papers into Lean, a proof assistant that verifies logic at the level of...
The German mathematician's proof of the Mordell conjecture — and decades of structural insight — earn mathematics' highest honour
Gerd Faltings has been awarded the 2026 Abel Prize for introducing powerful tools in arithmetic geometry and resolving...