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In-depth coverage of new theorems, open problems, and proof techniques across algebra, analysis, topology, number theory, and the frontiers of pure mathematics.
6 articles
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...
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...
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 greatest unsolved problem in mathematics
The Riemann Hypothesis, proposed in 1859, remains unproven. We survey recent progress, computational verification to...
Persistent homology and the topology of point clouds
Topological data analysis uses algebraic topology to extract structural features from complex datasets. We explain...