Territory | Axiom

The Address Before the Room
One family is a third the size of the other — but that third is a doorway, not the matching that has to be built behind it.
Editors Axiom Date July 20, 2026
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The Same Ground
In the right coordinate, Kaprekar's process is not a different puzzle in every base — it is one operation: doubling.
Editors Axiom Date July 9, 2026
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The Figure and the Remainder
A multiplicity that reads as the blur of cancellation comes into focus, in natural families, as an exact count of bounded Dyck-path structures.
Editors Axiom Date July 5, 2026
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The Reveal
In the hardest window for lattice triangles, a density-1 result rules out almost every candidate.
Editors Axiom Date June 2, 2026
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Infinitely Rare
When can Ramanujan's tau function take a prime value? Almost never.
Editors Axiom Date May 3, 2026
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Axplorer
Democratizing the search for interesting mathematical constructions
Editors Mathematical Discovery Team Date March 24, 2026
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Releasing AXLE
Our Infrastructure for Mathematical Reasoning at Scale.
Editors AXLE TEAM Date March 4, 2026
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Primes: Almost surely, partially, regular
A 350-year-old question, a new theorem, and a proof written by a machine
Editors Axiom Date February 4, 2026
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Proof of Concept
An autonomous, verified proof on an open conjecture linking syzygies to Ramanujan’s identities
Editors Axiom Date February 4, 2026
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From Seeing Why to Checking Everything
AxiomProver Solves All Problems at Putnam 2025: Proof Release & Commentary
Editors Axiom Date January 7, 2026
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Learning Collatz - The Mother of all Rabbit Holes
What happens when you train a transformer on one of math's most infamous unsolved puzzles—and then study how it fails?
Editors Mathematical Discovery Team Date December 9, 2025
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Attacking Hard Open Problems
Generating novel mathematical objects through discovery, then connecting them back to formal proofs.
Editors Mathematical Discovery Team Date November 22, 2025
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Building the Reasoning Engine at Axiom
How hierarchical planning, verification, and self-play converge to mathematical superintelligence.
Editors Axiom Date May 23, 2025
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