AI is doing math.
We follow the evidence.
An independent field guide to AI mathematics.
Understand the claims. Explore the evidence.
See what remains unresolved.
A machine-made claim reaches into one of mathematics’ deepest mysteries.
Primes look unpredictable. A new claim promises a sharper view of their hidden order. Let’s see what it actually says.
Explore the claimReported claim · Our examination has not started
The idea
No advanced math required
2, 3, 5, 7, 11, 13…
Simple to define.
Extraordinarily hard to predict.
Every whole number greater than one is a prime, or is made by multiplying primes. They are arithmetic’s building blocks. Yet the gaps between them keep changing.
Mathematicians can estimate how many primes lie below a given number. The deeper question is: how far can that estimate be from the truth?
That question has an extraordinary connection to the zeros of a function called zeta. A “zero” is an input that makes the function equal zero. Better knowledge of where those inputs cannot be means tighter control over the irregularity of the primes.
If it holdsNot a new way to count.
A sharper limit on the error
in prime-counting estimates.
The whole numbers from 2 to 79.
The claim
Move the boundary. See the difference.
The full Riemann Hypothesis puts every nontrivial zeta zero on one line. This claim excludes zeros from a smaller region. A striking possibility, but a different statement.
These inputs have two coordinates: a real part (across) and an imaginary part (up and down). The colored area shows where the selected statement would rule out zeros.
A comparison of statements, not a numerical experiment. No zeros are plotted. For ⅞ and ¹¹⁄₁₂, only the right-hand region inside the strip is highlighted.
Compare the statements
The main claim would exclude zeros to the right of this line. It still leaves a gap between the claimed boundary and the Riemann Hypothesis line.
A major advance in understanding the distribution of primes. Not the full Riemann Hypothesis. And not, by itself, a shortcut to breaking encryption.
The evidence
A claim is the beginning of the story
A paper, a formal statement, and an independent replay answer different questions. We keep them separate so you can see exactly what has—and hasn’t—been established.
Open the complete family recordSource snapshotadc7f1241b42…
OpenAI/math · 6 October 2026
A zero-free half-plane for zeta and the stated Dirichlet and Hecke L-functions. This feature focuses on the zeta statement; the broader family has additional hypotheses and scope.
Read the 7/8 manuscriptOpenAI supplies a Lean scope note covering the 7/8 bounds for zeta, Dirichlet L-functions, and finite-order Hecke L-functions over ℚ(√−3), plus a stated logarithmic Landau–Siegel exclusion. Later applications are outside that selected statement.
Having a Lean link is not the same as independently checking its axioms, dependencies, or agreement with the manuscript.
Inspect the pinned scope noteThe first job is to match the manuscript’s statement and assumptions to the pinned formal endpoint. Then inspect dependencies and attempt an isolated replay. No result from those checks has been recorded here.
See the examination planHere’s what examining a proof looks like up close.
A paper claims an extraordinary structure on the six-dimensional sphere. In our scoped replay, flipping one input changes the conditional relation determinant from 1 to 7.
The arithmetic is reproducible. Which sign the geometry supplies is still unresolved. That’s the part a successful calculation cannot answer for us.
Inside the S⁶ examinationInputs: λ₀ = 0 · λ₁ = 1 · λ₂ = −1
This tests the encoded arithmetic, not which sign is geometrically correct. Neither setting validates the paper’s headline claim.
Active examination / 2 scoped local replays published / Headline unresolved
The replay packetElsewhere in Paper Watch
A few stories worth your attention. These are tracked claims, not independently validated results.
Source-informed schematic · not simulation data
Foundational · Tracked 2026-09-08
The paper reports a proof that smooth, forced three-dimensional Navier–Stokes flow can break down in finite time.
See the check plan Examination not started
Illustration · proof dependencies
Methods · Tracked 2026-09-04
A reported Lean formalization turns the known proof of Fermat’s Last Theorem into steps a computer can check.
See the check plan Examination not started
Source-informed schematic · not simulation data
Foundational · Tracked 2026-09-08
The paper claims that smooth, unforced three-dimensional ideal-fluid flow can develop a finite-time breakdown.
See the check plan Examination not startedTracking a paper is not an examination. These collections are separate, not stages of a funnel.
Keep following the mathematics