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Proofs get cheap
About 3 hours of ChatGPT Pro thinking time per result. The rare, slow part of math is now fast and plentiful.
OpenAI's AI produced 372 new results from 4,000 open math problems. Which one touches your life?
Published . Made by Solenix.
OpenAI released 722 manuscripts, grouped into 372 result families. This page counts each family as one result.
Tap a stage to see what it means. Bars show each share of the 4,000. The dotted line is thinking time.
Each dot is one result from OpenAI's release. Tap a dot or a card to read it in four steps.
Across: how famous the question was. Up: how close it is to real-world use.
Keyboard or screen reader? Use Cards: every discovery is a button there.
Plain summaries, analogies and the fame and reach ratings were written by AI agents from OpenAI's official summaries on 2026-10-07. They are judgments, not measurements. Lean status comes from the release's own index.
Made by Solenix, a tech expert for small businesses in St. John's. See the sources.
A math result is trusted when it is checked: by a Lean computer check of every step, or by human experts who read it.
Five claims, strongest first. Each meter has five bars, and each status is named in words.
Place n dots on a flat page. Count every pair that is exactly 1 unit apart. Try the two simple patterns yourself.
Each line is one pair.
Drag the slider. The pairs update as you go.
In 1946 Erdős guessed that grid-like patterns are close to the best you can do. In May 2026 an OpenAI model showed that guess was wrong, with patterns built from algebraic number theory.
The triangle grid beats the square grid. Both stay near 2–3 pairs per dot. The AI's patterns grow faster than any grid as n gets huge. Mathematicians were shocked by it (ScienceAlert, May 2026).
Made by Solenix, one tech expert for small businesses in St. John's.
One equation describes most liquids and gases: weather, wings, smoke. OpenAI claims it proved that speed can blow up to infinity, if a smooth force keeps pushing. The Millennium Prize pays $1M for the answer. Drag to stir, then press Squeeze.
Then slide the viscosity toward honey, and watch the swirl.
Tap a term to see what it means.
The squeeze pushes a swirl into a smaller spot, so the peak speed climbs. Thick fluid fights back and smooths the swirl out. That tug-of-war is the whole problem.
A computer can never show infinity. Its grid cells set a floor on how small the spot can get. Only a proof can settle whether the real equations reach infinity in finite time.
OpenAI's claimed proof covers the case with a smooth outside force, f. The case with no force is still open. The Clay Institute lists the problem as active.
Made by Solenix, a tech expert for small businesses in St. John's. The simulation uses Jos Stam's stable fluids method.
Lean is a program that checks proofs. This one shows that two even numbers add up to an even number. Lean refuses any step that does not follow from earlier steps. So a proof it accepts has no gaps in its steps, even when an AI wrote it. Lean cannot check that the statement is the one you meant.
Run the check to see the verdict.
A demo of how Lean reads this proof. Made by Solenix, one tech expert for small businesses in St. John's.
Tap a name to see where they stand, from worried to excited.
For centuries, finding a proof was the slow, rare part. If an average result costs about three hours of ChatGPT Pro thinking time, finding stops being the bottleneck. Checking, understanding and using become the hard part. Pick a horizon to see what changes.
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About 3 hours of ChatGPT Pro thinking time per result. The rare, slow part of math is now fast and plentiful.
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Hundreds of papers wait for human readers. Lean makes some of that checking automatic.
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Who owns a result? Was a human's draft used? Rules for this do not exist yet.
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The same checking by computer can prove code, chips and crypto have no bugs of a given kind.
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Results on fluids, plasma and magnets can sharpen simulations for weather, fusion and materials.
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Anyone can ask why a result is true and get a checked, step-by-step answer.
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Science could move at the speed of experiments, with theory produced on demand.
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We could hold true results that no human understands. Tao's 'Math 1.0' worry at full scale.
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Today the model is unreleased. If discovery depends on a few labs, so does access to new knowledge.
Solenix's reading of the facts above. It is not a forecast from any source.
Solenix is one tech expert for small businesses in St. John's, Newfoundland and Labrador. We set up one AI at the centre of the tools you already use. We cut the tools you don't need. Then we teach your team to use it.
A fixed price, in writing. Agreed on the call. No surprise invoice.
SolenixSt. John's, NL
Open any link to check it.
Whether the results without a main proof checked by computer are all correct. 245 of the 372 main results (66%) have none. OpenAI's own notes say some may have problems.
Whether the Navier–Stokes blow-up proof holds. The Clay Institute still lists the problem as open, and a credit dispute continues.
How many attempts failed. OpenAI posed about 4,000 problems and has not said how the rest went.
Who can check the work. The model is unreleased, so nobody outside OpenAI can rerun it.