OpenAI released proofs it says settle ten previously open problems in mathematics and computer science

Mathematics

OpenAI released a Lean proof file for each of ten newly settled math and CS problems¹

OpenAI posted the repository on August 1: ten Lean 4 files, one for each result, running from a high-dimensional sphere-packing bound that had not improved since 1978 to the first explicit construction of a non-sofic group.¹² Every problem was genuinely open, and each result now sits behind a machine-checkable proof. But no one outside OpenAI has confirmed them yet: the README hands verification to a separate Comparator challenge, and the manuscript's claim of zero unproven steps is still its own.¹

The ten results and the Lean 4 file that formalizes each in OpenAI's repository.¹²

Lean file	What it settles
SpherePacking.lean	Fixes the exact high-dimensional decay rate of the Cohn-Elkies sphere-packing bound, its first improvement since 1978.
MetricCodes.lean	Improves the classical upper bounds for binary and spherical codes by exponential factors.
NonSoficGroup.lean	Constructs an explicit non-sofic group, settling whether every countable group has finite permutation approximations.
ConnesRigidity.lean	Disproves Connes's rigidity conjecture with infinitely many property-(T) groups sharing one von Neumann algebra.
Permanent.lean	Proves circuit and formula lower bounds for the permanent.
QuantumParallelRepetition.lean	Establishes exponential parallel repetition for every finite two-player entangled game.
GapCVP.lean	Reduces 3SAT to give new hardness for the Euclidean closest vector problem.
EhrhartVolumeInequality.lean	Proves Ehrhart's sharp volume conjecture in every dimension.
MulticolorTriangleRamsey.lean	Proves a superexponential lower bound for the multicolor Ramsey numbers of a triangle.
CompactnessAndDegeneracy.lean	Disproves two extremal-graph conjectures of Erdos, on compactness and on degeneracy.

OpenAI credits an internal model it calls Astra, its next major model, and puts the compute to generate all ten proofs at about $2,000 at its Sol API rates.²

Scientific Computing

Coding agents sped up eight scientific codebases by as much as 60-fold in an OpenAI field report³

Across eight case studies, most in the life sciences, research groups turned coding agents loose on aging software. One quality-control tool for RNA sequencing dropped from 15.5 hours to under 15 minutes per run, and a 20,000-line C and C++ genome aligner was rebuilt from scratch in Rust.⁴ The developer Philip Ewels, quoted in the report, found the agents "eloquent, convincing, and confidently wrong in ways that are easy to miss," and every gain rested on a scientist fixing what "correct" meant and checking that the rewrite met it.⁴ The agents did the engineering. Defining the question and verifying the answer stayed human work.³⁴

Neuroscience

The Feinstein Institutes mapped more than 200,000 fibers in the human vagus nerve⁵

More than 200,000 individual fibers run through a single human vagus nerve, and a team at Northwell Health's Feinstein Institutes has now traced them across 60 nerves from 30 donors, the first comprehensive anatomical atlas of the nerve.⁵⁶ The three-year effort, Reconstructing Vagal Anatomy, ran on a $6.7 million NIH grant awarded in 2022, combined microCT imaging, immunohistochemistry, and ultrasound, and put its data in public on the NIH-backed SPARC platform.⁵ Which fascicle carries which organ's signals is exactly what vagus-nerve-stimulation devices need in order to reach one organ without disturbing the rest, the use the Feinstein team says the atlas is meant to inform.⁵

Security

Attackers are exploiting a Cisco firewall flaw rated only 5.3⁷

The Cisco firewall bug that is actually being exploited, CVE-2026-20316, carries a CVSS score of just 5.3: a static credential in the Secure Firewall Management Center web interface that lets an unauthenticated attacker sign into a low-privilege account and read system data.⁷ Cisco's advisory says its security team saw the flaw exploited in the wild in July 2026. Cisco rates its Security Impact High despite the 5.3 score, because the flaw "can be used with other Cisco Secure FMC Software vulnerabilities to elevate privileges."⁷ Those other bugs are the ones scored 10.0. The authentication-bypass flaw CVE-2026-20079, disclosed in March, was shown to reach root in a proof of concept, and Cisco says it has seen no sign of anyone exploiting it.⁸⁹ Cisco shipped hot fixes for FMC releases 7.0 through 10.0 with no workarounds.⁸