Analysis: Science & Technology — 20 October 2026
OpenAI AI proof of the quasi-Riemann hypothesis unpacked by number theorists
Among 377 results OpenAI announced on 6 October, one claimed a proof of the “quasi-Riemann hypothesis,” a weaker form of the 160-year-old Riemann hypothesis on the zeros of the zeta function. Stanford’s Jared Duker Lichtman called it the most significant AI-for-math result so far. Human number theorists have now reconstructed the argument; NYU’s Maksym Radziwiłł said most consequences of the full Riemann hypothesis already follow from this weaker bound.
The Riemann hypothesis asserts that all nontrivial zeros of the zeta function have real part 1/2, which would tightly constrain how primes thin out. Riemann showed zeros lie in a strip between 0 and 1; the 1896 prime-number theorem followed from excluding the edges. Quasi-RH only requires a narrower strip. OpenAI posted two versions: a 199-page Lean-verified claim that zeros lie between 1/8 and 7/8, and a shorter 49-page paper placing them between 1/12 and 11/12.
Experts have set aside the longer paper because of poor exposition and are working from the shorter one, which a person edited before release. The novelty is a synthesis of existing tools—including metaplectic forms and a 2021 formula of Radziwiłł and Alexander Dunn—rather than new concepts. Peter Sarnak will not call it a theorem until humans check every detail; Will Sawin doubts the same methods reach the 1/2 line.
Surface-adsorbed molecules reach the Fourier limit of optical coherence
Researchers at the Max Planck Institute for the Science of Light report in Science that single molecules on a crystal surface can keep optical coherence at the Fourier limit, the bound set by how fast an emitter radiates. Until now, surface contamination destroyed that coherence hundreds to thousands of times faster than the limit.
The team used sublimation of an organic crystal in a cryostat to strip contaminants, then froze the surface near a few kelvin and evaporated molecules onto it. Coherence times then matched the Fourier bound, the first such result for surface-adsorbed molecules.
Surfaces would let STM and AFM tips address individual emitters, but environmental noise had blocked that path. The experiment shows the environment can be quiet enough; combining it with scanning probes is still unproven. Surface interactions also shift alignment, energy levels, and possibly vibration, so control and decoherence remain coupled.
Bennu sample cracks explain the asteroid’s unexpectedly low thermal inertia
OSIRIS-REx samples show that Bennu’s boulders lose heat quickly because they are both porous and riddled with internal cracks, according to a Nature Communications study led by Andrew Ryan at the University of Arizona. Spitzer data from 2007 implied low thermal inertia, like sand, yet the spacecraft found a boulder-strewn surface that should have cooled slowly.
Porosity alone did not match spacecraft measurements. X-ray computed tomography at NASA Johnson and lock-in thermography at Nagoya University mapped crack networks; simulations scaled those structures to boulder size and recovered the observed thermal inertia.
Remote thermal data had been hard to invert without ground truth. The result ties telescope and spacecraft heat signatures to laboratory structure, but returned particles are much smaller than boulders, so the scaling step is the main inference. Similar cracks may affect other carbonaceous asteroids used in thermal models.
Sources: Quanta Magazine; ScienceDaily (Max Planck Institute for the Science of Light; University of Arizona).