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AI Helps Disprove 87-Year-Old Mathematical Conjecture

New Scientist | Scientific Research

AI Helps Disprove 87-Year-Old Mathematical Conjecture

“A mathematician has cracked an 87-year-old conundrum with the help of AI and announced the solution unceremoniously in a tweet. The finding is the most difficult mathematical problem yet solved by AI, say experts.

Levent Alpöge at Harvard University wrote on X on 19 July that the Jacobian conjecture – which academics have spent decades trying to prove was true – is actually false, giving a tiny, 216-character counterexample as proof…

The Jacobian conjecture – which suggests that a certain type of mathematical function would also work in reverse – was formally set out by Ott-Heinrich Keller in 1939. It was also on an influential list of 18 fiendishly difficult problems for mathematicians to tackle in the 21st century drawn up by Stephen Smale in 1998…

Abhishek Saha at Queen Mary University of London says AI’s recent advances in mathematics, such as the OpenAI model that recently cracked a decades-old conjecture by Paul Erdős, have been surprising, but this latest finding has stepped things up significantly.

'Probably this is the biggest conjecture that AI has played a significant role [in proving or disproving] so far in mathematics,' he says. 'This is a pretty big deal. AI has [made] remarkable progress in the last year.'

The single line of mathematics posted by Alpöge was simple to verify and many mathematicians have already done so, says Saha. Now the big question is how it was done.”

From New Scientist.

Anthropic | Scientific Research

AI Finds a New Enzyme System in a Virus

“Many discoveries that have revolutionized biology and medicine started with a scientist noticing something odd in the staggering diversity of molecular machines found in nature. Restriction enzymes, proteins that cut DNA at specific short sequences, were found in bacterial immune systems, where they destroy the DNA of invading viruses. Researchers realized they could use these enzymes to cut DNA at chosen places and splice genes from one organism into another, which launched the biotechnology industry. Taq polymerase, an enzyme that copies DNA at high temperatures, was identified in a bacterium in a Yellowstone hot spring. It became the basis for PCR, the DNA-copying method used in much of modern diagnostics. CRISPR was first noticed as an unusual repeat sequence in the DNA of certain bacteria, and is now the foundation of gene editing-based medicines.

In the spring of 2026, we formed a research group to see whether general AI models can systematize and accelerate such discoveries. We believe that this acceleration will come from establishing a new way of doing biology research, in which agents collaborate with humans in every step of the process. Developing this new way of working required that we build our own lab and a single team working on everything from training Claude in biology to running experiments in the lab.

Today, we’re sharing early results from one of our first research programs, in which Claude autonomously discovered a novel enzyme system that is associated with an array of DNA repeats, a pattern reminiscent of CRISPR. Although we don’t yet know its function, the system that Claude discovered has a set of characteristics that have only ever been found together in a handful of other systems, all of which are programmable and perform operations like cutting, copying, and pasting DNA. Beyond CRISPR, which has already transformed science and medicine, several other such systems are now in development as promising tools.

The system that Claude found is based on a reverse transcriptase (RT), enzymes that copy RNA into DNA. While this underlying RT, found in a jumbo phage, had been identified in previous studies, Claude appears to be the first to notice the system’s defining features—an associated array of non-coding DNA sequences and an additional accessory protein of unknown function.”

From Anthropic.

Wall Street Journal | Scientific Research

AI Offers Hundreds of Potential Math Solutions

“On Tuesday night, OpenAI published hundreds of proofs for mathematicians to wrap their minds around.

An unprecedented number of answers that had eluded mathematicians for decades arrived in a single night. The deluge included AI solutions to more than 300 problems across number theory, algebraic geometry and other fields with names that could give anyone haunted by high-school math a migraine. Among the major findings in a collection of 722 papers were advances related to three of the five remaining Millennium Prize Problems, including the Riemann hypothesis.

'If a human did this, it would be an instant Fields Medal, no questions asked,' Alex Kontorovich, a Rutgers University distinguished math professor, wrote on X about the 'quasi-Riemann hypothesis' proof.

The understated rollout of such monumental results marked a shift in OpenAI’s approach to publishing scientific discoveries, part of an effort to win back mathematicians who have become allergic to AI hype in recent months. On late Tuesday and early Wednesday, many of them reported feeling a sense of awe.

As stunned math experts scrolled through the results and began to absorb them, even a researcher inside Anthropic called the release 'obviously the most significant moment in mathematical history.'”

From Wall Street Journal.

The Keyword | Scientific Research

Lab Tests: Watermarked AI Proteins Stay Functional

“Today, we’re introducing SynthID Bio, a new technology that watermarks AI-designed proteins while preserving their biological function.

SynthID Bio embeds an imperceptible, verifiable watermark directly into biological designs, such as AI-generated protein sequences and predicted 3D structures.

In laboratory tests across target proteins, our watermarked designs successfully matched the performance and natural diversity of unwatermarked versions. This creates a vital provenance layer to strengthen biosecurity and preserve the integrity of open scientific databases.”

From The Keyword.

NPR | Scientific Research

Two New Sea Spider Species Discovered in the Salish Sea

“Researchers in Canada have discovered two new species that are related to spiders, but you don't have to worry about them crawling across your living room.

The new species are part of the sea spider family and were found in shallow waters in the Salish Sea between Washington State and the Canadian province of British Columbia. These sea spiders are the first to be found in that area in more than 100 years, according to the researchers. The newly discovered species, which measure about a centimeter across, were collected between September 2023 and August 2024 off of the islands of Vancouver and Quadra in British Columbia.”

From NPR.