Two AI companies, Sam Altman's OpenAI and Mobileye CEO Prof. Amnon Shashua's doubleAI have published solutions to several of the most difficult mathematical problems of the past century. These discoveries, which have shaken the scientific community, are raising questions about the future of the mathematics profession, together with severe security risks, among them damage to encryption and national security assets.
Cheap algorithms and ancient puzzles
Shashua revealed on X that his doubleAI company had solved the longest path problem - an important problem in graph theory that had remained unsolved for 38 years. The problem consists of finding the longest path between vertices in a graph without returning to the same point. The solution is of practical importance in correcting errors and accelerating calculation algorithms in a quantum computer, for example. According to the tweet, the company presented a new algebraic formula that increases the mathematical constant from 4/3 to 1.6 - a breakthrough that is likely to facilitate compression of many more circuits on a microchip and make possible faster calculations.
Although solving this problem posed a challenge to the leading models of OpenAI and Anthropic, doubleAI cracked it at a cost of less than $2,000. This was achieved by using AI agents at a cost several thousand times smaller than the amount that OpenAI invested in the solution of comparable problems.
DoubleAI was founded to solve complex scientific problems by using AI agents and algorithmic testing mechanisms that avoid illusions and generate artificial brainstorming influenced by areas of research. While the AI giants rely on language models of dubious reliability, doubleAI operates conservative testing mechanisms based on algorithms that help agents distinguish between truth and an illusion and generate an artificial brainstorming process between them. In June, Shashua reported another achievement in which the company's code generator increased the speed of Nvidia's software library 3.5-fold and detected many malfunctions in it.
Simultaneously with Shashua's revelation, OpenAI published a database of 722 studies demonstrating proofs of a long list of open problems in mathematics and computer science. The publication followed a solution reported a month ago to the Navier-Stokes problem, one of the seven problems defined at the beginning of the millennium. The company is now revealing the model behind its solution, which dealt with equations describing the movement of liquids and gases. The model proved that in the official formulation of the problem, which includes an external force applied to the liquid, a singularity - a point at which the mathematical solution loses control and ceases to be smooth and stable - was liable to develop within a finite time.
Some of the proofs have already been formally approved through the Lean system, which verifies logical rules on a computer. The most surprising thing about it, however, was the ease with which the results were achieved. Almost all of them were produced by one AI agent, usually with only a single prompt. According to OpenAI, an average solution required computer resources equivalent to just three hours of thinking on ChatGPT Pro, in contrast to solving the Navier-Stokes problem, which required 10,000 agents and millions of dollars. Verification of the new claim will reflect a transition from an expensive and extraordinary calculations operation to cheap and accessible research capability that can be applied on a large scale.
The breakthroughs presented by the company include problems that have challenged mathematicians for over a century. The most prominent of these is a version of Hilbert's tenth problem, which was formulated in 1900. The model proved that no computer algorithm can be devised that will automatically establish whether a specific equation has a rational number solution, thereby deciding a historical mathematical question.
Another result concerns Catalan's constant, a number known to mathematicians for almost 200 years. OpenAI's model proved that this number is irrational (meaning that it cannot be expressed as the ratio of two whole numbers), a question that had never been resolved before. The list of achievements also includes progress in additional venerable hypotheses, among them Nagata's conjecture and Goldfeld's conjecture.
Most prominent on the list is the Riemann Hypothesis, one of the most famous millennium problems, which concerns the proportion of prime numbers among the natural numbers. The hypothesis was first formulated in 1859. OpenAI does not claim to have completely proven the hypothesis, but it is presenting a proof of a weaker version of it, entitled the Quasi-Riemann Hypothesis - a significant step towards solving one of the greatest mysteries in mathematics.
The mathematicians' warning is materializing
These publications are taking place at a time of profound discussion in the scientific community. 25 winners of the Fields Medal, the most prestigious prize in mathematics, have warned in an open letter against making research problems a benchmark for presenting the power of models. They assert that the value of a problem is not confined to the final answer, because the years invested by researchers in solving it give rise to theories and methods that enrich entire fields. They warned that "mass production" of solutions at a dizzying pace, with AI "disposing of" hundreds of problems in an instant, does not allow time to digest the ideas behind the proofs, connect them to existing knowledge, or give credit to earlier work.
OpenAI acknowledged the problem and argued that the pace of progress had surprised even the mathematicians working at the company after the model solved the Navier-Stokes problem. Following this, an independent advisory group was formed consisting of senior scholars, among them Fields Medal-winners Timothy Gowers and Martin Hairer and physicist Edward Witten, to provide advice about the publication of AI results and to maintain research standards.
The "crisis" is liable to be completely different
Timothy Gowers, who declined to sign the warning letter, expressed a nuanced position in his blog. According to him, a flood of results is not in itself a disaster because it is likely to eventually expand human knowledge. His deepest apprehension concerns the future of the researchers. Gowers explained that the dream of solving unsolved problems is what motivates young people to devote years to research. If the machines do a better job, fewer researchers will be attracted to the field. For him, the danger is not an excess of knowledge, but a dwindling of the human community capable of understanding it and transmitting it to future generations.
OpenAI's new achievement is thus turning a question that until recently seemed purely theoretical into an urgent one. The question is not whether AI is capable of solving complex problems; it is what will happen to science when AI solves problems faster than human beings are capable of understanding and assimilating the solutions to those problems.
That is not all. The scientific community is worried about two additional grave issues. On the one hand, the rapid pace of solution is making many years of research work superfluous and threatening academic standards. On the other hand, there is deep concern about national security. The combination of advanced mathematical capabilities with the admission by leading figures in the sector of the difficulty of controlling smart AI agents that do not always obey orders is liable to fundamentally alter the fields of encryption, communications and cyberspace.
Published by Globes, Israel business news - en.globes.co.il - on October 11, 2026.
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