What if AI discovered that our knowledge is incomplete?

The anecdote that made mathematicians sit up and take notice

In May 2025, DeepMind released AlphaEvolve, an AI system designed to discover new algorithms (an algorithm is a set of instructions for solving a problem or carrying out a task). On the specific problem of 4x4 matrix multiplication (a matrix is an array of numbers arranged in rows and columns; multiplying matrices is a fundamental mathematical operation used everywhere in computing, from graphics to AI), AlphaEvolve found an algorithm using only 48 scalar multiplications, beating the 50-year-old record set by Strassen in 1969.

This news may sound technical and anecdotal. It is not. For the first time since the invention of mathematics, a significant discovery in a fundamental field was not made by a human. AlphaEvolve found on its own what generations of human mathematicians had failed to find. And it did so by exploring a space of solutions too vast for any human brain to grasp in full.

This anecdote raises a profound question, in keeping with our article on AI consciousness: if AI can discover things no human has seen, what is to stop it from discovering, tomorrow, that some of our fundamental knowledge is incomplete, or even wrong?

What AI has already discovered

Before speculating, let us look at the facts. Here are the major scientific discoveries made by AI since 2020.

AlphaFold (2020-2024): 200 million proteins mapped. DeepMind released in 2021 and then in 2024 (with AlphaFold 3) the structure of virtually every known protein on Earth. That is a century of biological work condensed into a few years. Today, any biology researcher can consult this database free of charge, which massively accelerates pharmaceutical research. As we explored in our article on the medicine of the future, these advances are transforming therapeutic research as a whole.

FunSearch (2023): the cap set problem solved. A mathematical problem open for decades (finding the largest size of a certain type of set in combinatorial mathematics) was partially solved by an LLM (Large Language Model) guided by evolutionary search (an optimisation technique that mimics natural selection to evolve solutions). It was the first mathematical discovery attributed to an AI system.

AlphaGeometry and AlphaProof (2024): silver medal at the Olympiad. DeepMind's AI systems reached silver-medal level at the International Mathematical Olympiad (the IMO, the annual competition bringing together the world's best secondary-school students on mathematical problems of extreme difficulty).

Gemini Deep Think (2025): gold medal at the Olympiads. A year later, a more advanced version of Gemini solved 5 out of 6 problems perfectly at the IMO 2025, scoring 35 points out of 42 (gold medal threshold). To give some idea, barely 50 humans worldwide reach that level each year.

AlphaEvolve (2025): 20% of open problems solved or improved. The system was applied to more than 50 open problems in mathematical analysis, geometry, combinatorics and number theory. In 20% of cases, it improved on the best known solutions. On some, such as matrix multiplication, it beat records that had stood for 50 years.

New antibiotics. In 2023, MIT published the discovery of Halicin, an antibiotic of an entirely new type, identified by AI. Several other candidates are in clinical development.

New materials. In 2023, DeepMind announced the discovery of 2.2 million new stable materials by AI (GNoME, Graph Networks for Materials Exploration). Several of these materials have properties never seen before for batteries, solar energy and conduction.

The angle no media outlet really digs into

Here is the intellectual question that genuinely deserves to be asked. All our current scientific knowledge was built by humans, with human brains that have human biases, human limits, human blind spots. Our current mathematics comes from a tradition going back to the ancient Greeks. Our physics was shaped by minds like Newton, Einstein, Bohr, Feynman. Our biology by Darwin, Mendel, Watson, Crick. What if part of what we believe to be true were simply an approximation, a culturally contingent framework that other forms of intelligence would see differently?

This question is not a philosophical provocation. It is a legitimate scientific question. Here are a few concrete examples of fields where AI could theoretically shift the goalposts.

Mathematics. For a long time, Euclidean geometry (the classical geometry taught in schools, in which two parallel lines never meet) was believed to be the only possible geometry. In the 19th century, mathematicians discovered non-Euclidean geometries (Bernhard Riemann, a German mathematician, and Nikolai Lobachevsky, a Russian mathematician), which later provided the basis for Einstein's general relativity. An AI systematically exploring spaces of mathematical structures could in theory discover other, entirely unknown "geometries" or "algebras", which would prove relevant to describing physical phenomena we do not yet understand (dark matter, dark energy, quantum phenomena).

Quantum physics. The interpretation of quantum mechanics (the theory describing the behaviour of subatomic particles, where the rules of our everyday world no longer apply) remains a mystery after 100 years. Why does observation change the reality observed? An AI capable of systematically generating and testing alternative conceptual frameworks could propose a coherent interpretation that no one has seen. Several teams (notably at DeepMind and OpenAI) are actively working on these subjects.

Evolutionary biology. Classical neo-Darwinism may be incomplete. Several phenomena (epigenetics, horizontal gene transfer, phenotypic plasticity: an organism's ability to change its characteristics without any modification to its DNA) suggest that evolution is more complex than simple natural selection. An AI capable of analysing genomic data at scale could formulate new, more precise evolutionary theories.

Cosmology. 95% of the universe is thought to consist of dark matter and dark energy (hypothetical forms of matter and energy that would make up the majority of the universe but which we cannot detect directly), about which we know nothing. This is probably the largest "gap" in our current knowledge. An AI capable of generating new physico-cosmological hypotheses could propose frameworks that would shed light on this mystery.

What Terence Tao, the mathematician of the century, says

To avoid lapsing into speculation, let us listen to one of the sharpest human minds in the world on this subject. Terence Tao (an Australian-American mathematician, professor at UCLA, regarded as the greatest living mathematician and holder of the Fields Medal, the equivalent of the Nobel Prize for mathematics), has collaborated closely with DeepMind on AlphaEvolve. Here is the substance of what he says in his public contributions.

First, AI does not replace human mathematical intuition. It augments it. Tao describes the experience of using AlphaEvolve as having "a brilliant but inexperienced student" capable of rapidly testing hundreds of ideas that would have taken months to explore by hand.

Second, AI brings to light relationships between mathematical domains that humans had not seen. Several of AlphaEvolve's discoveries reveal unexpected bridges between combinatorics, analysis and number theory. These connections were invisible because no single human masters all of these domains.

Thirdly, Tao predicts that no major open problem will be solved by AI alone in the next decade. But AI could enable human-machine collaborations to solve problems that neither would have solved alone. This is probably the most measured and credible position available today.

Can AI really think "differently" from humans?

This question is at the heart of the matter. Current LLMs are trained on human data. So they fundamentally reproduce human structures of thought. How could they discover something non-human?

Three serious arguments suggest that it is possible, despite this initial limitation.

Argument 1: combinatorial exploration exceeds humans. A human can test dozens, perhaps hundreds of ideas in their lifetime. An AI can test billions in a few hours. Even if each individual idea is "human", the combination of millions of ideas can produce results that no human would have formulated. This is exactly what AlphaEvolve does: generate-test-select in an evolutionary loop.

Argument 2: human cognitive biases are absent. Humans tend to favour aesthetic hypotheses (symmetry, simplicity, elegance). This preference has produced great results (Einstein seeking beauty in equations), but it can also blind us to "ugly" yet correct solutions. An AI does not have this bias: it evaluates solutions on their correctness, not their elegance.

Argument 3: memory and long-term coherence. A human cannot hold in mind simultaneously all the mathematical proofs published in history. An AI can. This global memory allows it to spot connections invisible to a human brain limited by its biological capacities.

That said, genuine conceptual breakthroughs (the "scientific revolutions" in the sense of Thomas Kuhn, the American philosopher of science whose 1962 book popularised the concept of the scientific paradigm) remain a mystery. Einstein did not discover relativity through combinatorial exploration. He had a radical intuition that reorganised the entire conceptual framework. No one knows whether AI can do that. For now, it excels at optimising within existing frameworks, but not at inventing new conceptual frameworks. This is probably the last human fortress, and no one knows how long it will hold.

The fields where a breakthrough could occur

If we take on the game of serious foresight, here are the fields where a major AI discovery could redefine our knowledge over the next 10-20 years.

Theoretical computer science: the P vs NP problem. The P vs NP problem is one of the most important open mathematical questions: it concerns whether every problem whose solution can be verified quickly can also be solved quickly. A sufficiently powerful AI could resolve this question, with massive consequences for cryptography, optimisation and computer science.

The Riemann hypothesis. Stated in 1859 by the German mathematician Bernhard Riemann, it concerns the distribution of prime numbers (whole numbers divisible only by 1 and themselves). Its resolution would revolutionise number theory and probably several related branches.

Physical unification. Reconciling quantum mechanics and general relativity (Einstein's theory describing gravitation on an astronomical scale) has been the holy grail of physics for 100 years. Several teams now use AI to systematically explore alternative "string theories" (string theory proposes that elementary particles are not points but tiny vibrating "strings").

The origin of life. How did inert molecules give rise to biological life? AI simulating chemical evolution over geological timescales could shed light on this fundamental mystery.

Consciousness. As we explored in our article on AI consciousness, understanding what creates subjective experience remains a mystery. Paradoxically, AI itself could contribute to this question, by contrast: if we manage to create a system that behaves as if conscious without being so, we learn something about what consciousness is.

What this changes for you, today

This discussion may seem abstract. Three concrete implications for 2026.

First, the idea that "AI cannot really think, it only recombines" is now factually debatable. AlphaEvolve genuinely discovered an unknown algorithm. No human had made that discovery. Whether or not we call this "thinking", the objective result is there.

Second, research professions are being transformed. A mathematician, a physicist, a biologist in 2030 will probably be someone who collaborates daily with an AI to explore hypotheses. The skills that are valued will evolve: asking the right questions, verifying results, intuiting promising directions, rather than solving alone.

Third, our relationship to knowledge is changing. For 2,500 years, science was the exclusive product of human intelligence. For the first time, it is becoming a collaborative human-machine effort. This transition is as profound as the one that accompanied the invention of writing or printing. It is not measured in years but in generations.

Nobody knows how far AI can go in scientific discovery. But it has already done things that were thought impossible five years ago. To go further, you can read our article on the medicine of the future, which sets out the concrete applications in biology and longevity, and our analysis of the 30-year scenarios, which places these discoveries within a broader civilisational trajectory. If you have children born in 2025, they will probably grow up in a world where saying "AI discovered that" will be as commonplace as saying "Google found that for me" is today. And what that means for our identity as an intelligent species, we have not yet begun to think about seriously.