Mark Hamilton, the periodic table of machine learning and a bet on mathematics
On May 20, at AI Week in Milan, I interviewed Mark Hamilton after his speech. Hamilton works between MIT and Google DeepMind and I asked him just one question: setting aside the language models and agents that everyone is already talking about, what is the currently underrated scientific field where AI will produce the next AlphaFold? He answered mathematics. To understand where someone who thinks this way comes from, it's worth starting from the talk he had just given.
The public debate on AI has, for months, revolved around two objects: the chatbot that answers better than the competitor's and the agent that should book your flight without causing disasters. Hamilton's talk went in an entirely different direction, closing with an image that at first glance seemed almost like a joke: a periodic table. Not Mendeleev's table hung in chemistry classrooms, but a version built for machine learning algorithms, that is, for the methods by which a program learns to recognize patterns in data instead of following handwritten instructions.
A grid for algorithms
The idea in the paper is called I-Con. It starts from two families of algorithms that anyone studying machine learning learns as separate entities. The first is clustering. You give a machine a pile of photos without telling it anything, and it groups them: cats near cats, cars near cars. No one explained to it what a cat is; it simply saw similarities and traced boundaries on its own.
The second is contrastive learning. Here the model learns by looking at pairs of examples and adjusting accordingly: when two things are of the same type, it treats them as close; when they are different, it keeps them apart. By "treating them as close" I mean something specific because a model does not work on images but on their representation, which is a list of numbers summarizing their essential traits. Two similar photos end up with similar lists of numbers. This is the mechanism that underlies much of today's systems that recognize images and language.
For years we treated clustering and contrastive learning as distinct tools, and Hamilton and his colleagues showed that they can be rewritten as special cases of the same equation. From there, the idea grew. In the paper, presented at ICLR 2025, one of the industry's most important conferences, more than twenty classic algorithms are included, covering a century of research, from old spam recognition programs to deep learning that powers language models. Arranged in a grid according to the type of signal they use to learn and the type of representation they produce, some boxes remain empty, just as in Mendeleev's periodic table, where empty boxes indicated undiscovered elements. Hamilton mentioned that one of those boxes, filled by combining clustering and contrastive learning, produced a new algorithm that classifies unlabeled images about eight percentage points better than the best methods available.
In the talk, there were two examples of what can be done with this kind of algorithms. One discovers objects within images on its own and manages to classify every single pixel of a dataset without a human ever labeling them. The other does something similar with language, identifying words and trying to reconstruct what they mean, and Hamilton is applying it even to dolphins' vocalizations to see if there is something resembling a vocabulary in those sounds.
A detail says a lot about how research works. Hamilton made sure to clarify that the real mind behind the periodic table is not him, but Shaden Alshammari, who built the theoretical framework during her master's thesis, writing something like fifteen proofs to hold all the pieces together. He said this from the stage, introducing the colleague who spoke immediately after as "two orders of magnitude smarter" than him. One can debate how much this was a mere modesty, but the substance remains.
The metaphor of the periodic table works very well to explain things to an audience; I am even using it right now. However, it is worth remembering that it is a metaphor. Mendeleev's table predicted measurable physical properties of elements that were later found in nature. Here we face a very elegant taxonomy that organizes something that humans have built, helping to imagine new combinations because it shows us the empty spaces. That alone is enough to justify it, without needing to promote it to a law of nature.
The question about AlphaFold
The question I had prepared came from AlphaFold. AlphaFold is the DeepMind system that learned to predict how a protein folds, that is, what three-dimensional shape it takes from its chemical sequence. It is a significant problem because a protein's shape determines its function, and biology had been stalled on this for decades: in 2024, that result earned a Nobel Prize in Chemistry for Demis Hassabis and John Jumper. I asked him: five years ago, no one would have bet on that Nobel, and looking at the next five or ten years, what is the currently underrated field where AI will have a comparable impact?
His response was that field is mathematics, and his reasoning has its logic. Mathematics is a kind of frontier of the human mind, the place where the most difficult ideas are born, which then filter into all other fields. Language models are becoming capable not only of doing mathematics (though mathematicians themselves might not particularly agree...), but also proving the results they produce, that is, constructing the chain of logical steps that certifies that a conclusion is true. And here lies the difference that Hamilton believes matters more. In experimental sciences, to validate an idea you need to go to the laboratory, which is a slow and costly process; in mathematics, once a proof is correct, it is closed, and you can move on to the next problem. It is a domain where AI encounters few of the limits of the physical world and remains mostly constrained by its capacity to reason. If the rate of improvement remains what it has been in recent years, Hamilton says, it is reasonable to expect that long-stuck concepts will be proven.
Some numbers: in 2024, DeepMind's systems dedicated to mathematics, AlphaProof and AlphaGeometry, had solved four problems out of six at the International Mathematical Olympiad, the level of a silver medal. In particular, AlphaProof works within Lean, a formal language where every step of a proof can be verified by the machine. This is a significant detail because it reduces space for hallucinations, that is, those confident yet incorrect answers produced by an AI system. In 2025, a version of Gemini solved five out of six problems with a gold medal score, reasoning directly in natural language. However, it is advisable not to get overly excited because some of those problems were solved in quite brute-force ways, through sheer computation, and it remains open whether they genuinely possess what we call mathematical intuition or if they are bypassing it.
I asked him if he saw other fields besides mathematics, and here he was more cautious, stating he was not an expert on AlphaFold. His point was that AlphaFold is just the first step because understanding protein structure paves the way for targeted drugs and other important molecules, and the group working on it continues with proteomics and genomics, that is, the systematic study of proteins and genetic heritage, with the declared goal of impacting human health. Nothing as spectacular as a prediction, but the honest response from someone who prefers not to shoot for sensational headlines.
What I take home
There is a thread connecting the talk and the interview, and it involves us more than it seems. In one of the accompanying interviews to the paper, Alshammari said that we are starting to see machine learning as a structured system, a space to explore rather than a ground to guess. For researchers, this is a significant shift in posture, as inventing a new algorithm stops being a stroke of luck and becomes something that can be searched for by looking at the empty boxes.
What remains to be understood is what all this means for those engaged in research as a profession. On the one hand, it is good news because a tool that shows where to look saves years of trial and error. On the other hand, the discovery we are talking about still emerged from a master's thesis, from someone who took the time to write fifteen proofs by hand to make sense of it all. The periodic table of machine learning was not discovered by a machine sifting through the algorithm space, but by someone who had the intuition to take two seemingly distant things and wonder if they might not be the same. For now, the interesting part of the work, that in which you decide which question is worth asking, remains firmly ours. May as well enjoy it while it lasts, and in the meantime, learn to use the tools that continue to arrive properly.