There is no final level in mathematics.
An AI can master chess or Go by finding an optimal strategy. Mathematics offers no such endpoint. There is always another problem, another theorem, another layer of complexity that nobody has yet solved.
That open-endedness is one reason Tudor Achim chose mathematics as the starting point for Harmonic, the AI research company he co-founded with Robinhood founder Vlad Tenev. Harmonic’s system, Aristotle, has since achieved gold-medal-level performance at the International Mathematical Olympiad, with its solutions formally verified.
For Tudor Achim, however, mathematics is not the destination. It is a testing ground.
He believes it offers an unusually demanding environment for teaching machines how to reason. A mathematical proof cannot rely on confidence or persuasion. It is either correct or it is not. That makes mathematics a useful place to explore whether AI can develop the capacity to tackle increasingly difficult problems while reliably checking its own work.
As AI moves from helping people write and search towards taking on more complex work, organisations will face a practical problem. When does an answer become reliable enough to act upon? When can a machine’s work be trusted in software, engineering, scientific research or other fields where a convincing mistake may still carry real consequences?
Achim is clear that more capable AI does not simply make human expertise redundant. In his view, as machines gain access to greater “reasoning firepower”, the human challenge may increasingly lie elsewhere: deciding which problems are worth solving, where to direct that capability and how to interpret what comes back.
That may prove to be the more important question behind Harmonic’s work. If AI can eventually explore problems beyond the limits of individual human expertise, intelligence itself becomes less of a bottleneck. The challenge becomes knowing what to ask it.
Before Harmonic, Tudor Achim co-founded Helm.ai, an autonomous-driving company. Earlier, his path took him through machine learning and computational biology, after an initial period of serious musical training.
