# In search of the atoms of mathematics

Combining geometry and number theory. That is what Dr Jan Vonk of the Institute of Mathematics receives a Vidi grant for today. ‘By fusing these two disciplines we may be able to solve a century-old mathematical problem.’

The research of Jan Vonk, assistant professor at the Mathematisch Instituut, mainly focuses on number theory. ‘We study the underlying structures of mathematics,' he explains. ‘How, for instance, do prime and rational numbers work exactly? We try to solve deep mathematical problems.'

‘Solving Hilbert's problem mainly serves as motivation'

### The top 23 mathematical problems

Some of those unsolved problems are very old. The problem that Vonk is going to study, dates back to the last century. ‘In 1900 mathematician David Hilbert made a list of the 23 most important mathematical problems’, Vonk explains. ‘It is the twelfth problem on his list that I am going to focus on.’

### The atoms of mathematics

Hilbert's twelfth problem is about the building blocks of all numbers. ‘And I am not talking about prime numbers (the numbers that form the basis of all other possible numbers, ed.)', Vonk continues, 'but about the so-called singular moduli. These singular moduli would be, among other things, the building blocks for all number bodies. A kind of atoms of mathematics."’

### A fusion of fields

It is these atoms that must be mapped to solve Hilbert's problem. Vonk will try to do so by applying his earlier experience in geometry to number theory. ‘By connecting these two disciplines, a new method could emerge that would finally allow us to solve Hilbert's problem.’

### Connecting disciplines as the ultimate goal

And to Vonk, that is just the beginning. As far as he is concerned, building bridges between different disciplines can solve even more problems of this kind. ‘Solving Hilbert's problem mainly serves as motivation. Connecting the two disciplines is actually the ultimate goal. The proof that you can approach problems from one mathematical discipline with techniques and insights from the other.’