In the deeply intertwined worlds of mathematics and physics

When Marcel Vonk talks about his work as a mathematical physicist, he is often told that people found mathematics so difficult at school. Books about physics therefore often contain as few formulas, graphs and other mathematics as possible, so as not to frighten readers. Understandable, but also a pity. Mathematics is an indispensable tool in physics.

In his earlier books on string theory and black holes, Vonk did not shy away from mathematics. But in From number to universe mathematics plays a major role. In such a way that the content can be followed with some secondary school knowledge of the subject.

The fact that you can describe physics with mathematics is amazing. Why should nature obey mathematical laws? To that fundamental question From number to universe no answer, but it does show how closely the disciplines have been intertwined for centuries.

Imaginary numbers

The book begins with seemingly simple math: counting. But within a few pages that leads to quantum physics, where light particles are packets of energy that you can describe with discrete, countable numbers. And the math of imaginary numbers (roots of negative numbers) comes into play when quantum particles behave like waves.

With clear explanations, Vonk takes you further and further into mathematics, along four- or more-dimensional spaces and topology, the mathematics of shapes, in which donuts and coffee cups can no longer be distinguished from each other (after all, both have one hole). He shows how mathematics comes in handy in describing the universe and in string theory, where there are no particles, only small vibrating strings that can move in 10 or 26 dimensions.

There’s even an application for mathematical knots, which you can think of as a piece of string with ends tied together that tangles with itself. Knot theory appears to be able to tell something about the quantum mechanics of particles. And even more surprising: in 1989 a physicist with that quantum knowledge helped advance the mathematical theory of knots.

Into the depths

The book is not an easy read. Vonk regularly dives into the depths. Prior to spicy parts, he emphasizes that those parts can also be read quickly. That sometimes feels a bit patronizing.

But even the interested reader sometimes needs a breather. They offer light-hearted anecdotes. Vonk, a fanatical poker player himself, writes that he feels a bond with the 16th-century Italian Gerolamo Cardano, who supplemented his meager income as a scientist by earning money with chess and gambling games.

From number to universe is an intensive journey through an abstract world, pleasantly led by a tour guide who provides clear and interesting explanations of the sights: infinities, curved spacetime, mathematical knots, string theory and five-dimensional spherical shells.