He is getting closer to solving the equation that explains everything

It describes virtually everything we know.

The Earth we are standing on, the water in the sea, and the stars shining on us from the heavens at night.

The Schrödinger equation is one of the fundamental equations of quantum mechanics, and it describes pretty much everything from the atomic to the stellar level. And recently, the UCPH mathematics professor Søren Fournais got a staggering DKK 15 million from the European Research Council to solve it.

»There are huge things in the universe, galaxies and that kind of stuff, that it does not describe. But apart from that, it is involved in everything we know,« says the professor of mathematics when we meet him at the UCPH research centre QMATH.

With Søren Fournais in charge, a team of researchers, postdocs and PhD students will over the course of the next five years learn more about that part of the equation that deals with the so-called Bose-Einstein condensates, which deals with the cooling of atoms to a phase transition that is neither liquid, fixed, gas or plasma.

READ ALSO: Danish scientist gets huge five-year EU grant to understand quantum physics phenomenon

»The phase transitions are extremely exciting because we have a very large physical system, i.e. a system that consists of many atoms, but which is also significantly quantum mechanical. We only know quantum mechanics from small things – atoms, molecules, and so on – and suddenly we see a much larger physical system that also develops quantum effects,« he says, and continues:

»As a mathematician, I would like to study the equations and try to understand what mathematical tools we can develop to get a better description of these very peculiar physical systems.«

I think very few people know what mathematics actually is before they start at university.

Søren Fournais, Professor of Mathematics, UCPH

It does not work by simply ‘solving’ equations, says Søren Fournais. There are many equations that cannot be solved. But this does not mean that we cannot approach a solution, or study the path towards it.

»The Schrödinger equation is not just one equation, it covers a large system of thousands of equations – there is one for an atom, ten atoms, a billion atoms. And the ‘solution’ we have to find will not be a number, but a function that consists of hundreds of thousands of variables.«

Striking mathematical beauty

Unlike what most people might have learned in primary or secondary school, mathematics – especially mathematical research – can be more creative and abstract than logical, according to Søren Fournais.

»I think very few people know what mathematics actually is before they start at university. At school you learn that mathematics is all about finding a correct answer, but more often it may be more about asking the right questions.«

The researcher remembers how surprised he was when he started studying mathematics and physics at the university. A completely new world opened up for him – and luckily, it turned out that he really thrived in it.

»It was quite different from what I had expected. And I was pleasantly surprised, but it was actually a bit of a coincidence, because I had no prerequisites for knowing what it was I was getting into. That’s why I also have a great understanding for students who start on a study programme and perhaps quickly find out that they have chosen incorrectly.«

Hard mathematics is not for everyone, he admits. But those who see and understand its particular nature, find a beauty that can be difficult to convey to the uninitiated.

»It can seem very complicated and abstract. But sometimes you suddenly see it from the right angle, and a simplicity arises that lets you understand incredibly complex things about how the world is interconnected. And this is pretty fantastic,« says Søren Fournais.

Shower with a Gordian knot

However, it is not every day that the beauty breaks out of the shield of complexity in mathematics, according to the professor. He also explains how sometimes you feel trapped within knots that seem impossible to loosen.

»When you’re working on a mathematical problem for a very long time, as we’re going to be doing here at QMATH in the coming years, it will start sneaking into your thoughts all the time. It will pop up in the evening, just before you go to sleep, while taking a shower, when you take a walk, or when you have a conversation,« says Søren Fournais.

»But then, at some point or other, the many abstract objects will start to take shape inside your head. You will be able to see them separately, and manipulate them until they suddenly fall into place.«

This is rarely the case in the stories about the genius, like Newton, who is hit on the head by an apple and gets a brilliant idea, the researcher says.

»You will often solve small knots gradually, typically in conversations and in brainstorming with colleagues. It is therefore also extremely stimulating to be here at QMATH, where so many clever and talented minds are gathered together. I’m so very, very happy to be a part of it,« says Søren Fournais.

In connection with the large-scale research grant, he moved with his family from Aarhus to Copenhagen to become part of the UCPH Centre for Quantum Mechanics, which, according to him »is competing with the very best in the world.«

Expensive mysteries best solved with chalk

Mathematics can be both beautiful and abstract – but can it also be so expensive that it can cost DKK 15 million to solve an equation?

»Mathematics is actually a very inexpensive field of research, because we do not need labs or other expensive equipment. We mostly use our computers to write e-mails and manuscripts, because the actual work is mostly on these boards,« he says, pointing towards a whiteboard that is overwritten with digits and mathematical notation.

It will pop up in the evening, just before you have to sleep, while taking a shower, when you take a walk, or when you have a conversation

Søren Fournais, Professor of Mathematics, UCPH

»In fact, we would rather have had ordinary, old-fashioned blackboards with chalk, because it is much easier to work with. As it is now, we often end up getting smeared with marker ink when we stand here writing.«

Research funding is therefore almost almost exclusively spent on salaries for the many talented people who will be involved in the project in the coming years, he explains.

And all these mathematical complexities you are trying to solve… What can they actually be used for in the real world?

»I can’t answer. Our job is to learn and create tools that allow us to understand the mathematics of the world better,« he says, and pauses for reflection.

»And as a rule, it turns out to be useful when we understand the world a little bit better. But there will be some other researchers who might want to look at what the results can be used for. This is how all basic research works – we do not know exactly what we will find, but it is usually in this process that the most important research results emerge.«