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María Jesús Esteban «In mathematics sometimes ancient themes are recovered»

He is a research mathematician at Paris-Dauphine University. He is now a visiting professor at the University of Leioa for a doctoral course. He is a columnist on the newspaper's scientific pages.

Guillermo Roa Zubia

• Mathematics •

«In mathematics sometimes old subjects are recovered»

He also works in the field of outreach and sometimes offers lectures to remember that mathematics is not exhausted science. Many times people have asked if you can do math research... of course. Mary Jesus also says that more and more are being done. Once a month, it gives us a column on these scientific pages on Tuesday. As he himself says, integrating in a single column all you want to write is a work of enormous synthesis.

Mathematics is not exhausted, but does it have exhausted branches?

You never know if an area is exhausted or not. Number theory is a good example. It was previously thought to be a very theoretical and abstract field. But today it is very important to develop coding systems, that is, to encode secret messages, languages, card numbers, etc. the theory of numbers is used. Recovering topics investigated long ago. When you do something you don't know if it will later be useful or not.

Is Fermat's theorem purely anecdotal?

The demonstration of Fermat's theorem has been a symbolic work. The truth is that I think it's not very important whether they've shown it or not, but a lot of work has been done and many new things have developed. Therefore, more important than the theorem itself has been the work of the environment.

Today the most striking areas within mathematics can be statistics and fractals, right?

Statistics are widely used, fractals are also important. But I don't think they are more important than other areas. What happens to fractals is that very beautiful images come out and it is fashionable. It has curious applications, but it is not more important than other areas, that is, there are people who work on it but no more than in other areas.

The basic algorithms used in computers are only mathematical, but on the other hand they are essential tools for computing computers. What is the relationship between computer science and mathematics?

Sometimes solutions to complex problems cannot be explicitly discovered. Therefore, we must look for approximate results. To achieve this, you have to write a close problem and the associated algorithm and enter it into the computer. Improve the algorithm and gradually get closer to the solution. Writing the algorithm and the approximate problem is math. It is present in the language, types of programming (parallel or vector), etc., used in computing. It is another area. The boundary between the two is very difficult. Theoretical computing and mathematics, at least in some things, are very close.

Do you work with computer?

Yes. We also work with physicists. The work is done in a group and everyone must do their own. Often the origin of the obstacle is the way of working. At first, for example, before I was afraid to talk to physicists, but then you see that they have gone with the same fear. The other is afraid not to understand the stranger. But if you are clear that working with them will be beneficial, you have to overcome fear. An effort must be made. For example, in my department there is a lot of work on image processing, and in that group there is a computer scientist who is not a mathematician. And the multimedia department of some universities is organized by mathematicians. There we also work with computer scientists.

In some banks more and more mathematicians and scientists are hired. Why?

In banks there has always been accounting, but there is really no new math. However, very complex products are now manufactured and their price must be measured. In the world of insurance, for example, we have to measure risk. These things are calculated by mathematical models. These models are very complex. Additionally, they need to find the results very quickly. Speed is very important. Count seconds. If others decide before you, you lose a lot. Therefore, there is work for us and for other scientists. On the other hand, keep in mind that not the whole economy can enter a model, but there are quite good models to describe some things.

Are they patented models?

It really hurts. ; only when they are quite public. At first they keep the secret well. The program used by a bank is not public. But there are well-known and public models and programs.

Therefore, the university mathematicians will have a lot of collaboration with the companies, right?

For example, more than half of my department's budget comes from contracts. We are involved in projects quite applied, but not all. And we don't just work applied. That is, our work has differences: on the one hand, a totally theoretical and fundamental work (demonstrating theorems, etc. ), and then, in many cases, we also take care of their applications. For example, the former director of my department, Pierre-Louis Lions, received five years ago the Fields medal (equivalent to the Nobel prize in mathematics) for his mathematical and theoretical works. Even so, apart from theoretical work, he is also very involved in applied fields and works in financial mathematics and fluid mechanics. Therefore, it does both and can be done.