# “How high is a 100-year wave around an oil rig in the North Sea?”

Meet the magician Talagrand, winner of the Abel 2024 Prize.

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French mathematician Michel Talagrand He won this year's Abel Prize. His brilliant mathematical understanding of random phenomena made probability calculations in a number of important fields possible.

How high is a 100-year wave around an oil rig in the North Sea? How powerful are wind turbines in a 50-year perspective?

The phenomena appear random and cannot be precisely calculated. But when designing platforms and wind turbines, engineers also need to be able to estimate how intense the waves and winds are.

With climate change, the weather is becoming more brutal and unpredictable. Therefore, this becomes increasingly important. This year's Abel Prize winner has contributed significantly to understanding the mathematical basis of these questions.

## Who is Talagrande?

Talagrande was born in 1952. He spent most of his career in Paris, where he worked for the large research organization Center National de la Recherche Scientifique (CNRS). In 2017, he retired from his position as Director of Research. Since 2004, he has been a member of the prestigious French Academy of Sciences, and in 2011 he was awarded the French Legion of Honor.

Due to a hereditary disease, he lost the sight in one eye when he was five years old. When, ten years later, he was in danger of losing his other sight as well, he had to stay home from school for six months. It was a historic event. His father, who was also a mathematician, gave him assignments in mathematics and physics.

Here Michel's interest and talent in the subject became clear.

Talagrande's method is to simplify the problem as much as possible, and then study it there. Finally, it can make the problem more general, for example, by changing the assumptions and transferring them to other situations.

Taking such basic action is not easy. Talagrande said he worked for 15 years to understand The important concept of “general sequence”. Now he's made it so simple that you can understand it in ten minutes!

When Talagrande builds his theory the way he wants, he writes a study of it. These books had a great influence on mathematics.

## Coincidence mathematics

Mathematics is an exact science where nothing is left to chance. That mathematics is the best tool we have for understanding coincidences is perhaps paradoxical.

It cannot predict the outcome of rolling the dice or dealing the cards in a bridge hand. But it can describe how likely an outcome is, and which distributions are most likely. In this way, it provides the best estimates we can get of, for example, extreme waves.

This can be done using historical data and computer simulations of wave heights. But simulations require access to complete information about the coast, winds, temperature, tides, and ocean currents—information we don't have. Hence, we have to resort to probability calculations.

Consider the coin flip analogy: We don't know the outcome of the coin flip, but we include in the model that both outcomes are equally likely. As coins are tossed successively, it suddenly becomes difficult to predict what will happen. As for ocean waves, the problem is more complex. We then have to figure out how heavy all these coincidences are against each other, and how big the waves can get over a long period of time. Tough problem!

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Randomness of variation in wave height creates a series of wave heights Random processThat is: something that occurs randomly, but with a known distribution. Talagrande studied the greater value that a random process can have. The problem is that this cannot be calculated precisely, but Talagrande is adept at making estimates.

Making such estimates is an art. You're sitting down with a calculation that you can't find the answer to, so you change it until you arrive at a calculation that you can actually calculate the answer to. It takes great vision to know exactly what needs to change for the estimate to be accurate. Here Talagrande is charming.

## Athletic feats

Talagrande has also worked in an area known as “goal concentration.”

If you have a lottery where 1,000 tickets are sold, each for one kroner, and the winnings are one thousand kroner, the average value of one ticket is one kroner. But the most likely value is zero kroner. The potential value is more interesting but also more difficult to study than the average value. Talagrande has calculated this quite generally.

Talagrande is also known for calculations related to a phenomenon in physics called “glass rotation.”

Although we can see directly through window glass, it has an unusual and interesting microscopic structure. While most materials organize themselves upon cooling, glass behaves very differently. The microscopic structure remains chaotic. Spin glasses are materials in which the electron spin, the internal spin of the electron, is arbitrary and chaotic.

An example of this is the substance obtained by soiling cups with iron. Iron atoms have internal spin and magnetic moments, and the organization between them can be chaotic. If you then expose the copper to an external magnetic field, the iron atoms will be oriented in the same direction. They get the same “spin” and the copper becomes magnetic. When the external magnetic field is removed, copper slowly loses its magnetism.

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To understand why this happens, in 1980 the Italian physicist Gheorghe Parisi developed what is now called the Parisi energy formula, which in 2021 secured him the Nobel Prize in Physics.

Talagrande's achievement is that in 2004 Prove Parisian's formula mathematically. In Parisi's words: “Now we know the formula is correct!”

## Pass the award

Problems that Talagrande finds interesting, but is unable to solve himself, he posts on his website. Under the tab “Be rich in my rewards”, “Get rich with my prices”, offers cash prizes to those who solve the tasks. Not many people can afford the challenges, but a \$5,000 problem has been solved.

In 2019, Talagrande received Prestigious Shaw Award Worth \$1.2 million. Then he decided to use the entire prize amount Create the foundation Which awarded prizes in the areas of mathematics in which he was interested.

Now he has also decided to give the entire prize money of the Abel Prize – NOK 7.5 million – to the same foundation. Working within Talagrande's areas of interest may be lucrative, but it's not easy money.

### Dalila Awolowo

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