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  • Jacob Bennett-Woolf

The Frontiers of Mathematics

Last week, mathematicians from all over the world gathered in Rio de Janeiro for the International Congress of Mathematics 2018. There were representatives from every mathematical field and country across the globe. People came for many reasons, however almost all were there to see what new research had been discovered in fields that they may not normally frequent. While there were many fascinating talks on extremely diverse areas, the most anticipated talks were those by the Fields medalists, and this year, they did not disappoint.

The Fields medal is one of the highest honours in mathematics, many think of it as the equivalent of a Nobel prize in other fields, and it can be awarded to any mathematician in any discipline, as long as the mathematician is under the age of 40. It is used to encourage rising stars to even more greatness and this year, the recipients truly were great.

However it must be remembered that even the recipients of the Fields medal are human, some have struggled to get where they are and all tackle their field with the determination that is required to be a mathematician. The thing that set the medalists apart this year was the humanity of their stories, from humble beginnings to obvious talent.

Although the mathematics that won the prizes was certainly complicated, the questions that were being answered didn't have to be. To showcase this, the website Quanta magazine ( ran an in depth profile into each Fields medalist. In the opinion of this author, these are some of the most illuminating descriptions of research mathematics.

There is Akshay Venkatesh, a man that finds the concept of genius to be discouraging, working all over mathematics.

There is Peter Scholze, an algebraic number theorist that makes sure that all can understand.

There is Caucher Birkar, coming from humble and painful origins to look at the geometry of algebra.

And finally, Alessio Figalli, attempting to figure out problems that began with the best way to transport objects, but had surprising implications for the rest of the world.

For those interested in the full details, all of the talks at the International Congress of Mathematics can be found here and all of the talks from the past Congresses can be found here.

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