# What is category theory and how it has become a trend | Science

Recently, a branch of mathematics called category theory has captured the attention of various scientific means after gaining quite popularity within the mathematical community in recent years. The situation has reached the point where some mathematicians are complaining on Twitter that there are researchers who *tweet* more about category theory than about their own specialties. But what is this branch of mathematics and why is it so fashionable?

Some people call the category theory "The mathematics of mathematics", since it is situated above many mathematical disciplines, connecting them. It was proposed in 1945 as a tool to move mathematical problems from one field to another, in which they could be solved more easily. For example, we know that at any time there must be a point on the surface of the Earth where the wind speed is zero. But to demonstrate this precious result we must translate it into an algebraic statement, for which it is useful to use a pinch of category theory. Usually, more complex results require more category theory. The proof of Fermat's last theorem, for example, is based on a large number of mathematics of the s. XX and category theory also played its role there.

Unfortunately, this high level of abstraction exceeded even the degree of tolerance of mathematicians themselves and, for years, many of them have considered this theory as an "abstract nonsense" and have limited themselves to using it when it was totally necessary for their work. However, others did accept with open arms the beauty and power of this discipline, which made its influence gradually spread not only in mathematics, but also in other sciences. Starting in the 1990s, he began to infiltrate computer science: new programming languages such as Haskell and Scla, for example, used ideas of category theory. Currently new applications of this theory appear to chemistry, electrical engineering or even to design car brakes! The applied category theory, which once had been considered an oxymoron, is becoming a real research topic.

A category consists of a class of *objects* next to a class of *morphisms* –A kind of processes, or paths– on those objects

a program is also a way to transform a series of input data into output data and the simplest way to build complicated programs is to compose simpler programs

Translation: **Agate A. Timon G-Longoria**

** Coffee and theorems** It is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social and cultural expressions and remember those who marked their development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: "A mathematician is a machine that transforms coffee into theorems."

Editing and coordination: **Agate Timon** (ICMAT).

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