# In Memory of an Extraordinary Mathematician

The world of mathematics is mourning the recent loss of Alexander Grothendieck, one of the most important mathematicians of the 20th century. Between 1950 and 1968, Grothendieck worked on the modern theory of algebraic geometry, publishing numerous articles. He later went on to expand his work into the elements of commutative algebra, homological algebra, cluster theory and category theory, bringing a new outlook into abstract mathematics and advancing the fields he worked in. Grothendieck’s most important achievement in algebraic geometry was his generalized proof of the Riemann-Rock-Hirzebruch Theorem. In 1966, he received the Fields Medal for his contributions to algebraic geometry, and later earned his doctorate degree for his work in topological vector spaces with Laurent Schwartz. As a student, Grothendieck was already on his way to become a bright mathematician, and the following anecdote with his doctorate thesis advisor is particularly illustrative of his talent: Schwartz, an accomplished mathematician at the peak of his career, having only just received the Fields medal,(the highest honor in mathematics, on par with the Nobel Prize) gave Grothendieck, a student without any apparent distinction, a paper with fourteen of the unsolved problems in mathematics, for him to take a look. Grothendieck solved the problems within just a few months.

After 1968, Grothendieck distanced himself from mathematics, taking an anti-war stance and engaging in social movements. Concluding his academic career in 1973, Grothendieck took retreat in a small town.

In 1977, Grothendieck was arrested for his political activities and sententenced to pay a heavy fine and a jail term of six months. His sentence was postponed, but Grothendieck turned down subsequent offers from many universities including the University of Montpellier. In 1991, he burned all his work on mathematics and abandoned the field, moving to a mountain village where he could only be contacted by mail. Several mathematicians tried to persuade him to resume his work in mathematics in the early 2000s, but Grothendieck persisted in his seclusion.

We shall never know exactly why the great genius left the field of mathematics, which he was so fond of, but his work in the short period in which he was active has been a great contribution.

*Notes…*

**Algebraic geometry: **As the name implies, this branch of mathematics brings the methods of abstract algebra (particularly, commutative algebra) together with the language and problems of geometry. Algebraic geometry plays a central role in contemporary mathematics, and is closely related to other branches of the field such as complex analysis, topology, number theory.

**Fields Medal:** The Fields Medal is regarded as the Nobel Prize of mathematics. The medal is awarded by the International Mathematical Union in its International congress held every four years, to mathematicians under the age of 40. Canadian mathematician John Charles Fields was instrumental in awarding the first medal in 1936, and after 1950, the Medal was awarded every four years. Widely regarded as the highest honor in mathematics, the Fields Medal aims to ensure the recognition and support of young mathematicians who have made internationally significant publications.