Who is Giancarlo Rota?

Who is Giancarlo Rota?

Gian-Carlo Rota — American Mathematician 

May 8, 2022 

Early life 

Gian-Carlo Rota Italian-born American mathematician and philosopher was best known for his work in combinatorics. Combinatorial mathematics, the field of mathematics concerned with problems of selection, arrangement, and operation within a finite or discrete system. [1] The significance of Rota’s work brought the uncertain field of combinatorics into prominence as a studying goal. Rota started with functional analysis and research, but his professional interests later turned to combinatorics and became an outstanding combinator. 

Rota also writes popular books [2] as the faculty of Massachusetts Institute of Technology. Furthermore, Rota studied at Princeton University and Yale University. But he spent most of his life at MIT and he was the first MIT’s professor of applied mathematics and philosophy in 1972. 

Rota conjecture 

At the Sixteenth International Congress of Mathematicians held in Nice, France in 1970, Rota proposed the famous Rota’s Conjecture. The proposition can be summarized as: For each finite field, there is a set of finite obstacles to prevent such realization. Rota’s conjecture is also called the finite forbidden array conjecture; it has received considerable attention and research in the field of discrete mathematics for more than 40 years.

Rota’s conjecture is related to matroid theory (a modern mode of geometry) in the field of mathematics. Matroid theory explores a geometric structure completely different from the world in which we live; the structure does not change under projection, rather than focusing on distance and angle.

For example, are three points always on a straight line, and whether four points are always on a plane. Rota’s conjecture is a way of using mathematics to understand these alternative structures. 

A research team composed of Jeff Whittle, a mathematician from the University of Victoria in New Zealand, Jim Gillen, a mathematician from the University of Waterloo in Canada, and Bert Geralds, a mathematician from Maastricht University in the Netherlands, recently announced that they passed After 15 years of hard work, I finally found all the necessary evidence to prove the famous Rota guess. This news shocked the mathematics community. Although Whittle and others have spent a long time working to verify Rota’s guess, other hard work has only really begun now, because they have to start writing the results of their work. They predict that it will take at least three years to complete the writing task. Only in this way can it be verified by other mathematicians. 

Mathematician Gian-Carlo Rota in Nizza.
Konrad Jacobs – Oberwolfach photo collection Who is Giancarlo Rota?

Regarding their proof of Rota’s guess, Chinese mathematician and linguist Zhou Haizhong believes that if the proof is confirmed, it will be a great achievement; the methods and ideas they use will also become the solution to graph theory, A powerful tool for problems such as matroid theory, combinatorial theory, and optimization. 

Written by Hong Cao 

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References 

[1] Branko Gr¨unbaum. “Combinatorics”. In: Convex Polytopes (Aug 14, 2013). doi: http : / / https://www.britannica.com/science/combinatorics. [2] Gian-Carlo Rota. Discrete Thoughts. 1986.

Who is Giancarlo Rota?