Maurício Peixoto

Maurício Matos Peixoto, (April 15, 1921, in Fortaleza, Ceará – April 28, 2019, in Rio de Janeiro),^[1][2] was a Brazilian engineer and mathematician. He pioneered the studies on structural stability, and was the author of Peixoto's theorem.

Biography

Once, while talking with his mentor, Solomon Lefschetz, Maurício Peixoto commented that no one cared about structural stability of dynamical systems and that was the main problem in working with it. But to Peixoto's surprise Lefschetz's answer was no less than "No Mauricio, this is no trouble, this is your luck. Try to work as hard and as fast as you can on this subject because the day will come when you will not understand a single word of what they will be saying about structural stability; this happened to me in topology." Lefschetz's support was very important to Peixoto at the time. In 1957, Peixoto went to research the subject with Lefschetz at the Princeton University, where he spent uncountable hours talking to the Russian professor about Mathematics and other subjects. Despite of the great age difference (Peixoto was 36 years old and Lefschetz 73), they became good friends.

With Lefschetz incentive, Peixoto wrote his first paper on structural stability, that would be later published on the Annals of Mathematics, of which Lefschetz was editor. In 1958, they went to the International Mathematical Congress, in Edinburgh, Scotland, where Lefschetz introduced Peixoto to the Russian mathematician Lev Pontryagin, whose work on dynamical systems was used by Peixoto as a basis for his studies. Pontryagin, though, showed no interest whatsoever in Peixoto's work.

Back to Princeton, Peixoto met Steve Smale, the mathematician that would later become a reference in dynamical systems. Smale was interested in Peixoto's work and realized he could extend his own based on it. Their contact intensified and, when Peixoto came back to Brazil, the American mathematician spent six months at the Instituto Nacional de Matemática Pura e Aplicada (Institute of Pure and Applied Mathematics or IMPA) at Rio de Janeiro. Through Smale, Peixoto would meet the French mathematician René Thom, who would help Peixoto to formulate his theorem, that was finalized during Thom's visit to IMPA.

Awards

For his theorem, Peixoto won the Bunge Foundation Award in the year of 1969. According to Bunge Foundation, "the theorem of Peixoto on the structural stability in two-dimensional varieties inspired the mathematician S. Smale to create the general theory of dynamic systems".

In 1986, Peixoto was awarded the TWAS Prize by the Third World Science Academy, "for his fundamental and pioneer studies on structural stability in dynamical systems, in particular for proving that surface flows are generically structurally stable."^[3]

Personal life

Peixoto married engineer and mathematician Marília Magalhães Chaves (who was known professionally by her married name) Marília Chaves Peixoto in 1946, with whom he had two children, Marta and Ricardo.^[4][5] The couple collaborated in their work, jointly published "Structural Stability in the plane with enlarged boundary conditions" in 1959,^[6] before Marília Chaves Peixoto's early death in 1961. It would be a key paper which led to the development of Peixoto's theorem.^[7]

References

1. "FALECEU O ACADÊMICO MAURÍCIO MATOS PEIXOTO". Brazilian Academy of Sciences (Press release) (in Portuguese). 28 April 2019. Retrieved 2019-04-28.^{[permanent dead link]}
2. "Morre o matemático Maurício Peixoto, um dos fundadores do Impa" (in Portuguese). Folhapress. 28 April 2019. Retrieved 2019-04-28.
3. "Prizes and Awards". The World Academy of Sciences. 2016.
4. "Marília Chaves Peixoto, pioneer of science in Brazil". Vermelho. 1 May 2016. Retrieved 30 August 2018.
5. "Marília Chaves Peixoto, pioneira da ciência no Brasil". Vermelho (in Brazilian Portuguese). 2016-01-04. Retrieved 2021-03-07.
6. Silva, Circe Mary da. "Politécnicos ou matemáticos?". História, Ciências, Saúde-Manguinhos (in Portuguese). 13 (4): 891–908. doi:10.1590/S0104-59702006000400007. ISSN 0104-5970.
7. Pujals, Enrique R. (2011), Peixoto, Mauricio Matos; Pinto, Alberto Adrego; Rand, David A. (eds.), "From Peixoto's Theorem to Palis's Conjecture", Dynamics, Games and Science I: DYNA 2008, in Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8–12, 2008, Springer Proceedings in Mathematics, Berlin, Heidelberg: Springer, pp. 743–746, doi:10.1007/978-3-642-11456-4_47, ISBN 978-3-642-11456-4, retrieved 2021-03-07

• Bunge Foundation. "Awarded: Maurício Matos Peixoto". Retrieved 5 August 2012.

• TWAS. . Archived from the original on 18 October 2012. Retrieved 5 August 2012.