Maurício Peixoto

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Maurício Peixoto
Born(1921-04-15)15 April 1921
Fortaleza, Ceará, Brazil
Died28 April 2019(2019-04-28) (aged 98)
Rio de Janeiro, Brazil
EducationUniversidade Federal do Rio de Janeiro
Known forPeixoto's theorem
Scientific career
FieldsMathematics
Institutions
Doctoral studentsJorge Sotomayor Tello

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

Biography[edit]

Maurício Peixoto, born in Fortaleza in 1921 to José Carlos de Matos Peixoto and Violeta Rodrigues Peixoto, pursued a career in mathematics since his adolescence. To fulfill his goal, Peixoto enrolled in engineering at the School of Engineering of the current Federal University of Rio de Janeiro (UFRJ).[2]

While still working at the School of Engineering around 1955, Peixoto came into contact with the work of De Baggis, a student of Solomon Lefschetz. Through this work, he learnt about the problem of structural stability of dynamical systems.[3] After some correspondence with Solomon Lefschetz regarding this problem, Peixoto was invited and went to Princeton University in 1957 to work as Lefschetz's student on the topic of structural stability of differential equations.[2] Despite of the great age difference (Peixoto was 36 years old and Lefschetz was 73 years old), Peixoto and Lefschetz became good friends.[4]

Once, while talking with Lefschetz, 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."[4]

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.[4]

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.[4]

Awards[edit]

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".[5]

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."[6]

Personal life[edit]

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.[7] The couple collaborated in their work, jointly published "Structural Stability in the plane with enlarged boundary conditions" in 1959,[8] before Marília Chaves Peixoto's early death in 1961. It would be a key paper which led to the development of Peixoto's theorem.[9]

References[edit]

  1. ^ "Morre o matemático Maurício Peixoto, um dos fundadores do Impa" (in Portuguese). Folhapress. 28 April 2019. Retrieved 2019-04-28.
  2. ^ a b Freire, Dianara Figueirêdo; Queiroz, Antonio José Melo De (2020). "AS CONTRIBUIÇÕES DE MAURÍCIO PEIXOTO PARA A MATEMÁTICA BRASILEIRA". Boletim Cearense de Educação e História da Matemática (in Portuguese). 7 (20): 57–66. doi:10.30938/bocehm.v7i20.2854. ISSN 2447-8504. S2CID 225551989. Retrieved 2022-05-18.
  3. ^ Tatiana Roque (2007). "De Andronov a Peixoto: A Noção de Estabilidade Estrutural e as Primeiras Motivações da Escola Brasileira de Sistemas Dinâmicos". Revista Brasileira de História da Matemática (in Portuguese). 7 (14). UFRJ - Brasil: Sociedade Brasileira de História da Matemática: 233–246. ISSN 1519-955X.
  4. ^ a b c d Sotomayor, Jorge; Garcia, Ronaldo; Mello, Luis (2020). "Maurício Matos Peixoto". Revista Matemática Universitária (in Portuguese). 1 (1). doi:10.21711/26755254/rmu202013. ISSN 2675-5254. S2CID 226539649.
  5. ^ Bunge Foundation. "Awarded: Maurício Matos Peixoto". Archived from the original on 9 February 2016. Retrieved 5 August 2012.
  6. ^ TWAS. "Recipients of TWAS Awards/Prizes: 1986 TWAS Award Winners". Archived from the original on 18 October 2012. Retrieved 5 August 2012.
  7. ^ "Marília Chaves Peixoto, pioneira da ciência no Brasil". Vermelho (in Brazilian Portuguese). 2016-01-04. Retrieved 2021-03-07.
  8. ^ Silva, Circe Mary da (2006). "Politécnicos ou matemáticos?". História, Ciências, Saúde-Manguinhos (in Portuguese). 13 (4): 891–908. doi:10.1590/S0104-59702006000400007. ISSN 0104-5970. PMID 17533730.
  9. ^ 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, vol. 1, 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
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