{"id":314438,"date":"2019-12-09T16:58:16","date_gmt":"2019-12-09T19:58:16","guid":{"rendered":"https:\/\/revistapesquisa.fapesp.br\/?p=314438"},"modified":"2019-12-09T16:58:52","modified_gmt":"2019-12-09T19:58:52","slug":"a-devout-mathematician","status":"publish","type":"post","link":"https:\/\/revistapesquisa.fapesp.br\/en\/a-devout-mathematician\/","title":{"rendered":"A devout mathematician"},"content":{"rendered":"

Maur\u00edcio Matos Peixoto, a pioneer among the first generation of professional mathematicians in Brazil, is also known for his role in cofounding the Institute for Pure and Applied Mathematics (IMPA) in the 1950s. IMPA was the first research unit to be created by the Brazilian National Council for Scientific and Technological Development (CNPq), of which Peixoto served as president from 1979 to 1980. He also headed the Brazilian Academy of Science (ABC) from 1981 to 1991. Born in Fortaleza, Cear\u00e1, northeastern Brazil, Peixoto died in Rio de Janeiro on April 28, at the age of 98.<\/p>\n

\u201cHe regarded mathematics almost as a holy calling, to which he was utterly devoted,\u201d says mathematician Marcelo Viana, director general at IMPA. In 2010, Viana offered to compile and publish a selection of articles authored by Peixoto who, at the age of 89, was then an emeritus professor at the institute. \u201cAfter avoiding the subject for a while, he finally asked me whether I could wait a year or two as he was working on a paper that would be the crowning work of his oeuvre. He seemed immune to time.\u201d<\/p>\n

Peixoto\u2019s skills in mathematics were initially shown to be sorely lacking when he failed the subject in the second grade of high school at Col\u00e9gio Pedro II, in Rio de Janeiro. But his after-school tutor\u2019s enthusiasm about math caught on with him as well. His grades soon improved and after he passed the year-end examination, he became determined to pursue a career involving mathematics.<\/p>\n

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L\u00e9o Ramos Chaves<\/span><\/a> The IMPA, in Rio, was founded in 1952 as the brainchild of L\u00e9lio Gama, Leopoldo Nachbin, and PeixotoL\u00e9o Ramos Chaves<\/span><\/p><\/div>\n

Because higher education programs in mathematics proper were then in short supply\u2014the first was created in 1934 at the then recently created University of S\u00e3o Paulo (USP)\u2014Peixoto decided to attend the School of Engineering at the then University of Brazil, now the Federal University of Rio de Janeiro. He graduated in 1942 and completed his doctorate in 1945. Although he successfully registered as a chartered engineer, he chose not to pursue a career in the field. Instead, he lectured in mathematics until in 1947 he was hired to a position at the School of Engineering.<\/p>\n

He also lectured in the US on three different occasions, as a visiting professor at the University of Chicago (1949\u20131951), Princeton (1957\u20131958), and Brown University (1964\u20131970). He subsequently taught at USP\u2019s Institute for Mathematics and Statistics (IME) (1973\u20131978). When he returned from his first spell in the US, in 1952, he and two former faculty colleagues, Leopoldo Nachbin (1922\u20131993) and L\u00e9lio Gama (1892\u20131981), developed a proposal to create the IMPA.<\/p>\n

Peixoto specialized in geometry and topology, a branch of mathematics concerned with the spatial properties of geometric objects that are preserved through continuous deformations. \u201cAlthough he was a pure mathematician, he always had a way of translating the concepts he was teaching into geometrical figures,\u201d recalls mathematician Pedro Leite da Silva Dias, head of the Institute for Astronomy, Geophysics, and Atmospheric Sciences (IAG-USP).<\/p>\n

As a researcher at IMPA, he developed a theorem later named after him which he described in papers published in 1959, 1962, and 1963. His theorem revived the concept of structural stability in dynamical systems proposed in 1937 by Soviet physicist Aleksandr Aleksandrovich Andronov (1901\u20131952) and his fellow countryman, the mathematician Lev Pontryagin (1908\u20131988). Systems\u2014or phenomena involving objects in causal interaction\u2014are said to be dynamical if they have states that change over time according to a mathematical law. A dynamical system is said to be structurally stable if a slight alteration in the law governing state change over time will not affect its topological properties. Peixoto\u2019s Theorem establishes mathematical conditions necessary and sufficient for a specific type of dynamical system, known as a two-dimensional autonomous dynamical system, to be structurally stable.<\/p>\n

Although his training was in engineering, Peixoto chose to teach mathematics<\/p><\/blockquote>\n

Tiago Carvalho, a mathematician in the Department of Computing and Mathematics at USP Ribeir\u00e3o Preto, says the theorem is useful in understanding phenomena such as the dynamics of machines, chemical reactions, predator-and-prey relationships, or the evolution of disease. \u201cThis was the first high-level theorem in the field of dynamical systems,\u201d says Viana. Peixoto\u2019s work is also historically significant in that it strengthened interaction with mathematicians at the University of Chicago and the University of California (UC) in Berkeley, leading them to expand collaboration in this field and extend invitations to young Brazilian researchers, such as Jacob Palis, who pursued his doctoral studies at UC (1967) and, years later, served as president of IMPA (1993\u20132003) and ABC (2007\u20132016).<\/p>\n

Peixoto was a friend of Candido Lima da Silva Dias, a professor at IME-USP and the father of Pedro Dias. \u201cThey often talked into the wee hours of the night, discussing politics and mathematics. I learned from them the importance of people putting aside their differences in pursuit of broader goals,\u201d he says.<\/p>\n

Toward the end of 2007, when he took a position as director at the National Laboratory of Scientific Computing (LNCC), Pedro Dias paid a visit to the rural school that Peixoto then ran in Petr\u00f3polis, a hillside town near Rio\u2014the institute had extended support to the school under the previous director. \u201cI remember the sparkle in Maur\u00edcio\u2019s eyes as he showed me around and talked about the local \u2018farm kids,\u2019 as he called his students,\u201d says Dias. LNCC continued to provide support, including technicians to install or repair equipment and computer networks at the school, which Peixoto had inherited from his first wife, Mar\u00edlia Chaves (1921\u20131961), who was also an engineer and mathematician, and the first female student to attend ABC, in 1951.<\/p>\n

Peixoto married three times. Mar\u00edlia Chaves was succeeded by Maria Lucia Alvarenga, then Alcil\u00e9a Augusto. He had four children: Martha, Marcos, Elisa, and Ricardo.<\/p>\n","protected":false},"excerpt":{"rendered":"Maur\u00edcio Peixoto was one of the founders of IMPA","protected":false},"author":17,"featured_media":314439,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[1348],"tags":[246],"coauthors":[5968],"class_list":["post-314438","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-obituary","tag-mathematics"],"acf":[],"_links":{"self":[{"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/posts\/314438","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/comments?post=314438"}],"version-history":[{"count":6,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/posts\/314438\/revisions"}],"predecessor-version":[{"id":314919,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/posts\/314438\/revisions\/314919"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/media\/314439"}],"wp:attachment":[{"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/media?parent=314438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/categories?post=314438"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/tags?post=314438"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/coauthors?post=314438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}