Marília Chaves Peixoto (24 February 1921 – 5 January 1961) was a Brazilian mathematician and engineer who worked in

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

s. Peixoto was the first Brazilian woman to receive a

doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''l ...

in mathematics and the first Brazilian woman to join the

Brazilian Academy of Sciences The Brazilian Academy of Sciences ( pt, italic=yes, Academia Brasileira de Ciências or ''ABC'') is the national academy of Brazil. It is headquartered in the city of Rio de Janeiro and was founded on May 3, 1916. Publications It publishes a lar ...

Early life and education

Marília Magalhães Chaves was born on 24 February 1921, to Tullio de Saboia Chaves and Zillah da Costa Magalhaes, in

Santana do Livramento Santana do Livramento is a city in the state of Rio Grande do Sul, Brazil. It is located along the border with the city of Rivera, Uruguay, forming together an international city of almost 170,000 inhabitants. Santana do Livramento was founded on J ...

. She had two siblings, Lúcia de Magalhaes Chaves and Livio de Magalhaes Chaves. In an interview from 1952, she would describe her educational upbringing, stating that despite the high school in Santana do Livramento not accepting girls as students, the priests helped her enroll as a private student and take tests in the school. She later moved to

Rio de Janeiro Rio de Janeiro ( , , ; literally 'River of January'), or simply Rio, is the capital of the state of the same name, Brazil's third-most populous state, and the second-most populous city in Brazil, after São Paulo. Listed by the GaWC as a b ...

, studying at the Colégio Andrews, a secular school that allowed boys and girls to study. She graduated as an outstanding student. She studied superior courses and studied for the entrance exam of the Escola Nacional de Engenharia (National School of Engineering) at the

Federal University of Rio de Janeiro The Federal University of Rio de Janeiro or University of Brazil (UFRJ; pt, Universidade Federal do Rio de Janeiro or ') is a public research university located in the state of Rio de Janeiro, Brazil. It is the largest federal university in the ...

. She achieved third place in the entrance exam rankings and was accepted. In 1939 she enrolled at the Escola Nacional de Engenharia, working alongside

Leopoldo Nachbin Leopoldo Nachbin (7 January 1922 – 3 April 1993) was a Jewish-Brazilian mathematician who dealt with topology, and harmonic analysis. Nachbin was born in Recife, and is best known for Nachbin's theorem. He died, aged 71, in Rio de Janeiro. ...

and

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

(whom she would later marry).

Career

Peixoto graduated from the

in 1943 with a degree in engineering, having also studied mathematics at the university and acted as a monitor for the university's National Faculty of Philosophy. In 1948, she received a doctorate in mathematics, and began teaching at the

Escola Politécnica da UFRJ The Polytechnic School of Federal University of Rio de Janeiro (Portuguese: ''Escola Politécnica da Universidade Federal do Rio de Janeiro''), also called "''Poli''", founded in 1792, is the third oldest engineering school in the world and oldest i ...

. In 1949, Peixoto published "On the inequalities

y'' \ge G(x,y,y',y'')

" in . Following her work on

convex function In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of a function, graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigra ...

s, Peixoto was appointed an associate member of the Brazilian Academy of Science on 12 June 1951. She was the first Brazilian woman to join the organization, and the second woman after

Marie Curie Marie Salomea Skłodowska–Curie ( , , ; born Maria Salomea Skłodowska, ; 7 November 1867 – 4 July 1934) was a Polish and naturalized-French physicist and chemist who conducted pioneering research on radioactivity. She was the first ...

, a foreign associate of the academy. Peixoto married

in 1946. In 1949 they traveled to Chicago for the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

of 1950. Despite being a participant in her own right, in the list of members she was listed as Maurício's spouse ("Mrs. Peixoto") rather than her full title. In 1955, Peixoto published Cálculo vetorial (Vector calculus), a book aimed at students that is more focus on applications of

vector calculus Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subject ...

than proofs of results. Marília and Maurício jointly published "Structural Stability in the plane with enlarged boundary conditions" in 1959, one of several papers which led to

Peixoto's theorem In the theory of dynamical systems, Peixoto's theorem, proved by Maurício Peixoto, states that among all smooth flows on surfaces, i.e. compact two-dimensional manifolds, structurally stable systems may be characterized by the following properti ...

. She died on 5 January 1961, aged 39. She received a number of posthumous honors, including: * ''Rua Marília Chaves Peixoto'' - A street in her hometown of

, named after her. * ''Municipal School Marília Chaves Peixoto'' - A school in

Petrópolis Petrópolis (; ), also known as The Imperial City, is a Municipalities of Brazil, municipality in the Southeast Region, Brazil, Southeast Region of Brazil. It is located in the state of Rio de Janeiro (state), Rio de Janeiro, northeast of the ci ...

her husband helped establish in her name in 1971. It was funded by award money he received for

Peixoto's Theorem In the theory of dynamical systems, Peixoto's theorem, proved by Maurício Peixoto, states that among all smooth flows on surfaces, i.e. compact two-dimensional manifolds, structurally stable systems may be characterized by the following properti ...

Personal life

Peixoto had two children, Marta and Ricardo, with Maurício Peixoto.

Published works

* 1949: ''On the inequalities

y'' \ge G(x,y,y',y'')

''. - Ph.D. thesis. * 1955: ''Cálculo Vetorial: notas de aula''. - book. * 1959: ''Structural stability in the plane with enlarged boundary conditions.'' - paper.

References

{{DEFAULTSORT:Peixoto, Marília Chaves 1921 births 1961 deaths People from Santana do Livramento 20th-century Brazilian mathematicians 20th-century women engineers 20th-century Brazilian engineers Brazilian women mathematicians