Mário Schenberg

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2 July 1914
Recife, Pernambuco, Brazil
10 November 1990
São Paulo, Brazil

Mário Schenberg was a Brazilian mathematical physicist who made highly significant advances in the theory of stellar evolution. He also worked on cosmic rays and the theory of relativity. He spent the later part of his career as an art critic.


Mário Schenberg was the son of Salomão Schönberg (1885-1953) and Fânia Musij (1893-1980); the family had Jewish origins. Let us note that the name Schenberg was originally Schönberg or Schoenberg and Mário Schenberg was given the name Mayer Schönberg when he was born and most of his publications appear under that version of his name. Note also that Musij was originally Mushier. Salomão Schönberg was born in Kiev, Ukraine and emigrated to Brazil in the early 1900s. Fânia Musij was born in Djora, on the outskirts of Kishenev, Bessarabia. Today Kishenev, Bessarabia is known as Chisinau and is the capital and largest city of Moldova. Fânia Musij was known as Fanny and she came to Brazil shortly before the outbreak of World War I. Ana Clara Guerrini Schenberg, Mário Schenberg's daughter, said [23]:-
My father told me that we were related to the Austrian musician Arnold Schoenberg and Groucho Marx, whose mother was also Schoenberg. ... Fanny came to Brazil to meet Salomão, who was in partnership with her brother in Recife. Salomão had fallen in love with a photo of Fanny that her brother had shown him! They married in Recife and had 3 children: Mário, Saul and José. José died prematurely, aged 10, after falling from the top of a staircase. Saul graduated in Medicine ...
Mário Schenberg attended primary, junior high and high school in Recife, a large city on the northeast corner of Brazil. He attended the Colégio Americano Batista which had been founded in 1906 with the aim of providing quality education for those who could not afford private schooling. When he was about ten years old, Schenberg began to read French technical books which he bought with money he won in a game and these started his interest in science. He was influenced by trips made with his parents to Europe, where he came into contact with Gothic architecture and began to be interested in history.

At the time Schenberg was growing up, Brazil had various movements seeking democratic changes. It was a period when many cultural ideas were being promoted and the young Schenberg read articles describing Marxist views which attracted him. By the age of thirteen, Schenberg had developed a passion for mathematics but his life was certainly not all studying for he spent much leisure time wandering on the beaches of Recife and Olinda.

Schenberg's family could not afford to send their son to Europe for his university studies so, in 1931, Schenberg entered the Pernambuco Engineering School. There he was taught by Luís de Barros Freire (1896-1963) who had been awarded a civil engineering degree from the Escola de Engenharia de Pernambuco in 1918 and, in the following year, had been appointed to the chair of mathematics at the Escola Normal de Pernambuco. He joined the Pernambuco Engineering School in 1920 and became a full professor of physics there in 1934. He realised that his student Schenberg was very talented and he advised him to transfer to the Polytechnic School of São Paulo. This Schenberg did in 1933 knowing that a school of science was about to open there [23]:-
Schenberg arrived in São Paulo at a time of important transformation in scientific activities in Brazil. It was the transition from a science of positivist, utilitarian, professional inspiration, taught by the polytechnics at the end of the Empire and the beginning of the Republic, to the teaching of pure, non-applicable science, which would be taught by the faculties of philosophy, now equipped with laboratories for research. This transition occurred in the midst of the Constitutionalist Revolution of 1932, when the State of São Paulo rebelled against federal interventionism and saw the foundation of University of São Paulo as the path to the formation of an elite capable of promoting the country's development through knowledge.
The University of São Paulo was founded in 1934 and several mathematicians and physicists were brought in from Europe so that the new university would begin life with high quality teachers and researchers. Those who were to be influential in Schenberg's development were Gleb Vassielievich Wataghin (1899-1986), Giuseppe Paolo Stanislao Occhialini (1907-1993), Luigi Fantappiè (1901-1956) and Giacomo Albanese (1890-1948). Wataghin was a Ukrainian who had moved to Italy in 1919 when the Civil War broke out. His dislike of the Fascist government in Italy persuaded him to accept the invitation to São Paulo in 1934 where he worked on astrophysics and particle physics. Wataghin invited Giuseppe Occhialini to join him in São Paulo in 1937. Occhialini was an Italian who had worked at the University of Cambridge before returning to Italy but, like Wataghin, was unhappy with Fascism. He also worked on particle physics. Fantappiè and Albanese are both mathematicians with biographies in MacTutor.

Schenberg studied at the Polytechnic School of São Paulo beginning in 1933 and graduated with an Electrical Engineering degree in 1935. He was already studying in the Faculty of Philosophy, Sciences and Letters at the University of São Paulo and graduated with the degree of Bachelor of Mathematical Sciences in 1936. He published the paper Erratum zu: Sull'interazione degli elettroni on Quantum Electrodynamics in the journal Il Nuovo Cimento and was employed as an Assistant in Experimental Physics (1936-37) working with Gleb Wataghin. After Giuseppe Occhialini arrived in São Paulo in 1937, Schenberg was employed as an Assistant in Theoretical Physics working with Occhialini on cosmic rays (1937-38). Schenberg also became an assistant in charge of courses in relativity in 1937.

On 10 November 1937, there was a coup and Getúlio Vargas became the leader of Brazil taking powers of a dictator. He used these powers to censure the press and by December political parties were abolished. There was political persecution of university professors which led to Schenberg applying for a grant to move to Italy. In 1938, having been awarded the grant, he travelled to Italy where he worked with Enrico Fermi at the Institute of Physics. While in Rome he published the paper Relativistic commutation rules in the quantum theory of fields (1938). It was written in English, submitted in May 1938 and has the following abstract [31]:-
In the present paper are discussed the commutation rules between the field quantities at different times. Commutation rules for electron waves are established with the general assumption of a variable electromagnetic field. For an arbitrary material field with first order equation of motion the commutation rules are seen to be analogous to those of the electron, the case of the neutrino field is examined. Jordan and Pauli's rules for the electromagnetic field strengths are analysed in connection with Maxwell's equations, it is shown that the rules can be written in a symmetrical form similar to those of a material field.
In October 1938 he submitted a second part of the paper with the following abstract [32]:-
The analysis of the commutation rules between field variables at different times, begun in the first part of this paper, is extended to more general cases, in connection with the Heisenberg-Pauli quantum theory of wave fields. This theory is discussed in connection with the wave equations of the classical field. The theory involves difficulties in the case of first order equations of motion. It is shown that the commutation rules between field quantities at different times can be determined by means of the commutation rules at the same time and the equations of motion, when these equations are linear. The case of second order wave equations is explicitly treated, the commutation rules for the same time being known from the Heisenberg-Pauli theory. The study of the functions involved in the relativistic rules shows that the knowledge of these functions is equivalent to the complete solution of the wave equations, any solution being calculable by integrations involving the initial values.
Unhappy with the signs that war was about to break out, he went to Zurich, still in 1938, and worked there with Wolfgang Pauli. In 1939 he moved to Paris where he worked with Frédéric Joliot-Curie at the Collège de France. He published Équations relativistes de mouvement du premier ordre en Mécanique quantique (1939) in the Academy of Sciences journal Comptes Rendus. In this paper he investigated the problem of linearization of the Gordon-Klein relativistic equation. He gave a new form of spinor equations in addition to those given by Dirac. In the same year he published another paper on relativity, First order relativistic equations of motion in quantum mechanics, in the Annals of the Brazilian Academy of Sciences.

Also in 1939 he was appointed Acting Professor of Physics at the University of São Paulo. After Schenberg returned from Paris to São Paulo in 1940, Wataghin commented how his research had developed [36]:-
Mário was a different person and had learned much more than I could have taught him. He had done fine work in cosmic rays and had later began working on electrodynamics. ... He had learned a lot in Rome, and I decided that he didn't have much more to learn from me, and he should travel again ...
Schenberg applied for a Guggenheim Fellowship which he was awarded in 1940 [19]:-
Mário Schenberg is appointed for studies of the application of nuclear and atomic physics to astrophysics; tenure, twelve months from the autumn of 1940.
Schenberg travelled to the United States, sailing on the S S Argentina from Buenos Aires on 11 October 1940 and arriving in New York on 26 October 1940. He joined George Gamow's research team at George Washington University in Washington, D.C. Their joint work quickly made a major breakthrough, Alberto Luiz da Rocha Barros writes [28]:-
Schenberg introduced the neutrino into astrophysics to explain the stellar collapse that causes cosmic explosions known as novae and supernovae.
Antonio Carlos da Silva Miranda writes [38]:-
It was during a conversation with Gamow that Schenberg had an epiphany and realised that the loss of neutrinos from a star could cause a supernova.
Their first joint paper, sent to the Physical Review in November 1940 was The Possible Role of Neutrinos in Stellar Evolution. It has an abstract which you can read at THIS LINK.

In February 1941 they sent the second highly significant paper Neutrino Theory of Stellar Collapse to the Physical Review. It has an abstract which you can read at THIS LINK.

George Gamow called this the Urca process [14]:-
Urca is the name of a casino in Rio de Janeiro, and was used by George Gamow to name the process, as Schenberg once joked to him that "the process makes the energy disappears from the core of a supernova as fast as money in the roulette game during a visit to Casino da Urca."
You can read Schenberg's own description of this work with Gamow at THIS LINK.

Schenberg was awarded a second Guggenheim Fellowship for the academic year 1941-42 which he spent partly as a member of the Institute for Advanced Study in Princeton, and partly at the University of Chicago's Yerkes Observatory with Subrahmanyan Chandrasekhar. Schenberg's joint work with Chandrasekhar quickly produced another major breakthrough with the paper On the Evolution of the Main-Sequence Stars (1942). The paper has the following abstract [34]:-
The evolution of the stars on the main sequence consequent to the gradual burning of the hydrogen in the central regions is examined. It is shown that, as a result of the decrease in the hydrogen content in these regions, the convective zone (normally present in a star) eventually gives place to an isothermal core. It is further shown that there is an upper limit ( 10 per cent) to the fraction of the total mass of hydrogen which can thus be exhausted. Some further remarks on what is to be expected beyond this point is also made.
For an extract from the paper, see THIS LINK.

He returned to Brazil from the United States on 20 July 1942. Back at the University of São Paulo, Schenberg taught courses on Classical Mechanics and Celestial Mechanics. He wrote the thesis Princípios da Mecânica which he defended in a public competition in 1944 and became Professor of Rational and Celestial Mechanics at the University of São Paulo. The delay in holding the competition prevented Schenberg returning to the United States to continue research in astrophysics and resulted in changes in his research interests. He said [41]:-
I thought about returning to the United States, but, as I had entered a mechanics competition, which took several years to complete, I was unable to return. During that time, I became interested in other problems, not dealing directly with astronomy and astrophysics. I turned my interest to some branches of physics, such as, for example, the theory of general relativity, which, of course, is linked to those sciences.
Schenberg had held left-wing political views since he was a young boy, but now he became more involved in politics. He was elected Federal Deputy for the Brazilian Communist Party in 1945. In fact the Brazilian Communist Party had been illegal under the dictatorship of Getúlio Vargas but after this ended in 1945 the Brazilian Communist Party became a legal organisation and by 1947 had 200,000 members. Schenberg was elected as a State Deputy to the Constituent Assembly of São Paulo in 1946 as a Communist Party representative. He was involved in drafting the São Paulo State Constitution in 1947 and put into that Constitution an Article calling for the State to provide research funding.

Eurico Gaspar Dutra became President of Brazil in January 1946 and by 1947 his government moved against the Brazilian Communist Party. Schenberg was impeached and arrested for his involvement with the Communist Party. In 1948 he left Brazil and went to the University of Brussels where he spent five years. Giuseppe Occhialini, whom Schenberg had worked with in São Paulo, had left Brazil and, after spending time in England, had been appointed to the Free University of Brussels in 1948. Schenberg collaborated with Occhialini's research group and also worked with Ilya Prigogine (1917-2003), a Russian born Belgium physicist who shared with Schenberg a love of art and architecture.

Schenberg returned to the University of São Paulo in 1953 where he was appointed as head of the Department of Physics. Between 1953 and 1962 he published papers on a variety of topics; 19 of these papers are in MathSciNet. These include: A generalization of the quantum mechanics (1953); On the hydrodynamical model of the quantum mechanics (1954); A non-linear generalization of the Schrödinger and Dirac equations (1954); On the Grassmann and Clifford algebras (1956, 1960); Quantum mechanics and geometry (5 papers, 1957-58); and On the Clifford and Jordan-Wigner algebras (1962). During these years, at the University of São Paulo [14]:-
... he founded the Solid State Physics Laboratory and participated in the purchase of the first computer of the Universidade de São Paulo, showing remarkable ability to predict the course of science and technology.
César Lattes (1924-2005) was a physicist who had trained at the University of São Paulo with Gleb Wataghin and Giuseppe Occhialini, and had spent time with Occhialini in England studying cosmic rays. He was appointed to the Federal University of Rio de Janeiro but, in 1957, Schenberg persuaded him to accept a position in the Department of Physics at São Paulo. Schenberg, Lattes and others worked as a Brazilian cosmic rays group. Always interested in art as well as science, Schenberg began making both major interests. The artist José Roberto Aguilar said [27]:-
I attended several meetings at Schenberg's home. In the same evening, he'd be discussing atomic particles with Lattes one minute, and the next he'd be talking to the musician Jorge Mautner ...
Mautner had been born in in Rio de Janeiro in 1941, a month after his Jewish parents had emigrated from Austria to escape the Holocaust. He studied music in São Paulo and was invited by Schenberg to join the Brazilian Communist Party in 1962. It was in 1962 that Schenberg was elected for a second term as a State Deputy to the Constituent Assembly of São Paulo, this time as a representative of the Brazilian Labour Party. Schenberg had made a more major move from science to art in 1961 when he resigned as head of the Department of Physics and organised an exhibition by the artist Alfredo Volpi in the São Paulo Biennial. This art exhibition had been founded in 1951 and is the second oldest art biennial in the world.

On 1 April 1964 there was a military coup in Brazil leading to a dictatorship. Because of his membership of the Brazilian Communist Party, seven days after the coup Schenberg was arrested, forced to resign his university position and put in prison. He was 50 days in prison and, while there, the police raided his apartment, took away a Baroque statue of a saint, thinking it was a statue of Lenin, and, after checking though all his books, removed several including Plato's Dialogues. His daughter, Ana Clara Schenberg, said [27]:-
After he was released, the court gave my father permission to go to the police station and explain that there was no way Plato could have been a communist. He managed to get his book back, but not before spending several hours expounding on Platonic philosophy at the police station. For several months, he went to the police station every Thursday and spent the afternoon explaining the contents of the books they had seized until he was able to recover them.
Schenberg could have left Brazil and continued his mathematical physics research but he chose to stay in the country and devote most of his energies to art. He was invited to act as a judge for the São Paulo Biennial in 1965 and 1967. Because of pressure from the authorities, however, they did not appoint Schenberg as a judge for 1969 and this caused the Art Advisory Board to almost stop functioning. For more details of this, see [42], [43] and [44].

Although now essentially a full-time art critic, Schenberg did not give up mathematical physics completely, publishing Time and mass in relativity (1973). For Schenberg's Abstract to this paper, see THIS LINK.

In 1979 he was included in the Amnesty Law promoted by President João Figueiredo and returned to teaching at the Physics Institute of the University of São Paulo. In 1983 he received the Science and Technology Award from the National Research Council.

Schenberg was married to the author Julieta Bárbara Guerrini (1908-2005). In addition to being a poet, she was a painter and wrote articles for the Rio newspaper A Manhã. She had previously been married to the poet Oswald de Andrade (she was the fourth of his five wives), and to the artist Lourdes Cedran. Mário Schenberg and Julieta Guerrini had one daughter, Ana Clara Guerrini Schenberg, who is a geneticist.

Schenberg died in São Paulo in 1990 at the age of 76. In 1989 the conference Clifford algebras and their applications in mathematical physics was held in Montpellier, France. In the Proceedings published in 1992, Schenberg's paper Algebraic structures of finite point sets. I, which dated back to 10 November 1964, was printed with the note:-
This is being done today as reparation for the suffering inflicted on this man of Peace and Science by a regime of injustice.
The paper, intended to be the first in a series, had never been published as a result of the 1964 Brazilian coup. Alum Morris writes in a review:-
It contains a very original construction of Clifford algebras and was intended as the first of a number of articles. Its publication now is an important contribution to the history of the subject.

References (show)

  1. J S Azevedo, Mário Schenberg: Um breviário de suas contribuições e alguns desdobramentos para o ensino de física, Caderno de física da UEFS 20 (1) (2022), 1601.1-8.
  2. L Cedran, (ed), Diálogos com Mario Schenberg (Nova Stella, São Paulo, 1985).
  3. A B Coelho, Mário Schenberg na rede cientí ca transnacional de Gleb Wataghin: a primeira geração de físicos brasileiros, EMConstrucao 7 (2020), 55-78.
  4. A B Coelho and I Gurgel, Antirrealismo e indução: a epistemologia da física no jovem Mário Schenberg, Revista Brasileira de História da Ciência 12 (2) (2019), 158-176.
  5. Document - Carta de Mario Schenberg a Clarice [Lispector], Faculdade de Filosofia, Ciênias e Letras, Universidade de São Paulo (2024).
  6. Entrevista: Mário Schenberg, Revista de Filosofia da UNESP 3 (1980), 9-62.
  7. F de Castro, Mario Schenberg, art critic, Agência FAPESP (4 July 2012).
  8. H Fleming, O último trabalho de Mário Schenberg, Rev. Bras. Ensino Fís. 23 (4) (2001), 34-38.
  9. G Gamow and M Schoenberg, The possible role of neutrinos in stellar evolution, Physical Review 58 (1940), 1117.
  10. G Gamow and M Schoenberg, Neutrino theory of stellar collapse, Physical Review 59 (1941), 539-547.
  11. J L Goldfarb, Mário Schenberg e a história da ciência, Revista da SBHC 12 (1994), 65-72.
  12. J L Goldfarb, Voar também é com os homens: O Pensamento de Mário Schenberg (Universidade de Sao Paulo, 1994).
  13. G K Guinsburg and J L Goldfarb, Mário Schenberg: Entre-Vistas (Perspectiva e IF/USP, São Paulo, 1984).
  14. M M Guzzo and N Reggiani, Mário Schenberg: Physicist, politician and art critic, American Institute of Physics Conference Proceedings 1693 (1) (2015), 040001.1-4.
  15. A I Hamburger, Publicação da obra científica de Mário Schenberg, Estudos Avançados 16 (44 (2002), 215-218.
  16. A I Hamburger, Nota biográfica e entrevista con Mário Schenberg, Universidade de São Paulo (June 1984).
  17. A I Hamburger (ed.), Obra científica de Mário Schönberg, Volume 1 - 1936 a 1948 (Edusp, São Paulo, 2009).
  18. D L Kinoshita, Mario Schenberg: o cientista e o político (Fundação Astrojildo Pereira, Brasília, 2014).
  19. Mário Schenberg, John Simon Guggenheim Foundation.
  20. Mário Schenberg, Personalidades do Muro, UNIFEI (2024).
  21. J B Martins, Minhas conversas com Mário Schenberg, Cad. Bras. Ens. Fís. 23 (3) (2006), 405-417.
  22. A Micali and A L da Rocha Barros, Notice biographique sur Mário Schenberg, in A Micali, R Boudet and J Helmstetter (eds.), Clifford algebras and their applications in mathematical physics, Montpellier, 1989 (Kluwer Academic Publishers Group, Dordrecht, 1992), 501-503.
  23. A C S Miranda, Mário Schenberg, pioneiro da astrofísica teórica brasileira, in História da Astronomia no Brasil (Companhia Editora de Pernambuco, 2014), 461-484.
  24. A M Oliveira, Aproximações entre arte, comunicação e ciência em Mário Schenberg, Arte e Cultura da América Latina (2009), 35-46.
  25. A M Oliveira, Mário Schenberg: Crítica de arte e comunicação, Communicare 8 (2) (2008), 51-63.
  26. A M Oliveira, Mário Schenberg in between Art and Science, Universidade de Sao Paulo (2012).
  27. B de Pierro, Entre estrelas, políticos e artistas: O recifense Mario Schenberg se destacou na física teórica, foi deputado e escreveu sobre artes plásticas, Revista Pesquisa FAPESP (2021).
  28. A L da Rocha Barros, Schenberg: nada que é humano lhe era estranho, Estudos Avançados 5 (11) (1991), 195-198.
  29. Saiba quem foi Mario Schenberg, globo.com (18 September 2006).
  30. M Schenberg, Pensando a Física (Editora Brasiliense, 1984).
  31. M Schönberg, Relativistic commutation rules in the quantum theory of fields, Physica 5 (7) (1938), 553-560.
  32. M Schönberg, Relativistic commutation rules in the quantum theory of fields (II), Physica 5 (10) (1938), 961-968.
  33. M Schönberg, Mário Schenberg (depoimento, 1978) (CPDOC, Rio de Janeiro, 2010).
  34. M Schönberg and S Chandrasekhar, On the evolution of the Main-Sequence stars, The Astrophysical Journal 96 (1942), 161-172.
  35. C S Schroeder, Considerações sobre a atuação de Mário Schenberg na X Bienal de São Paulo, Revista de História da Arte e da Cultura 19 (2021), 159-173.
  36. S Schwartzman, A formação da comunidade científica no Brasil (Companhia Editora Nacional and FINEP, 1979).
  37. Scientific papers of Professor Mário Schenberg, in A Micali, R Boudet and J Helmstetter (eds.), Clifford algebras and their applications in mathematical physics, Montpellier, 1989 (Kluwer Academic Publishers Group, Dordrecht, 1992), 519-523.
  38. A C da Silva Miranda, História da astronomia no Brasil (Mast, MCTI, 2014).
  39. A Q de Souza, A visão de ciência de Mário Schenberg: intuição e imaginação nas origens das ideias científicas, Master thesis (Pontifícia Universidade Católica de São Paulo, São Paulo, 2012).
  40. M C Vieira, Mário Schenberg, Pion (2024).
  41. M Schenberg, Formação da mentalidade científica (Transcript of a lecture given on 16 May 1982), Estudos Avançados 5 (12) (1991), 123-151.
  42. C S Schroeder, Considerações sobre a atuação de Mário Schenberg na X Bienal de São Paulo, Revista de História da Arte e Arqueologia 19 (2013), 159-171.
  43. C S Schroeder, The Biennial Under Contestation: Local Perspectives on the Tenth São Paulo Biennial (1969), Tate Papers 34 (2022).
  44. A P C Pismel, Schenberg e as Bienais (Doctoral Thesis, University of São Paulo, 2018).

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Written by J J O'Connor and E F Robertson
Last Update June 2024