{"id":17450,"date":"2012-09-12T19:02:43","date_gmt":"2012-09-12T22:02:43","guid":{"rendered":"http:\/\/revistapesquisa.fapesp.br\/?p=17450"},"modified":"2016-05-24T15:14:12","modified_gmt":"2016-05-24T18:14:12","slug":"between-theorems-and-railways","status":"publish","type":"post","link":"https:\/\/revistapesquisa.fapesp.br\/en\/between-theorems-and-railways\/","title":{"rendered":"Between theorems and railways"},"content":{"rendered":"

\"\"Larissa Ribeiro<\/span>According to many historians, the foundation of the University of S\u00e3o Paulo, in 1934, was the beginning of modern science in Brazil. In the words of Sergio Milliet, this event \u201cis the intellectual and scientific revolution that will change Brazilians\u2019 economic and social concepts.\u201d Historians add that up until that time, Brazil had been \u201cscientifically isolated,\u201d this being the fault of the \u201cauthoritarian and anti-science group\u201d that had imposed \u201corder and progress\u201d on the Brazilians and added this slogan to the Brazilian flag. This unusual distortion resulted in \u201cdemonizing\u201d of positivism \u2013 whose creed was faith in science to leverage progress and civilization \u2013 and led to blaming positivism as the major obstacle to national scientific development.<\/p>\n

The accusation gains controversial contours when it falls on mathematics, the discipline viewed by France\u2019s Auguste Comte (1798-1857) – the creator of positivism \u2013 as the base of education. \u201cThe Brazilian-style positivism during the First Republic (1889-1930) was, and still is, analyzed in a simplistic and general manner because of its \u201cscientific-like\u201d vision that advocated pragmatic science and mathematics as the practical instruments to solve national problems and provide material progress and social modernization. Superficial, interested interpretations accuse positivism of over-rating applied science, thus creating constraints for scientific progress, whose main driver is pure, uninterested science, \u201c explains mathematician Rog\u00e9rio Monteiro de Siqueira, a professor at the Postgraduate Program in Cultural Studies at the School of Arts, Sciences, and Humanities (EACH\/USP) of the University of S\u00e3o Paulo. He is the author of the study Modernismo, modernidade e moderniza\u00e7\u00e3o nas ci\u00eancias matem\u00e1ticas brasileiras <\/em>[Modernism, modernity and modernization in the Brazilian mathematical sciences}, sponsored by FAPESP.<\/p>\n

\u201cOf course, before 1930s, what was going on in mathematics in Brazil was nothing like what was going on in Europe. But we can\u2019t simplify matters and say that we lacked any kind of mathematical development before USP was established. Individual mathematicians were regularly publishing papers on original themes in international journals. Therefore, the belief that the positivists prevented the attempt to develop pure science \u2013 as some of their early and current detractors state – is misleading,\u201d he says. \u201cNonetheless, many people continue to insist that progress was achieved only because of \u201cthe escapes from positivism.\u201d This throws a veil on the past, reducing mathematical progress to a restricted pantheon of \u2018modern\u2019 anti-positivists, such as Otto de Alencar (1874-1912), Manuel de Amoroso Costa (1885-1928), Theodoro Ramos (1895-1935) and L\u00e9lio Gama (1892-1981),\u201d Rog\u00e9rio adds.<\/p>\n

The battle between pure science and applied science is very complex and seldom researched, as the researcher found out when analyzing articles published in specialized journals. \u201cSome \u2018positivist\u2019 mathematicians criticized Comte. In Brazil, positivism was not a single, radical movement; it was split into various factions with different levels of orthodoxy,\u201d he says. The leader of the positivist movement in Brazil, Benjamin Constant de Magalh\u00e3es (1833-1891), a staunch republican and professor of mathematics at military academies, was openly against the Comte interpretation of mathematics. \u201cOne must also be familiar with the entire production of the \u2018moderns.\u2019 Nowadays, we have an incomplete depiction of the debates, from which political variables and interests were extracted. Only the \u2018modern\u2019 articles they wrote are selected, and many other articles on issues related to applied science are disregarded. People also forget that the so-called \u2018pioneers of pure mathematics\u2019 were \u2018hybrids,\u2019 because, besides developing theorems, they accepted government jobs and wrote about the practice of engineering, without limiting themselves to \u2018uninterested science,\u2019\u201d he adds.<\/p>\n

\"078-081_Matematica_196\"<\/a><\/p>\n

Even Amoroso Costa, who held positivism responsible for the sorry state of the exact sciences in Brazil, was obliged to admit that \u201cour terrain is still not ready to cultivate pure science, this contemplative, uninterested, and supreme flower of the spirit.\u201d \u201cThis battle was a symptom of the realignment of political forces with national sciences, as exemplified by a group of engineers. These engineers, who had invested in mathematics that was foreign to their applications, following a pattern that was in vogue at that time in Europe, gradually became aware that they were no longer valuable and there was no room for them. This happened in an environment in which mathematics was increasingly being seen as an instrument of practical work for the country\u2019s progress,\u201d Rog\u00e9rio analyzes. Having been discarded, this group began to advocate the creation of an institutional venue for \u201cuncommitted\u201d science; more specifically, this venue was the university, which they eventually dominated.<\/p>\n

\n

Actually, a small group of radical positivists was against creating this space, as it was highly aware of the arm-wrestling that was under way. Many other factions disagreed with this \u201ccensorship,\u201d and took on a non-dogmatic attitude towards Comte\u2019s texts. \u201cWe mustn\u2019t forget that the influence of positivism on the First Republic didn\u2019t last for very long and the generation of 1870 – more specifically, the military summit influenced by Comte\u2019s social reform ideas – was jettisoned from power by the oligarchies,\u201d explains Angela Alonso, a professor at the Sociology Department of the University of S\u00e3o Paulo and author of Ideias em movimento: a gera\u00e7\u00e3o 1870 na crise do Brasil-Imp\u00e9rio<\/em> [Ideas in motion: the 1870 generation in the Brazilian Empire crisis] (2002). This group wanted to see a split between the military and the civilians; they felt contempt for the \u201cbachelor\u2019s degree community\u201d and its liberal views and romantic attitude towards a monarchy in Brazil. To this counter-elite comprised of military personnel, engineers and physicians, all of whom had a technical-scientific background, positivism was the confirmation of their awareness of the huge gap between the country and \u201ccivilization.\u201d<\/p>\n

Cannon<\/strong>
\n\u201cBrazilian positivists had a unique characteristic: instead of approaching the doctrine in religious terms, they used it to discuss political issues on a social terrain. Thus, science emerges as a source of solutions,\u201d says the professor. These positivists, fans of \u201cBrazilian illustration,\u201d viewed education as the panacea and saw themselves as having a \u201cmission,\u201d which was to become familiar with Brazil\u2019s social reality and nature, overcoming obstacles by resorting to science and practical solutions, and thus revealing the potential of the territory. \u201cThe point was not to enhance applied science to the detriment of pure science; the point was to practice scientific knowledge with a social objective, associated with the fundamental role attributed to scientists in the new positivist Brazil,\u201d explains Luiz Ot\u00e1vio Ferreira, a researcher at the Casa de Oswaldo Cruz center of Fiocruz, and coordinator of the research study O \u2018ethos\u2019 positivista e a institucionaliza\u00e7\u00e3o da ci\u00eancia no Brasil<\/em> [The positivist \u2018ethos\u2019 and the institutionalization of science in Brazil ](2007).<\/p>\n

\u201cThus, there was no room for \u2018pure mathematics\u2019 in this urgent clearing of territories. However, there were diverging opinions after the Central School of Engineering was established in 1858. This School split the teaching of engineering between civilians and the military. The military embraced positivism at the military academies,\u201d says Ferreira. The \u201cpure\u201d mathematicians aligned themselves with the civil engineers. The conflict began in 1896, when Benjamin Constant de Magalh\u00e3es, then minister of Public Instruction, closed down the physical, mathematical, and natural sciences courses at the Polytechnic School of Rio de Janeiro. \u201cEven though closing down these courses could be attributed to the fact that only 67 students had enrolled in these courses since 1874, some professors felt that the objective of this measure, was the imposition by the positivists that dominated the institution of the utilitarian view of the sciences,\u201d Ferreira explains.<\/p>\n

In the opinion of the \u201cscientistic engineers,\u201d this was a coup designed to take over their territory. The reaction came in 1898. Otto de Alencar, a former positivist, published the article \u201cAlguns erros de mathematica na Synthese subjectiva de A. Comte,\u201d the first \u201ccannon ball\u201d set off in the battle between \u201cpure\u201d and \u201c applied\u201d mathematics. This was low-caliber ammunition, but it acted as the \u201cfodder\u201d for the cannon set off in 1918, at the conferences of Amoroso Costa. \u201cThe new countries are fanatic about material progress; they disregard the existence of a scientific ideal that is far superior to the man who manufactures one thousand automobiles a day or removes an appendix in 10 minutes. There is a unanimous opinion: science is useful, because engineers, doctors and military personnel need it. It is not worthwhile doing it in Brazil, as it is cheaper and more convenient importing it from Europe. This is the predominant mentality among educators and government authorities,\u201d the mathematician stated.<\/p>\n

Contemplation<\/strong>
\nTen years later, L\u00e9lio Gama, in Rio, and Theodoro Ramos, in S\u00e3o Paulo, joined the battle to \u201cretrieve\u201d the territory of \u201cuninterested\u201d science. This ultimately led to the creation of USP and Rio de Janeiro\u2019s University of Brazil, in 1939. However, was there any room for \u201ccontemplative science\u201d prior to the 1930s? \u201cIn Europe, mathematics, physics, and engineering were soon separated; but in Brazil this didn\u2019t happen. The separation was possible in Europe because of its rapid industrialization in the nineteenth century. In Brazil, there was no demand for technical knowledge in all fields, as was the case of medicine, for example,\u201d points out Rog\u00e9rio. The anti-positivist criticisms were not \u201cpure\u201d either.<\/p>\n

\"\"

Reproduction from the book \"O Brasil\" by Marc Ferrez<\/span>Military Academy, Urca, Rio de Janeiro, 1885, a well-known center of positivistsReproduction from the book \"O Brasil\" by Marc Ferrez<\/span><\/p><\/div>\n

\u201cThe taints of \u00b4inaccuracy\u2019 and \u2018lack of scientific rigor\u2019 thrown on the positivists are debatable. Italian mathematicians, for example, were referred to as \u2018poets\u2019 because of their alleged inaccuracy yet nobody put the blame on positivism for this. The requested \u2018rigor\u2019 was not exercised in the writings of the \u2018modern\u2019 Brazilians, whose work was not on a par with the work being done in Europe,\u201d says the researcher. \u201cThe desire was to create \u2018distinction\u2019: the thesis of Theodoro Ramos, for example, used set theory less in favor of \u2018pure mathematics\u2019 than as a fighting strategy,\u201d says Rog\u00e9rio.<\/p>\n

Nevertheless, what was the motivation of the \u201cpurists?\u201d \u201cThey had a feeling that something was mismatched, that \u2018ideas were out of place.\u2019 Many of them had traveled abroad and had returned with knowledge on new scientific concepts being used in Europe,\u201d says Rog\u00e9rio. In the researcher\u2019s opinion, one cannot deny the constant existence of a political component in the battle among groups that excluded each other and that wanted their places under the sun. \u201cThis is evidenced by Ramos\u2019 link to the Revolution of 1930. It was no coincidence that he brought Italian mathematicians – many of whom were Fascists \u2013 to USP, to please Vargas, who admired Mussolini. This action was also in line with the demands of the enormous Italian community,\u201d he adds.<\/p>\n

Thus, the Germans and the Italians were left in charge of the exact sciences, while the French were in charge of the humanities. The first generation of mathematicians from the 1950s were the \u201cheirs\u201d of this decision, which included a disregard for didactics, instilled by such Italian professors as Luigi Fantappi\u00e9. National mathematics, which gained international prominence in the early 1960s, was based on an \u201cintellectual imbroglio.\u201d \u201cThe fans of \u2018pure science\u2019 appropriated articles that came from abroad without being familiar with the context and the discussions surrounding these articles. They were appropriated directly and this resulted in a kind of \u2018Brazilian-type\u2019 mathematics,\u201d says Rog\u00e9rio.<\/p>\n

Thus, the \u201cdemonizing\u201d of positivism deserves to be revised. \u201cCriticism of positivist scientific ideas was not only an undertaking of young, innovative mathematicians that wanted to break the cycle of the archaic conservatism of science in Brazil. This interpretation disregards the fact that the frontier between the archaic and the modern results from the processes of social construction,\u201d Ferreira points out. Positivism was the basis for the development of a class of scientists that was against it. \u201cThe positivists provided the ideological content necessary to shape the \u2018scientist\u2019 category. The model of the positivist intellectual, who was objective and precise, whether he was a social reformer or not, educated those who wished to be regarded as scientists.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"Debate on positivist mathematics led to pure science in Brazil","protected":false},"author":24,"featured_media":0,"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":[165],"tags":[241,246],"coauthors":[117],"class_list":["post-17450","post","type-post","status-publish","format-standard","hentry","category-humanities","tag-history","tag-mathematics"],"acf":[],"_links":{"self":[{"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/posts\/17450","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\/24"}],"replies":[{"embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/comments?post=17450"}],"version-history":[{"count":0,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/posts\/17450\/revisions"}],"wp:attachment":[{"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/media?parent=17450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/categories?post=17450"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/tags?post=17450"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/revistapesquisa.fapesp.br\/en\/wp-json\/wp\/v2\/coauthors?post=17450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}