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Godoy Kv Dr Rcla.Pdf (9.737Mb) UNIVERSIDADE ESTADUAL PAULISTA “JÚLIO DE MESQUITA FILHO” INSTITUTO DE GEOCIÊNCIAS E CIÊNCIAS EXATAS PROGRAMA DE PÓS-GRADUAÇÃO EM EDUCAÇÃO MATEMÁTICA KLEYTON VINICYUS GODOY UM BREVE PANORAMA DAS MATEMÁTICAS MISTAS E SEUS DESDOBRAMENTOS Rio Claro 2019 KLEYTON VINICYUS GODOY UM BREVE PANORAMA DAS MATEMÁTICAS MISTAS E SEUS DESDOBRAMENTOS Tese de Doutorado apresentada ao Programa de Pós-Graduação em Educação Matemática do Instituto de Geociências e Ciências Exatas da Universidade Estadual Paulista “Júlio de Mesquita Filho”, campus de Rio Claro, como requisito para o processo de obtenção do título de Doutor em Educação Matemática. Orientador: Prof. Dr. Marcos Vieira Teixeira Rio Claro 2019 KLEYTON VINICYUS GODOY UM BREVE PANORAMA DAS MATEMÁTICAS MISTAS E SEUS DESDOBRAMENTOS Tese de Doutorado apresentada ao Programa de Pós-Graduação em Educação Matemática do Instituto de Geociências e Ciências Exatas da Universidade Estadual Paulista “Júlio de Mesquita Filho”, campus de Rio Claro, como requisito para o processo de obtenção do título de Doutor em Educação Matemática. Comissão Examinadora Prof. Dr. Marcos Vieira Teixeira – Orientador (IGCE/UNESP/Rio Claro-SP) Prof. Dr. Gustavo Barbosa (UNILA/Foz do Iguaçu-PR) Prof. Dr. Fumikazu Saito (PUC/São Paulo-SP) Prof. Dr. Wladimir Seixas (CCTS/UFSCar/Sorocaba-SP) Prof. Dr. Zaqueu Vieira Oliveira (FE/USP/São Paulo-SP) Resultado: APROVADO Rio Claro, 21 de Maio de 2019 Dedico à minha mãe Maria Ester Nardon Godoy e a meu pai Antônio Carlos Tadeu Godoy por todo suporte e apoio durante a realização desse Doutorado e minha vida. AGRADECIMENTOS Meus agradecimentos vão a todos aqueles que contribuíram diretamente ou indiretamente para a realização dessa dissertação. Dessa forma, não poderia deixar de agradecer: Aos meus pais Maria Ester Nardon Godoy e Antônio Carlos Tadeu Godoy, e a minha família por todo apoio, carinho e incentivo que me deram para a finalização desse trabalho. Ao meu orientador Prof. Dr. Marcos Vieira Teixeira, por toda confiança, pela orientação dedicada fossem elas nas reuniões do Grupo de Pesquisa ou individuais, sugestão de materiais, compreensão, e pelo acolhimento numa fase delicada durante esse processo de Doutorado ao ter aceito uma nova orientação e um novo trabalho faltando apenas quatro meses para a data limite de entrega do material de qualificação. Aos professores componentes da banca examinadora: Prof. Dr. Fumikazu Saito, Prof. Dr. Gustavo Barbosa, Prof. Dr. Wladimir Seixas e Prof. Dr. Zaqueu Vieira Oliveira, agradeço pela leitura que realizaram do trabalho e também das críticas construtivas e sugestões de leitura e bibliografia tanto no exame de qualificação quanto nos encontros presenciais nos corredores da UNESP ou durante congressos que tivemos a oportunidade de participar. Aos professores suplentes da banca examinadora: Prof. Dr. Roger Miarka, Prof. Dr. Carlos Roberto de Moraes e Profa. Dra. Sabrina Helena Bonfim, por aceitarem participar como suplentes deste trabalho. Ao meu amigo e companheiro de Grupo de Pesquisa em História da Matemática (GPHM), Prof. Ms. Douglas Gonçalves Leite, que realizou uma leitura do trabalho buscando me auxliar em pontos contraditórios e também na correção ortográfica desse trabalho. Aos professores do Programa de Pós-Graduação em Educação Matemática, em especial, a Profa. Dra. Heloisa da Silva, Profa. Dra. Arlete de Jesus Brito, Prof. Dr. Marcos Vieira Teixeira, Prof. Dr. Marcus Vinicius Maltempi e o Prof. Dr. Henrique Lazari, que por meio de suas disciplinas durante o Doutorado, contribuíram para enriquecer minha compreensão em Educação Matemática, Matemática, História da Matemática e História da Educação Matemática. Aos funcionários do Departamento de Matemática e do Departamento de Educação Matemática: Elisa, Ana, Alessandra, Clô e José Ricardo por toda atenção quando lhes solicitei alguma ajuda. A secretária do Programa de Pós-Graduação em Educação Matemática: Inajara, por toda eficiência e empenho para resolver e auxiliar na condução dos assuntos burocráticos relacionados ao Doutorado, além de ser uma pessoa extremamente atenciosa e que ajudou muito com seus conselhos mediante situações que tive de superar na jornada desse doutorado. Aos meus amigos do Programa de Pós-Graduação em Educação Matemática: Juliana Martins, Maria Tereza Zampieri, Miliam Juliana Ferreira, Hannah Dora, Bruno Leite, Alan dos Santos Silva, Jean Toillier, Nilton Silveira, Marineia dos Santos, Vanessa Oechsler, Maroni Lopes, Davidson Azevedo, Maria Francisca, Douglas Gonçalves e outros que apesar de não estarem citados aqui, também compartilhamos momentos durante esses quatro anos nas atividades do Programa. Obrigado por dividirem momentos comigos, fossem eles de estudo, de lazer, idas a congressos, e outras atividades que contribuíram tanto para o espírito e para a mente. Agradeço ao meu amigo Prof. Ms. Diego Gondim, com quem dividi a representação discente do Conselho do Programa de Pós-Graduação em Educação Matemática durante o segundo e o primeiro semestre de 2017 e 2018, respectivamente. Ao Prof. Dr. Ricardo Scucuglia pela avaliação da primeira versão do projeto da tese durante a Atividade Inaugural do Programa de Pós-Graduação em Educação Matemática de 2016. Aos professores que tiveram contato com esse trabalho em congressos científicos nas seções de comunicação e contribuíram com ideias e sugestões para o trabalho: Prof. Dr. Iran Abreu Mendes, Prof. Dr. Wagner Rodrigues Valente, Prof. Dr. Gérard Émile Grimberg, Profa. Dra. Circe Mary Silva da Silva Dynnikov e Profa. Dra. Maria Cristina Araújo de Oliveira. As Professoras: Profa. Dra. Rosana Giaretta Sguerra Miskulin e Profa. Dra. Sueli Liberatti Javaroni por depositarem sua confiança em mim e terem enviado as cartas de recomendação para o meu ingresso no programa. Agradeço a Profa. Dra. Adriana Cesar de Mattos, que foi minha orientadora no Mestrado, pela confiança e oportunidade de dar continuidade aos estudos, por meio de ser com quem ingressei primeiramente no Doutorado no ano de 2015. Agradeço também a Profa. Dra. Arlete de Jesus Brito, que foi minha segunda orientadora, e que contribuiu em aprender novas visões da História, por conta de seus trabalhos fazendo uso da História Cultural. Agradeço meus amigos que não fazem parte do programa de pós, mas que fazem parte do meu dia a dia por toda a compreensão em entender que não poderia estar presente em alguns momentos por conta dos estudos, e em especial, todo apoio que me deram durante a realização desse doutorado. Agradeço ao Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) pelo apoio financeiro dado a este trabalho por meio da atribuição de uma bolsa de doutorado. RESUMO Realizamos um histórico da introdução das “matemáticas mistas”, e identificamos que o filósofo Francis Bacon (1561-1626) é creditado por meio das publicações “Proficience and Advancement of Learnings” em 1605 e “De Dignitate et Augmentis Scientiarum” em 1623. Entretanto, para responder questões pertinentes da Filosofia Natural, essa classificação matemática gerou um conflito entre as ciências matemáticas e a metafísica. Desse modo, as ciências físico-matemáticas surgem como uma tentativa de utilizar a matemática para abordar tópicos relacionados as causas naturais do mundo real. No ano de 1751, Jean le Rond D'Alembert (1717-1783), realizou uma nova classificação dos conhecimentos humanos, divulgada na obra Discours Préliminaire, que foi o texto de abertura da primeira edição da Encyclopédie, editada em conjunto com Denis Diderot (1713-1784). No que se refere a matemática, foi mantida como uma ramificação da metafísica, mas essa nova classificação a dividiu em: “matemática pura”, “matemática mista” e “ciências físico-matemáticas”. Porém, no decorrer do século XVIII, estimulado principalmente pelas críticas de Kant (1724-1804) em relação ao conhecimento puro, se deu início a uma discussão quanto a metafísica, e consequentemente refletiu nas ciências que estavam subordinadas a esse ramo do conhecimento. Desse modo, o século XIX culminou no desuso da expressão “matemáticas mistas”, contudo, veremos que essas ciências forneceram elementos para fomentar o aparecimento das “matemáticas aplicadas”, bem como contribuíram para o desenvolvimento de teorias da “matemática pura”. Além disso, investigaremos no contexto da Revolução Industrial, a importância das “matemáticas mistas” e das ciências físico-matemáticas no desenvolvimento tecnológico. Portanto, fixamos um local: Inglaterra; e uma sociedade científica: Sociedade Lunar de Birmingham. Assim, concluímos que essas contribuições consistiram principalmente na modernização de máquinas a vapor para dinamizar o processo de produção nas fábricas. Palavras-chave: Filosofia da Matemática. Matemática Mista. Matemática Pura. Físico- Matemática. História da Matemática. ABSTRACT Our aim is to realize a history of the introduction of the "mixed mathematics", and we find that the philosopher Francis Bacon (1561-1626) is credited through the publications "Proficiency and Advancement of Learnings" in 1605 and "De Dignitate et Augmentis Scientiarum" in 1623. However, to answer pertinent questions of Natural Philosophy, this mathematical classification generated a conflict between the mathematical sciences and metaphysics. In this way, the physico-mathematics sciences appeared as an attempt to use mathematics to address topics related to the natural causes of the real world. In 1751, Jean le Rond D'Alembert (1717-1783), made a new classification of human knowledge, published in the Discours Préliminaire, which was
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