OS CONJUNTOS INVADEM A GEOMETRIA
Autor: DIVULGANDO A MATEMÁTICA | Publicado: 2012-11-09T12:56:00-08:00


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David Hilbert (1862 - 1943)


David Hilbert nasceu em Konigsberg, na
Prússia Oriental.

Dinâmico e com ideias notavelmente
originais, participou de quase todos os Congressos internacionais de Matemática
que, a partir de 1893, passaram a ser realizados com frequência.

Em 1899 publicou os "Fundamentos da
Geometria", que exerceu grande influência sobre a Matemática do século XX.

Hilbert percebeu que nem todos os termos
podem ser definidos e por esta razão iniciou sua Geometria com três objetos não
definidos - ponto, reta e plano - e seis relações não definidas - estar sobre,
estar em, estar entre, ser congruente, ser paralelo e ser contínuo - formulando
vinte e um postulados conhecidos como Axiomas de Hilbert. A Teoria dos
Conjuntos passa a invadir a Geometria num grau crescente de generalização e
abstração.

Em 1900, Hilbert já era afamado professor
em Gtittingen, Alemanha, e depois de muito analisar as pesquisas dos fins do
século XIX, durante sua participação no Congresso de Paris, apresentou e propôs
vinte e três problemas os quais, segundo acreditava, ocupariam a atenção dos
matemáticos do século XX, numa tentativa de prenunciar os rumos que tomaria o
progresso neste século. Dizia ele: se quisermos ter uma ideia do
desenvolvimento provável do conhecimento matemático no futuro imediato devemos fazer
passar por nossas mentes as questões não resolvidas e olhar os problemas que a
Ciência de hoje coloca e cujas soluções esperamos no futuro.

Destes problemas, o primeiro trata de
Teoria dos Conjuntos, o segundo é sobre os axiomas da Matemática, e os outros
são sobre Topologia, Equações Diferenciais, Cálculo das Variações e demais
campos. Pode-se afirmar que muitos deles ainda não estão resolvidos e que a
Matemática neste século se desenvolveu em muitas direções não previstas como
disse o próprio Hilbert: Enquanto um ramo da Ciência oferece uma abundância de
problemas, ele está vivo.

Depois do Congresso de 1900, os matemáticos
se agruparam em duas escolas, dependendo da sua linha de pensamento: os
"formalistas" liderados por Hilbert, e os "logicistas"
tendo à frente Russel.

Hilbert interessou-se por todos os
aspectos da Matemática Pura, contribuindo para a Teoria dos Números, Lógica
Matemática, Equações Diferenciais e também para a Física Matemática, sendo
considerado uma figura importante de transição entre os séculos XIX e XX.



Fundamentos da Matemática Elementar – Vol. 7 – Gelson Iezzi