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Hermann Weyl

Data de nascimento: 9. Novembro 1885
Data de falecimento: 8. Dezembro 1955

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Hermann Klaus Hugo Weyl foi um matemático alemão.

Embora tenha passado boa parte de sua vida acadêmica em Zurique, Suíça e posteriormente em Princeton, Nova Jérsei, ele está intimamente identificado com a tradição da matemática da Universidade de Göttingen, representada por David Hilbert e Hermann Minkowski. Suas pesquisas possuem grande significado para a física teórica, bem como para outras disciplinas puras como a teoria dos números. Weyl foi um dos mais influentes matemáticos do século XX, e personagem-chave do Instituto de Estudos Avançados de Princeton em seus primeiros anos, em termos de criar uma visão integrada e internacional.

Weyl públicou obras técnicas e algumas gerais sobre espaço, tempo, matéria, filosofia, lógica, simetria e história da matemática. Foi um dos primeiros a conceber a combinação da relatividade geral com as leis do eletromagnetismo. Enquanto nenhum matemático de sua geração tenha aspirado ao 'universalismo' de Henri Poincaré ou Hilbert, Weyl chegou tão perto disso quanto possível. Michael Atiyah, em particular, comentou que para onde quer que olhasse numa determinada área, descobria que Weyl o havia precedido .

A semelhança de nomes levou por vezes a que fosse confundido com André Weil. Uma piada comum entre matemáticos é que, sendo ambos de grande envergadura científica, constituía-se num raro exemplo de caso onde tal confusão não ofendia a nenhuma das partes.

Citações Hermann Weyl

„It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship.“

— Hermann Weyl
Context: Space and time are commonly regarded as the forms of existence of the real world, matter as its substance. A definite portion of matter occupies a definite part of space at a definite moment of time. It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship. Introduction<!-- p. 1 -->

„It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought“

— Hermann Weyl
Context: It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought, a study which is dear to my heart. This could be done only by building up the theory systematically from the foundations, and by restricting attention throughout to the principles. But I have not been able to satisfy these self-imposed requirements: the mathematician predominates at the expense of the philosopher. From the Author's Preface to First Edition (1918)

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„Einstein's theory of relativity“

— Hermann Weyl
Context: Einstein's theory of relativity has advanced our ideas of the structure of the cosmos a step further. It is as if a wall which separated us from Truth has collapsed. Wider expanses and greater depths are now exposed to the searching eye of knowledge, regions of which we had not even a presentiment. It has brought us much nearer to grasping the plan that underlies all physical happening. From the Author's Preface to First Edition (1918)

„Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space.“

— Hermann Weyl
Context: The scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world, in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither "time" nor "space". Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space. Ch. 3 "Relativity of Space and Time"<!-- p. 217 -->

„Time is the primitive form of the stream of consciousness.“

— Hermann Weyl
Context: Time is the primitive form of the stream of consciousness.... If we project ourselves outside the stream of consciousness and represent its content as an object, it becomes an event happening in time, the separate stages of which stand to one another in the relations of earlier and later. Introduction<!-- p. 5 -->

„Kant was the first to take the next decisive step“

— Hermann Weyl
Context: In the field of philosophy Kant was the first to take the next decisive step towards the point of view that not only the qualities revealed by the senses, but also space and spatial characteristics have no objective significance in the absolute sense; in other words, that space, too, is only a form of our perception. Introduction<!-- p. 3 -->

„Matter... could be measured as a quantity and... its characteristic expression as a substance was the Law of Conservation of Matter... This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure.“

— Hermann Weyl
Context: The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. and certainty Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church... had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science "more geometrico". Matter... could be measured as a quantity and... its characteristic expression as a substance was the Law of Conservation of Matter... This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure. Introduction<!-- p. 1-2 -->

„It is the nature of a real thing to be inexhaustible in content; we can get an ever deeper insight into this content by the continual addition of new experiences, partly in apparent contradiction, by bringing them into harmony with one another.“

— Hermann Weyl
Context: It is the nature of a real thing to be inexhaustible in content; we can get an ever deeper insight into this content by the continual addition of new experiences, partly in apparent contradiction, by bringing them into harmony with one another. In this interpretation, things of the real world are approximate ideas. From this arises the empirical character of all our knowledge of reality. Introduction<!-- p. 5 -->

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„In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.“

— Hermann Weyl
Weyl, Hermann. Invariants. Duke Math. J. 5 (1939), no. 3, 489--502. doi:10.1215/S0012-7094-39-00540-5. http://projecteuclid.org/euclid.dmj/1077491405.

„It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum.“

— Hermann Weyl
Riemanns geometrische Ideen, ihre Auswirkungen und ihre Verknüpfung mit der Gruppentheorie (1925), as quoted/translated by Erhard Scholz, "Philosophy as a Cultural Resource and Medium of Reflection for Hermann Weyl" (2004)

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