Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
Hermann WeylRead
Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]
Interpretation
What this quote means
Understanding mathematics requires knowledge of its historical development and foundational concepts.
Hermann Weyl emphasizes the importance of historical context in understanding contemporary mathematics. He argues that the achievements and aims of modern mathematics are deeply rooted in the concepts and methods established by earlier generations, including those from ancient Greece. Without this understanding, one cannot fully appreciate the significance of mathematical progress made in the past 50 years.
Themes
MathematicsHistoryEducationProgressKnowledge
In practice
Example use cases
In a lecture on mathematical philosophy, one might use this quote to emphasize the importance of historical knowledge.
More from Hermann Weyl
All quotes →We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.
Hermann WeylRead
Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.
Hermann WeylRead
You can not apply mathematics as long as words still becloud reality.
Hermann WeylRead
Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.
Hermann WeylRead
Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.
Hermann WeylRead
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