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This attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does.
Timothy Gowers
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Interpretation

What this quote means

This quote emphasizes the functional nature of mathematical objects, suggesting that their identity comes from their utility and actions.

Timothy Gowers highlights a perspective in mathematics where the definition of a mathematical object is rooted in its function or role in operations, rather than merely its physical or abstract representation. This viewpoint encourages a pragmatic approach to understanding mathematics, focusing on what these objects can accomplish in various contexts rather than solely their theoretical properties.

Themes

MathematicsFunctionalityAbstractionPhilosophyUtility

In practice

Example use cases

A lecturer may use this quote to illustrate the importance of understanding mathematical functions in a classroom.

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Quote by Timothy Gowers | QuoteProject