This attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does.
Interpretation
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.
In practice
A lecturer may use this quote to illustrate the importance of understanding mathematical functions in a classroom.
Most of us think of pride as self-centeredness, conceit, boastfulness, arrogance, or haughtiness. All of these are elements of the sin, but the heart, or core, is still missing. The central feature of pride is enmity - enmity toward God and enmity toward our fellowmen.
Nobody gets argued all the way into becoming a believer on the sheer basis of logic and reason. That requires a leap of faith.
There's nothing that makes you so aware of the improvisation of human existence as a song unfinished. Or an old address book.
Meditation is an insight that all goals are false. Meditation is an understanding that desires don't lead anywhere. Seeing that... And this is not a belief that you can get from me or from Buddha or from Jesus. This is not knowledge; you will have to see it. You can see it right now!
This survival of the fittest implies multiplication of the fittest.
Hegel was right when he said that we learn from history that man can never learn anything from history.
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