Saturday, January 1, 2011

What a way to define mathematics...

mathematics can generalize any scheme, change it, and enlarge it. And yet, every time this is done, the result still forms only a part of mathematics. In fact, it is perhaps characteristic of the discipline that it develops through a constant self-examination with an ever increasing degree of consciousness of its own structure. The structure, however, changes continually and sometimes radically and fundamentally.

In view of this, an attempt to define mathematics with any hope of completeness and finality is, in [Stanislaw Ulam and Mark Kac's] opinion, doomed to failure.

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