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Growth and Change in Mathematics

In: Infinite Processes

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  • A. Gardiner

    (University of Birmingham, Department of Mathematics)

Abstract

You may notice that the title (and the contents) of this and the previous chapter contradict the idea that mathematics consists of a fixed and unchallengeable stock of truths. Should this come as a surprise? How are mathematical ideas born? How do they grow? In what sense does mathematics itself “evolve”? There are as one might expect no easy answers. In the long term one simply has to keep such questions permanently in the back of one’s mind, ready to take advantage of any new example which might provide some unexpected insight. But in the short term, the challenge is to begin, somehow or other, to make sense of such questions. We should not perhaps expect at the outset to make much sense of historical examples, but we can at least begin by reflecting how our own view of mathematics has changed. If we do this, then it should soon become apparent that our own private view of mathematics is never rigidly fixed, but changes as we grow.

Suggested Citation

  • A. Gardiner, 1982. "Growth and Change in Mathematics," Springer Books, in: Infinite Processes, chapter 0, pages 13-23, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5654-0_2
    DOI: 10.1007/978-1-4612-5654-0_2
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