The Mathematical Intelligencer

, Volume 23, Issue 1, pp 16–29 | Cite as

Between discovery and justification

Department Mathematical communities

Abstract

This column is aforum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.

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References

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    The mathematics department may be the only spot on campus where belief in the reality of the external world is not only optional but frequently an annoying distraction.Google Scholar
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    Unless you claim, like the present French Minister of Education, that real numbers exist in nature, while imaginary numbers were invented by mathematicians. Thus tt would be a physical constant, like the mass of the electron, that can be determined experimentally with increasing accuracy, say by measuring physical circles with ever more sensitive rulers. This sort of position has not been welcomed by most French mathematicians.Google Scholar
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    Chapter 3 of Kitcher’sop. cit. [18] is devoted to a refutation of Kantian or Platonist intuition as a means to mathematical knowl edge, and what we mean when we use the word informally is presumably even less defensible. The quotation is fromFashionable Nonsense, pp. 143-44, note 183.Google Scholar
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    As Barry Mazur reminded me, “interest” in this context is generally used as shorthand for an intellectual criterion, such as “enhancement of understanding” (see Thurston’s comments, quoted below). Such a criterion is by nature not well-defined, yet we have the sense that we know what it means.Google Scholar
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Copyright information

© Springer Science+Business Media, Inc. 2001

Authors and Affiliations

  1. 1.Université de Paris VIIParis Cedex 05France
  2. 2.Department of MathematicsUniversity of Massachusetts LowellLowellUSA

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