Some my friends on FB started to discuss the nature and definition of Mathematics.<\/p>\n
I do not know a satisfactory definition of mathematics but I am happy to share my small collection of descriptions of mathematics (prepared a few years ago for Quora); some of them sound as attempts to define mathematics.<\/p>\n
I. Mathematics is an exact language for description, calculation, deduction, modelling, and prediction \u2014 more a systematic way of thinking than a set of rules.<\/p>\n
II. Using a legal analogy, mathematics is a language for writing contracts with Nature that Nature accepts as legally binding.<\/p>\n
III. The practical importance of mathematics lies in its ability to describe the real world.<\/p>\n
The real world consists of what matters. The word \u201cmatter\u201d as a noun is used for what the physical world is made of. But if we ask, \u201cWhat\u2019s the matter with Anne?\u201d we may be asking about a physical ailment, or we may be asking about an idea that is causing Anne to behave strangely. Ideas matter.<\/p>\n
The whole point of mathematical education is to make ideas real for students, ideas that were not real for them before. Ideas like fractions, for example. The fact that 2\/3 is smaller than 3\/4 matters in the real world.<\/p>\n
IV. Mathematically educated people are stem cells of a technologically advanced society. Because of the universality of mathematics, mathematicians and well educated users of mathematics are flexible in applying and inventing tools for work in technological environments which never existed before.<\/p>\n
V. Learning mathematics involves the profound assimilation of intellectual and aesthetic criteria as well as practically orientated ones. The very difficulty in learning mathematics makes it a personality-enhancing experience.<\/p>\n
[The above are borrowings from David Corfield, Tony Gardiner, Michael Gromov, Frank Quinn, David Pierce \u2014 I do not remember now in which order.]<\/p>\n
VI. Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. \u2014 Vladimir Arnold<\/p>\n
VII. Mathematics is the music of reason. \u2014 James Joseph Sylvester<\/p>\n
VIII. Mathematics: solving tomorrow’s problems yesterday. \u2014 Rob Wilson<\/p>\n
I\u0425. Mathematics is the study of mental objects with reproducible properties. \u2014 Philip J Davis and Reuben Hersh<\/p>\n
X. Finally, my own extension of the thesis by Davis and Hersh:<\/p>\n
Mathematics is the study of mental constructs with reproducible properties which imitate the causality structures of the physical universe \u0430nd are expressed in the human language which evolved for social interactions.<\/strong><\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
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