Posted by: Alexandre Borovik | December 20, 2010

My tentative take on a description of mathematics

Mathematics is an exact language for  description, calculation, deduction, modelling, and prediction  – more a systematic way of thinking than a set of rules.

Mathematically educated people are stem cells of the technologically advanced society.  Because of universality of mathematics, mathematicians are flexible and armed with tools for work in technological environments which never existed before.

At a personal level, mathematics is the music of reason. Learning mathematics involves deep assimilation of aesthetic criteria and efficient patterns of thinking.

This should be perhaps be read in conjunction with Definition of Mathematics, according to Confederation of British Industry.

Your opinion? Please give your definition /description of mathematics.

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  1. All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and by other institutions dealing with missiles, such as NASA). (V.I.Arnold)

  2. I seem to spend a lot of time trying to convince people that mathematics is not “all about numbers”, which of course leads to the question of what it IS all about. To this end, I tried to think up a definition completely free from any reference to numbers, or any of the words which tend to conjure up visions of numbers (“quantity”, “calculation”, etc.). My best stab was:

    Mathematics: the logical study of the abstract, and of the concrete through abstraction.

    The two parts of this definition give what I think of as “pure mathematics” and “applied mathematics” respectively. (I realise this doesn’t quite line up with the current “conventional” distinction between pure and applied, in which the solution of the most esoteric differential equation is “applied” but parts of abstract algebra or combinatorics driven by direct applications in computer science remain “pure”.). I also realise this definition takes mathematics closer to philosophy than some people might be comfortable with (one might argue whether it excludes “cogito ergo sum”, for example?). Other objections….?!

  3. Another Arnold’s aphorism is even better:

    Mathematics is part of physics. Physics is an experimental science, part of natural sciences. Mathematics is a part of physics where experiments are cheap.

  4. [...] Maths as stem cell. [...]

  5. Certainty (a certainty that admits of degree) figures centrally in mathematics, certainty of steps in reasoning and of results (final steps in reasoning). Deduction is thus central to mathematics. (It is questionable whether mathematical deduction can, in all cases, be rendered as, or reduced to, syntactical manipulation.) Since some perceptions can be certain, a way is cleared for claiming that geometry using diagrams (including traditional geometry) can be certain and genuinely part of mathematics. Of course, talk of certainty of mathematics and especially certainty of some perceptions is controversial, but not without precedent.

    Of course, any definition or description of mathematics is bound to fall short. Mathematics is monumentally complex.



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