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Mathematics: Invented or Discovered?

2 May 2014, 22:30 UTC
Mathematics: Invented or Discovered?
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The empirical sciences, like physics and chemistry, are partially invented and partially discovered. Although the empirical observations are surely discovered, the models that describe them are invented through human ingenuity. But what about mathematics which is based on pure thought? Are its results invented or discovered?
Not surprisingly there are different views on this topic. Some people maintain that mathematical results are invented, others claim that they are discovered. Is there a universe of mathematical results just waiting to be discovered or are mathematical results invented by the mathematician and would disappear, like a fairy tale, when mathematicians vanish in the heat death of universe when all the available energy is used up? Invented or discovered? Perhaps some results are invented and others discovered. There is, however, a third view, namely that mathematics is game played by manipulating symbols according to well defined rules. At some level this is probably true. All those who prefer Monopoly,® put up your hands!
What are the foundations of logic? Bertrand Russell (1872 – 1970) and Alfred Whitehead (1861 – 1947) tried to derive mathematics from logic. The result was the book: Principia Mathematica (1910), a real tour de force. Their derivation still required ...

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