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Key inventions

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In solidarity with rwenzori: Κοπρος φανεται

« Reply #15 on: July 22, 2012, 08:58:19 AM »

An invention is the discovery of a way to do or make something. :-)
Which is identically true in the realm of mathematics, the only differences being the latter’s formal rigour and that its subject matter exists as pure idealisations.  As said, all possible unrealised inventions in the real world already exist “out there” in a sense as potentialities, albeit that endless variations on a given theme are conceivable (e.g. there are many different toaster designs all having much the same purpose), whereas mathematical constructs typically don’t leave much, if any, of the same kind of wriggle room.  We discover mathematical objects and the rules for manipulating them, just as we discover the constituents of our universe and the natural laws that determine their nature and behaviour.  In both worlds, we discover truths; however, when we rearrange things in the former into something new and useful, we call it “invention” while in the case of the latter we still want to call it “discovery” even though the novelty in both cases only existed before as unrealised potentials.  On that basis, the only vaguely valid reason I can think of for objecting to the use of the term “inventing” in mathematics is a semantic one:  “Inventing” may carry with it a negative subtext of “artificiality” or “fabrication.”  To underscore the point, there are mathematical methods that have been patented.  Can you patent a discovery?

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