Slowly, without fanfare, and with an alliance built with the emergent post transistor age discipline of computer science, Category theory looks set to become the dominant foundational basis for all mathematics. In an article in Science News, Julie Rehmeyer describes Category Theory as "perhaps the most abstract area of all mathematics" and "where math is the abstraction of the real world, category theory is an abstraction of mathematics" (link ) Set theory and the ascending magnitude of infinities that were unleashed through the crack in the door that was represented by Cantor's diagonal conquered all before them. Of course that is exactly what has happened. Under attack from establishment figures such as Kronecker during his lifetime, Cantor would not have believed that set theory would become the central edifice around which so much would be constructed. But then neither could Cantor, have dreamt about his work on Set theory being adopted as the central pillar of "modern" mathematics so soon after his death. Neither Eilenberg nor Mac Lane could have thought that Category theory, which was their attempt to link topology and algebra, would become so pervasive or so foundational in its influence when they completed and submitted their paper in those dark days of WW 2. Whether we take our inspiration from Hardy or Dirac, or whether we experience a gorgeous thrill when encountering an austere proof that may have been confronted thousands of times before, the confluence of simplicity and beauty in maths may well be one of the few remaining places where the commonality of the "eye" across a spectrum of different beholders remains at its strongest. ![]() I, for one, don't doubt cross disciplinary excellence is alive and sometimes robustly so, but the industrially specialised silos that now create, produce and then sustain academic tenure are formidable within the community of mathematicians.īeauty, in the purest sense, does not need to be captured in a definition but recognised through intuition. ![]() ![]() In the 70 odd years since Samuel Eilenberg and Saunders Mac Lane published their now infamous paper "A General Theory of Natural Equivalences", the pursuit of maths by professionals (I use here the reference point definition of Michael Harris - see his recent publication "Mathematics without Apologies" ) has become ever more specialised. That might sound a little surprising, when, after all, what could be more objective than mathematics when thinking about truth, and what, therefore, could be more natural than for beauty and goodness, the twin accomplices to truth, to be co-joined ? Beauty, even in Maths, can exist in the eye of the beholder.
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