Archive for April, 2013


April 22, 2013

Next month, Jean-Pierre Serre will deliver a series of talks in the Distinghuised Lecture Series at the Fields Institute on several new topics. At 86. [edit: the 3 videos have now appeared: great talks!]

Looking for mathematicians who were born before him in the MacTutor website, it seems that Freeman Dyson is still active at 89, and Louis Niremberg, at 88, too.

Very impressive, and certainly as inspiring as centenarians that run, or cycle, or teach fencing.

Perhaps the reader will, one day, do even better, who knows?

Some geometric elegance

April 14, 2013

From a XIVth century Arabic manuscript (from Gallica), based on a treatise by Theodosius of Bithynia. I do wonder what this particular page says…


Edwards on platonism and patents

April 9, 2013

This month, there’s a strange but stimulating paper by David A. Edwards in the Notices of the AMS. It’s short and I encourage you to read it and make up your own mind.

He argues that “One should be able to patent anything not previously known to man.“, including algorithms and mathematical formulas — which is currently not allowed on the grounds that “ ‘mere’ recognition of a theretofore existing phenomenon or relationship carries with it no rights to exclude others from its enjoyment“. Edwards sees this as a Platonistic argument, and says that “There is no economic basis for the distinction between discovery and invention“.


I personally do not hold Platonistic views at all, and feel that any thoughts human may have are indeed inventions, new ways of describing ‘reality’, and not discoveries of pre-existing things. For instance, nothing satisfies Newton’s laws exactly in the Universe, on the contrary it is a first approximation of some phenomenas in certain cases. And what about recognising that 3^2+4^2=5^2 is true? Isn’t there a good case to say that it was true ‘before we noticed it’? No, as far as I’m concerned. It is human notation. You work things out for the first time, you explore consequences of the chosen rules, but before stating them these statements have no status, they are certainly not ‘out there, pre-exisiting’.

So, while I wouldn’t agree with patentable mathematical formulas or physics laws, it wouldn’t be based on Platonistic grounds, but rather on freedom of thought: if author A finds a consequence of a set of axioms that was not known to others before, fine, it enters the realm of actual human thoughts. But A can’t stop others to infer that consequence for themselves later: independently some author B may well write that same formula. What would it mean that B infringed A’s patent on that idea when B never heard of A in the first place?  The only reasonable thing to do is an anteriority claim based on a published paper, and leave open the possibility of renaming the formula ‘the A-B theorem’ if it appears clearly enough that B indeed found it independently (and this of course abounds in the history of science). But certainly not a patent.