Sunday, June 30, 2013


a mathematician with a computational orientation

You can keep counting forever. The answer is infinity. But, quite frankly, I don't think I ever liked it. I always found something repulsive about it. I prefer finite mathematics much more than infinite mathematics. I think that it is much more natural, much more appealing and the theory is much more beautiful. It is very concrete. It is something that you can touch and something you can feel and something to relate to. Infinity mathematics, to me, is something that is meaningless, because it is abstract nonsense.
Doron Zeilberger, "To infinity and Beyond", BBC2 Horizon, 9:00pm GMT Feb. 10, 2010

[Contemporary Pure] Math is far LESS than the Sum of its [Too Numerous] Parts, and Beware of Pure Mathematicians Preaching How Important Math is for Science and Technology. Of Course it is, but NOT their, Soon-To-Be Obsolete and PEDANTIC Style of Doing Math, but Rather the Way Physical Scientists Practice It: Experimentally, Heuristically and Non-Rigorously.

Mathematics is so useful because physical scientists and engineers have the good sense to largely ignore the "religious" fanaticism of professional mathematicians, and their insistence on so-called rigor, that in many cases is misplaced and hypocritical, since it is based on "axioms" that are completely fictional, i.e. those that involve the so-called infinity.

Platonism is unsatisfactory because it violates our instinctive drive to obey Ockham's principle of parsimony.

Intentionalism says that pure mathematics is a description of finite structures consisting of finitely many imagined objects.

The term intentionalism is chosen for its contrast with extensionalism which accepts actually infinite sets and leads naturally to Platonism.

Jan Mycielski, on The Meaning of Pure Mathematics*

Computicians are the class of mathematicians who think the jig is up on infinity and that the (finitary and probabilistic) computational way — computics — is the future of mathematics.

Count me in.

* A theorem by Mycielski proves that every theorem of infinitary mathematics has a finitary counterpart.