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Opinion 2: People who believe that Applied Math is Bad Math are Bad Mathematicians

Written: May 2, 1995.

I was just kidding. They are not bad mathematicians, because they are not mathematicians at all. A true mathematician has respect for all parts of mathematics, and does not believe in arbitrary divisions into `Pure', `Applied', `Theoretical',`Practical', `Conceptual', `Computational'. Mathematics is a Web, an infinite dimensional tapestry with everything intertwined.

Some people, like G.H.Hardy and Paul Halmos, deceive themselves, like Plato and Aristotle, that `pure', whatever it means, is purer than `applied', whatever it means. The fate of Platonic mathematics is nowadays quickly joining the fate of Platonic, a priori, non-experimental, physics.

My ranting and raving is a propos Halmos's article `Applied Mathematics is Bad Mathematics' reproduced in his`Selecta' volume. Paradoxically, as Peter Doyle pointed out to me, the example of pure math he gives there: Tutte et. al's `squaring the square', was motivated by `applied' math, i.e. Electrical Circuits.

On second thought, both Hardy and Halmos are mathematicians. Hardy, in spite of his philosophical errors, is still a great mathematician, even in the broad sense of the word. Halmos is also a good mathematician, he just sometimes says nonsense.

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It is six in the morning. The house is asleep. Nice music is playing. I prove and conjecture.

Paul Erdos

The mystery, as well as the glory, of mathematics lies not so much in the fact that abstract theories do turn out to be useful in solving problems but in that wonder of wonders, the
fact that a theory meant for solving one type of problems is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These
coincideness occur so frequently that they must belong to the essence of mathematics.

Gian-Carlo Rota

written by Joel H. Spencer (possibly), in the book <Probablistic Method>.

In the summer of 1985 I drove Paul to what many of us fondly remember as Yellow Pid Camp - a mathematics camp for talented high school students at Hampshire College. It was a beautiful day - the students loved Uncle Paul and Paul enjoyed nothing more than the company of eager young minds. In my introduction to his lecture I discussed the Book but I made the mistake of describing it as being "held by God". Paul began his lecture with a gentle correction that I shall never forget. "You don't have to believe in God," he said, "but you should believe in The Book."

We are as forlorn as children lost in the wood.  When you stand in front of me an look at me, what do you know of the grief's that are in me and what do I know of yours.  And if I were to cast myself down before you and tell you, what more would you know about me that you know about Hell when someone tells you it is hot and dreadful?  For that reason alone we human beings ought to stand before one another as reverently, as reflectively, as lovingly, as we would before the entrance to Hell.

--said to be written in his 20's

Today I start reading Kafka's letters to his lover,  Milena Jesenská

With Felice Bauer (Budapest, July 1917)

his photo album here:

http://www.cs.technion.ac.il/~eckel/Kafka/kafka.html