I am an isolationist.
The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.
In the simplest array of digits [Ramanujan] detected wonderful properties: congruences, symmetries and relationships which had escaped the notice of even the outstandingly gifted theoreticians.
When the most abstract and "useless" disciplines have been cultivated for a time, they are often seized upon as practical tools by other departments of science. I conceive that this is no accident, as if one bought a top hat for a wedding, and discovered later when a fire broke out, that it could be used as a water bucket.
Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications.
The self-regulating mechanism of the market place cannot always be depended upon to produce adequate results in scientific research.
The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.
I have been married twice, and those were not the happiest times of my life. Part of the problem, quite frankly, is that when you get married, the romance disappears and the children arrive and the love is transferred. It shouldn't be that way, but too often it is transferred to the children.
My 3am wake up call sounds a lot different now. Sweeter. . .
You write some material, go up on stage and try it out; go back home and throw it in the trash can. And the next day do it again.
You can't be pro-business unless you're pro-education.