It is strange that we know so little about the properties of numbers. They are our handiwork, yet they baffle us; we can fathom only a few of their intricacies. Having defined their attributes and prescribed their behavior, we are hard pressed to perceive the implications of our formulas.
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.
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.
To be sure, mathematics can be extended to any branch of knowledge, including economics, provided the concepts are so clearly defined as to permit accurate symbolic representation. That is only another way of saying that in some branches of discourse it is desirable to know what you are talking about.
Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunately there is never a lack of mathematicians for the job of transforming delectable ingredients into a dish that tastes like a damp blanket.
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.
There are... scientific works - star catalogues, for example - which are not art; but the theoretical structures of Gauss, Einstein, or Maxwell are original, individual, "very personal" responses and expressions of exactly the same kind as the creative works of Beethoven or Dostoievski.