When the most abstract and "useless" disciplines have been cultivated for a time, they are often seized upon as practical tools by other departments ….

The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new memb….

It is unnecessary to understand electromagnetic theory before wiring a lamp or to study physics in order to repair a pump. We count on our fingers an….

There are... scientific works - star catalogues, for example - which are not art; but the theoretical structures of Gauss, Einstein, or Maxwell are o….

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 d….

In the simplest array of digits [Ramanujan] detected wonderful properties: congruences, symmetries and relationships which had escaped the notice of ….

To be sure, mathematics can be extended to any branch of knowledge, including economics, provided the concepts are so clearly defined as to permit ac….

Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunate….

Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, ye….

The self-regulating mechanism of the market place cannot always be depended upon to produce adequate results in scientific research..

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 i….

The most painful thing about mathematics is how far away you are from being able to use it after you have learned it..