## - On "Useless Knowledge" - permalink

Published On: 02/10/17 Written By: Muhammad It has often been said that certain types of knowledge are "useless". All sorts of knowledge have been accused of this at some time or another. Despite the obvious overall utility of mathematics,puremathematics in particular has often been the target of these criticisms. It's very easy to turn up examples of people saying this:

- This position can be seen being argued for on Physics Forums of all places.
- The blog Math with Bad Drawings saw a need to defend pure mathematics in its own way.
- The question of the usefulness of pure mathematics has also been raised on Quora.
- The issue has also come up in
*The Journal of Mathematics and Statistics*. - The book
*A Mathematician's Apology*by G.H. Hardy basically centers around the notion that much of higher mathematics is "useless" but should be done for its own sake regardless.

"When the mathematician makes his calculations or looks for new relations among numbers, he does not look for truth with a practical purpose. To cultivate science only for its practical purpose is to despoil the soul of science. The theory that we study today, and that appears to us impractical, might have implications in the future that are unimaginable to us. Who can imagine the repercussions of an enigma through the centuries? Who can solve the unknowns of the future with the equations of the present? Only Allah knows the truth. And it is possible that the theoretical investigations of today may provide, within one or two thousand years, precious practical uses. "It is important to bear in mind that mathematics, besides solving problems, calculating areas, and measuring volumes, also possesses much more elevated purposes. Because it is so valuable in the development of intelligence and reason, mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. "Mathematics is, in conclusion, one of the eternal truths and, as such, raises the spirit to the same level on which we contemplate the great spectacles of nature and on which we feel the presence of God, eternal and omnipotent. As I have said, O illustrious Vizier Nahum ibn-Nahum, you have made a slight error. I count the verses of a poem, calculate the height of a star, measure the size of a country or the force of a torrent, and thus I apply the formulas of algebra and the principles of geometry, without concerning myself with the profit I might earn from my calculations and studies. Without dreams or imagination, science is impoverished. It is lifeless."

- Fast numerical techniques, such as the use of the Chinese remainder theorem, which make all sorts of other computation more efficient, or possible, including the others on this list.
- Pseudorandom number generation, handy for all sorts of things from games to evolutionary algorithms.
- Hash functions, which make it possible to map data structures other than single integers to other values in computing (briefly put, a very important abstraction).
- And, of course, modern cryptography, which makes all of e-commerce a possibility at all.