PURE MATHEMATICS

Pure mathematics is something I cannot professionally speak on, as I am a very simple-minded applied mathematician. Pure math involves largely proofs with some accompanying manipulations of symbols and equations. Applied math deals mostly with symbol manipulations within equations. Applied math is usually used in physics contexts and engineering contexts, and increasingly now is employed in chemistry and biology etc. applications. The dream of the applied mathematician is always to aspire to achieve results at an equal status with pure mathematics, with its precise language worded in to mathematical reasoning at the highest level. Pure mathematics is perhaps the highest form of beauty of human expression, and human creation, for correct proofs have eternal value and they represent eternally true statements that underlie the foundations of the allied fields of physics and chemistry and biology etc. The famous mathematician Perelman was quite eccentric, as pure mathematicians tend to be, and he did his greatest work on proving (a) the Thurston "Geometrization Conjecture" and followed this by proving the over 100 year old (b) Poincare conjecture by the extension of the results in (a). His eccentric demeanor led him to work alone in isolation on these very important unsolved problems in pure mathematics. Earlier in his career Perelman often collaborated on projects and he had several important proof-type results from this early period then as well. Perelman's story is one of the rare examples of professional and highly technical work in the mathematical sciences, not being performed in a conventional way at a conventional University setting or Institute setting etc....where Perelman dropped out from activity with the local Institute he had belonged to and chose to work in isolation in an apartment that his mother owned. It reminds one of Einstein's miracle year of 1905, about 100 years before Perelman's work was carried out, in which Einstein did his miraculous work while working as a patent examiner at the Swiss Patent Office in Bern. Finally, in closing, I note that one of William Thurston's colleagues at Cornell University, named Allen Hatcher, was the mathematician that moved me the most in to becoming an applied mathematician, after taking his 400 level course called "Applicable Math I" in Fall, 1990.