Harrelson News–2000
Mathematical Maxims and Minims
"Principles" of Mathematics
Principle of Conservation of Ignorance– A false notion once arrived at is not easily dislodged.
– George Cantor
Principle of Existence of Heaven and Hell– God exists because mathematics is consistent; the devil exists because we cannot prove the consistency.
– Hermann Weyl
– Albert Einstein
Principle of Least Astonishment– A theorem is true if everyone would be astonished if it were false.
Penultimate Principle– Everything is a special case of something more general.Ultimate Principle – This principle is so perfectly general that no specific application of it is possible.
Surprising!
Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contribute something to human though even more lasting than great literature, since it is independent of language.
– E.C. Titchmarsh
Normal Space
This nomenclature is an excellent example of the time–honored custom of referring to a problem we cannot handle as abnormal irregular, improper, degenerate, inadmissible and otherwise undesirable.
– John Kelley
Metric Spaces
Professor: What do you do when you have a metric space?
Student: You complete it.
Professor: Excellent! Now, what do you do next?
Student: I don’t know.
Professor: You name it!
Mathematics, a Game?
Not truth, not certainty. These I forswore in my novitiate, as young men called to holy orders must abjure the world. “If,..., then...”, this only I assert; and my successes are but pretty chains linking twin doubts, for it is vain to ask if what I postulate be justified, or what I prove possess the stamp of fact. Yet bridges stand and men no longer crawl in two dimensions. And such triumphs stem in no small measure from the power this game, played with the thrice attenuated shades of things has over their originals. How frail the wand, but how profound the spell.
– Clarence R. Wiley, Jr.
One Last Request
It so happened that a mathematics professor and a former student had both been convicted of heinous crimes and were awaiting execution on Death Row. According to custom each was given a chance to make one last request. The mathematics professor thought that he would like to give one last lecture on mathematics. The request was granted provided that the lecture be given to the other prisoners on Death Row. When the former student heard of the professor’s last request, he said “that makes my last request easy, I want to be executed before the professor’s lecture.”
Physicists and Mathematicians
Physicists know what's important but they don't know what is true. Mathematicians know what is true but they don't know what's important.