25 JUN 2013 by ideonexus

T T T=<em>N</em>

Occasionally he made a comment similar to Archimedes' "Eureka!" about a discovery, as he did when he wrong T T T=N. This is part of number theory, the field that Gauss called the Queen of Mathematics. A triangular number T is a number that you can get by adding up a string of consecutive whole numbers beginning with one. The number 6 is triangular because you can get it by adding 1 2 3, and 15 is triangular because you can get it by adding 1 2 3 4 5. The number 5,050, the sum of the first 100...
Folksonomies: mathematics
Folksonomies: mathematics

Gauss' beautiful mathematical discovery.

18 MAY 2012 by ideonexus

Teaching is a Waste of Time

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his preciou...
Folksonomies: education
Folksonomies: education

Quoting Carl Friedrich Gauss: Students who learn by lecturing go on to merely collect more facts, one who expands the boundaries of a field teaches themselves.

01 JUN 2011 by ideonexus

Carl Sagan's Insights from Smoking Marijuana

I find that most of the insights I achieve when high are into social issues, an area of creative scholarship very different from the one I am generally known for. I can remember one occasion, taking a shower with my wife while high, in which I had an idea on the origins and invalidities of racism in terms of gaussian distribution curves. It was a point obvious in a way, but rarely talked about. I drew the curves in soap on the shower wall, and went to write the idea down. One idea led to anot...

It is difficult to record the insights in such a way as to have them appeal to the sober mind, but Sagan, with much effort, got 11 essays out of an insight found while high.