The Four Cultures of Mathematics

A well-known point of agreement amoung mathematicians is an often sigted discussion by Tim Gowers, namely “Two cultures of mathematics“.

It has, however, been argued that there are other, perhaps more accurate, divisions of mathematicians. I sight Peter Cameron’s view that “those who delve
deep and those who range more widely.” This is, of course, not entirely incompatable, but it does rais several questions. If these two cultures both eist ae they entirely independent, ie is it more sensible to classify mathematicians as points on aplane, rather like the well known political compass? Or it simply the case that one is right and the other not, or worse that neither is right? If neither are right, then what is right? Is this case division a help or a hinderece? (I suspect the latter.)

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Upload an Avatar

…goes the imortal cry, but do wordpress actually know what they’re talking about? Acording to WordPress’s help pages:

An avatar is a small image that appears when you post to the forums and when you comment on any posts anywhere. It’s your profile picture. The avatar should be 128 * 128 pixels square. It will be smaller when used in comments so do check how good it looks when it shrinks.

The actualy concept of an avatar, however, goes back much further. In Hindu philosophy an avatar is the ‘descent’ or incarnation of a divine being (deva) or the supreme being (God) onto planet Earth. The Sanskrit word avatāra literally means “descent” (avatarati) and usually implies a deliberate descent into lower realms of existence for special purposes. There have been many people over the years claiming to be avatars, usually quite harmlessly.

The concept of an avatar was most recently re-invoked by the author Scott Adams in his wonderful books “God’s Debris” (which is freely available online, if you click on the link) and its sequeal “The Religion War” dicussing the philosophy of the mysterious, powerful and subtle control probabilities exert upon the world and our daily lives (taking a view largely justified through a sophisticated ammendment to Occam’s Razor). (And yes that’s Scott Adams as in the infamous Dilbert Comics.)

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Starting From An Early Age

There has been much chatter recently about early life experiencs of mathematics and the effect it has on subsequent learning and understanding.

Hence this research is rather well timed.

It would be interesting to survey how wide spread an early introduction to the subject correlates with later academic achievment in the subject.

(Personally I certainly remeber at comparatively young age forcing my dad to break a sweat struggling to remeber school-boy trigonometry)

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