On 8/4/07, David Wilson <davidwwilson@comcast.net> wrote:
Most people seem aware of their mathematical limitations, but a minority of circle-squarers, crackpots, and isolates of varying proficiency convince themselves that they are breaking new ground when in truth they are usually either retreading the beaten path or forging a new path to La La Land. I've had run-ins with Archimedes Plutonium and the Smarandache crowd and others of this sort, and my advice is not to acknowledge them. The benefits of dispossessing these people of their cherished illusions do not justify the effort.
Marc has no doubt studied this phenomenon in more detail than I have. For what it's worth, I'd say that most people are driven to study mathematics --- or to any other intellectual endeavour --- by a mixture of three motives: to indulge their curiosity; to earn approval from others; and (maybe) to control their environment. The people encountered on math-fun will as a rule be motivated by curiosity; the crackpots by approval. It's the difference between wanting to learn maths and just wanting to be "a mathematician". It follows that, in the unlikely event that one manages to put a serious dent in their self-image, they will respond by attempting to reinforce it with an ever-intensifying barrage of self-justification. [Or just possibly worse.] Which is, of course, exactly what happens. Fred Lunnon