maτhematica1 pr0spe¢ting.

i suppose that many mathematicians state theorems in a similar way as how gold prospectors once staked claims in the california gold rush of 1849.

the average prospector was as able-bodied as his peers; if he staked a claim on a good piece of land, then it was only because of circumstance.

some theorems are just waiting there and anyone can prove them. it's a matter of who proves it and puts it in print first. there's no guarantee of worth; one just stumbles upon the claim, decides that it may be worth the time and effort, and starts digging.

yesterday i drew up a very special case of some ideas i mentioned before. the setting is not at all generic -- the hypotheses are strong -- but i worked through it because it was the only case i suspected i could do.

for now, it feels like a piece of land with the stream that is almost dry. the ground is mostly loose soil and no rockface: no real chance of gold.

at the very least, i found it first. i get to see how much (or little) it's worth.

if proving theorems is like prospecting,
then conjectures are like hidden treasure ..

.. only there is competition for where it is hidden,
and everyone draws a different map, where X marks the spot! (: