reading & name-dropping.

life will surprise you, and so will mathematics. sometimes the least likely methods become convenient and useful.

for example, i never thought that i'd ever browse through J. Milnor's paper about smooth structures on exotic spheres.

at the time ..2 years ago?.. it was relevant to my work. to understand a few of those six pages that Milnor wrote (which i still don't fully or mostly understand, to be honest) it took a few months of reading about differential geometry and re-reading several chapters from differential topology) by M. Hirsch.

speaking of which, the Hirsch book is quite good. i'd recommend it to anyone.

i never thought that the banach-alaoglu theorem would be so useful in my current work, and i never thought i'd ever need to learn about the weak-* operator topology for linear maps between dual Banach spaces.

now, to the point:

today i browsed through an article i found on JSTOR. it's J. Nash's paper on isometric embeddings of smooth manifolds.

i never thought i would read anything that Nash has written. i don't know why. maybe the film made him larger than life and reasonably handsome (if you're a fan of russell crowe, that is) and i forgot that he's a mathematician and he writes papers just like any other mathematician active in research.

[shrugs]

at any rate, it's back to work for me, and i have to find a different paper. apparently the nash paper doesn't have the result i want. q:

added @ 15:15: never mind. i don't understand basic logic, and there wasn't a reason to think about isometric imbeddings at all.