reasonably-paradoxical

[reasonably-paradoxical]

Ohhhh ...

When I set up this blog, just in time to get locked out of it (passwords got lost), there were things I didn't know about how Tumblr's system worked, and I just got reminded of one of them. Because this is my primary blog, I can't invite other users to contribute to it.

For the blog that I intended for this to be, that's not good. So, I'm going to re-purpose this blog and turn it into a personal journal, and recreate this blog as a secondary blog. That way, someday, when I make the big jump up from being an adjunct and turn into a real professor, I'll be able to knock on a few doors, find a few collaborators and invite them to join.

I probably should narrow the focus, too. My interests in Mathematics do broaden with time, and I do intend to return to Geometry (my first love in Mathematics), but nobody has been a mathematical generalist since, when ... the time of Gauss? Throwing all of the counterexamples in Mathematics together into one blog would have been a severely dated idea from the very first day on which the word "blog" meant anything. Or "Internet" for that matter.

I started out in grad school thinking that maybe I was going to be a topologist or an algebraist or a logician, or (here was a little foreshadowing) a mathematical physicist (yes, that's applied math), but feeling absolutely certain that I'd want nothing to do with Statistics or Probability. I still have a laugh a little about that, and then frown for a bit, as I remember why that was. I got a horrible introduction to those last two subjects which left with a dislike for them that lasted for a long time. I'm sure that still happens, today, and that something needs to be done about that.

Relatively quickly, as my studies progressed, I moved, first away from Algebra and Topology toward Analysis, and from there found my way into Probability, after getting a far better (and more rigorous) introduction to that subject thanks to my distributional requirements. Today, my main areas of interest are in Analysis and Probability, and their applications. This will probably be reflected in the first secondary blog (or blogs) I set up. That's what I will focus on.

I might still do a topology blog, because those counterexamples can be so delightfully strange and there is a tie-in to Analysis, but if so, that will come later. As for work in Logic, Set Theory and Foundations in general, as delighted as I was by all of that in undergrad, I just don't have time for it, lately. Usually. Sometimes, I'll still wander in that direction, and I'll maybe talk more about that later, after a few papers have been published.

I'll post this, and then change the url from "counterexamples-blog" to something more fitting for what is about to turn into something more purely personal.

[reasonably-paradoxical]

Self-Explanatory

A counterexample, in Mathematics, is a mathematical object that, merely by existing, shows that a proposed theorem can not be valid, the failure of validity often being quite strikingly counterintuitive. The construction of these objects serves an intellectual purpose, in that they set limits on that which is provable. They serve an aesthetic purpose, in that they can be strikingly beautiful in their own way. They also serve an emotional purpose, in that they can be wonderfully effective in quieting whiny students, when the students confront the grader over the points they lost in making an invalid assumptions in some of the proofs they submitted, and say "but thaaaaat's obviouuuuuuus!", reducing the probability of the hapless grader developing an ulcer by the end of the week. Of course, it's a dead on certainty that he'll have one by the end of the year, but by then he should be able to go home and have his relatives nurse him back to health, just in time for another year of pulse pounding action in the back of the library, red pen in hand and papers stacked high. Yes, live the dream. Oh, dear G-d. This is a companion to "Doing Your Homework", a blog on which I'll be working a variety of math problems.