We were once so close to Heaven
Oct. 26th, 2009 01:13 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
matthewdalyI've been spending the weekend getting my math geek on. I have long thought that LaTeX deserved the Lisp Award for User Hostility in Otherwise Powerful Software. This has been largely muted by LyX, which is a GUI front end for LaTeX. They go out of their way to say that it isn't WYSIWYG, but what appears on the screen is really a great first-order approximation of the compiled output -- and not just PostScript anymore; you can also export to a PDF file and share it online with Acrobat. Here is a sample paragraph that that's pretty easy to create (at least once you've decided what it is that you want to say). Amazing!
But I digress.
I was playing around with transcribing my college notes into an electronic format when I came across a Math Studies Problem Seminar problem that I hadn't solved. (I had a lot on my plate that semester.) The problem was to find one or more interesting facts about antiprimes (often called "highly composite numbers", defined as numbers that have more factors than any number less than it) and to compute all antiprimes less than 100 without electronic devices. So I worked out a pretty routine algorithm that would do the latter part that needed two lemmas to justify it, and thought that those would be the interesting facts that I would prove. The first was routine (and is the first two observations about the prime decomposition of an antiprime given on the MathWorld link above if you were curious), but the second was harder. I wanted to show that if n is antiprime and greater than 1, then n has a prime factor p such that n/p is also antiprime. It seemed obvious from poring over the first few dozen antiprimes, but there wasn't an easy proof to be found. So I banged my head against that for a good long while, and then gave up and posted to xkcd's math forum to see if they could make anything of it. (Huh, in retrospect, Usenet is not only dead but the mourning period is over, because this is the first moment this weekend I've considered sci.math.) And after some other good people banged their heads for a while, damned if another of the good people there didn't find a counterexample.
362279431624673937974303738230488502933082643722886373107941760000
I know, why didn't I notice that before wasting the time of nice forum people, right? That is likely the biggest number that has ever been generated on my behalf. I suspect the hypothesis is more interesting than some boring old true one would be.
But I digress.
I was playing around with transcribing my college notes into an electronic format when I came across a Math Studies Problem Seminar problem that I hadn't solved. (I had a lot on my plate that semester.) The problem was to find one or more interesting facts about antiprimes (often called "highly composite numbers", defined as numbers that have more factors than any number less than it) and to compute all antiprimes less than 100 without electronic devices. So I worked out a pretty routine algorithm that would do the latter part that needed two lemmas to justify it, and thought that those would be the interesting facts that I would prove. The first was routine (and is the first two observations about the prime decomposition of an antiprime given on the MathWorld link above if you were curious), but the second was harder. I wanted to show that if n is antiprime and greater than 1, then n has a prime factor p such that n/p is also antiprime. It seemed obvious from poring over the first few dozen antiprimes, but there wasn't an easy proof to be found. So I banged my head against that for a good long while, and then gave up and posted to xkcd's math forum to see if they could make anything of it. (Huh, in retrospect, Usenet is not only dead but the mourning period is over, because this is the first moment this weekend I've considered sci.math.) And after some other good people banged their heads for a while, damned if another of the good people there didn't find a counterexample.
362279431624673937974303738230488502933082643722886373107941760000
I know, why didn't I notice that before wasting the time of nice forum people, right? That is likely the biggest number that has ever been generated on my behalf. I suspect the hypothesis is more interesting than some boring old true one would be.
no subject
Date: 2009-10-27 12:43 am (UTC)And to think that LaTeX was developed as user friendly front-end to TeX!
no subject
Date: 2009-10-27 02:05 am (UTC)LyX is a world apart. You'd have to go out of your way to commit a syntax error in a math equation. Plus, they installed MikTex and set up all the hooks perfectly for me and and and they automatically installed the AMS fonts too. Imagine, someone gets that Blackboard Bold fonts are something that the default mathematician would need. I think that any college math student should learn and use it. It might be a slight exaggeration, but I'll claim that it's faster to enter and maintain your math notes in LyX then it would be to write it out on paper, at least if it something that you would wind up transcribing at least once. On the other hand, it's still TeX, so I can use
my college roommate'smy TeX manual to remind me of which spacer is best for different bits and pieces.