That sounds like a great idea! Just keep in mind that Galois theory is gaduate-level algebra in most places in the US; hence, an explanation of the needed theory would be a good thing. If you’d like to submit your writing sample on the quintic, go ahead.

Cheers.

]]>For me, I think we should write on complicated subjects, especially those whose complexity discourages laymans to even look at it, in an easier (yet not incomplete) perspective.

I think it would be better to start with insolvability of quintics (my favorite subject, lol). I know, many people might think that galois theory might be too broad of a subject to introduce in it’s fullest, but it’s incorrect that we need galois theory in proving insolvability of quintics. Basic group theory (upto Lagrange) is sufficient to go through Abel-Ruffing-Kronecker line. This so-called pre-Galois _ad-hoc_ proof is very rare and I never saw it described in an openly available source in the internet, i.e., blogs and all. The ones who claim it is Abel-Ruffini just gives a brief idea of Galois’ proof (without FT of Galois theory!) but that’s just ridiculous.

In particular, we might want to focus on rare mathematical subjects and explain them thread bare and elementarily. I am speaking strictly of expository mathematical writings here, just to note.

]]>http://www.scottaaronson.com/blog/?p=1753#comment-103427

Max Tegmark is an interesting fellow. I think he is the first to admit his MUH is more “idea” than “fact”, and from the standpoint of “hard science” perhaps belongs more properly to “metaphysics” (an extremely rare use of BOTH meanings of that word here!).

Just so, there is a discipline known as “mathematical philosophy” which one does not need to be conversant in to be a working mathematician. While such a field may not have much to say in terms of “actual math”, it is sometimes good to ask ourselves: “what is it we are doing, and why are we doing it this way?”. Our activities do not occur in an intellectual vacuum, our beliefs and feelings inform the choices we make.

For example, some mathematicians exhibit a strong tendency towards “minimalism”, and write in as terse a style as possible. Thus the ease with which they communicate is drastically affected by an aesthetic consideration, or working within a system with minimal assumptions. Is logic developed through use of alternative denial “better” or “worse” than the classical connectives? I suppose it depends on your point of view, and this is a subjective, not objective, matter.

Of course, many “meta-mathematical” and/or philosophical topics deals with foundational issues. “Up here” computing Fourier coefficients, for example, the “truth” of the continuum hypothesis isn’t particularly relevant. On the other hand, one ought to be leery of “taking things on faith” in a logic-based discipline such as mathematics (such a position is absolute anathema in science, where empirical substantiation is the sine qua non), so the things we take as given ought to be examined, from time to time.

]]>Once comment though, after making the edit I was left “stranded” on the edit page and had to use my browser’s back button to escape. ðŸ˜€

]]>edit: Test edit…

]]>