The Narrow Road

May 1, 2007 1:46 PM

The Narrow Road : in which a professional mathematician guides you through pure mathematics (and touches on tangential issues).
posted by phrontist (10 comments total)

This is one of my favorite (and newly discovered) blogs. Clean design, good writing, references to other sites in context (and not as a substitute for content). Where as much of my time surfing is a postmodern nightmare of mindlessly tiny snippets linked together to form a substanceless attention deficit porridge that spends much of it's time thoroughly getting off on itself - finding stuff like this reminds me that the medium can do something substantive.
posted by phrontist at 1:58 PM on May 1, 2007

Ooooh. I feel some nerding coming on.
posted by chillmost at 2:15 PM on May 1, 2007

I prefer my mathematicians amateur. That way, I can say I'm a mathematician. ;-) This looks like cool stuff.
posted by teece at 2:18 PM on May 1, 2007

Seconded, I discovered this some weeks ago, and I'm loving it. Another good blog is "Good Math, Bad Math". It tends toward Computer Science and sometimes Darwinism, however.
posted by bkudria at 2:39 PM on May 1, 2007

Makes me miss my long-ago days as a math major. Thanks for the post!
posted by languagehat at 3:19 PM on May 1, 2007

I like this. Thanks!
posted by RussHy at 3:24 PM on May 1, 2007

I read the first essay.

He lingers at excruciating length over the Pythagorean discovery of the irrationality of the square root of 2-- a thing that anyone who has taken algebra has seen several times, and anyone who has looked at the wealth of popular expository mathematics on and offline has probably seen dozens of times-- then whips by the continuum, infinitesimals, Cauchy sequences, and completed infinity at just sub-light speed, casually tossing the law of the excluded middle out the window like a used gum-wrapper as he goes past.

To me, that bespeaks poor command of the more advanced materials, and means that for most of his readers, any sense they experience of having achieved a deeper delving into mathematics than they were capable of on their own is largely illusory.
posted by jamjam at 3:37 PM on May 1, 2007

jamjam: I got the impression he was only introducing those topics, and that they would be expounded at length in later installments.
posted by phrontist at 4:32 PM on May 1, 2007

While I agree with phrontist that he seems to be setting up a return to several of the more advanced topics, it seemed like he spoke of the "dissenting" infinitesimal theory as a mere aside that he would not be returning to. I suppose that is fine for the purposes of his "walk," but I'm sympathetic with jamjam's comment in the sense that the glancing introduction of topics like the law of the excluded middle without further elaboration seems like needless handwaving.

Still, I think the blog is a noble effort, and I daresay that there are those to whom this will appeal much more than existing takes on the subject of the nature of the reals (and beyond).
posted by sappidus at 4:47 PM on May 1, 2007

I do plan to read more, myself; this is certainly a very worthy post.
posted by jamjam at 6:24 PM on May 1, 2007