The January Notices of the AMS is available. It features an article with the intriguing title *You Could Have Invented Spectral Sequences*.

**Update.** I’ve finally found the time to look at this article, and it is the simplest introduction to the subject I’ve ever seen. It acheives its simplicity by concentrating on the special case of the spectral sequence for filtered chain complexes.

Up until spectral sequences there were lots of bits of mathematics I found hard, but never anything I couldn’t get past without some perseverance. Spectral sequences, however, were a kind of wall for me. I could go through the motions and even answer exam questions but the whole thing seemed completely mysterious and unmotivated to me. So just reading the quotation from Whitehead in the first paragraph makes my ego feel a little better. I look forward to seeing if I ‘get’ the concept by time I’ve finished the article.

For those who don’t have access to the AMS, Timothy Chow has a copy of this article on his website at http://www-math.mit.edu/~tchow/spectral.pdf . It’s actually a version of an article he’s had there for some years.

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Sigfpe: I felt the same way about homological algebra. Chain complexes in algebraic topology made sense, but I found homological algebra incomprehensible. The arguments weren’t hard to understand, but the definitions seemed meaningless, the theorems meaningless, and the ability prove non-homological theorems in algebra shocking. It took me years to make my peace with the subject.