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The narrative suggests another reason for the "legend."

He wrote a manuscript spelling them out when he was 20, the night before he was killed in a duel. A Norwegian mathematician and contemporary of Galois's named Niels H. Abel died of tuberculosis at age 26 after solving a 300-year-old problem and discovering what are now known as Abelian functions.

Life expectancy has increased dramatically in the last century, so results from before that would be skewed young.

Why does the legend persist in mathematics more than other fields?
Mathematicians want to live fast and die young? There is another legend that there is no nobel prize in mathematics because Gosta Mittag-Leffler cheated on nobel's wife even though its probably not true. See http://almaz.com/nobel/why_no_math.html
I wish the article proper had treated fields other than mathematics.

(Though that won't keep me from exclaiming: Woohoo! Go Geology! I still have a chance!)

I just spent 10 minutes trying to think up a joke that combined research in geology, a rock and a hard place. I couldn't think of any, geology is such a dry subject.
I have a feeling that the Field's Medal requirements help drive down the age for Mathematicians a lot more than the article gives it credit.
I talked with David Goodstein at Caltech once about the youth legend in physics. His basic view was that people took two data points---Newton and Einstein---and over-extrapolated. He pointed to Feynman (among others) who continued to make major contributions throughout their careers. Of course, a couple counterexamples isn't enough to disprove a trend, but it does seem like the legend is build on a rather flimsy foundation.

N.B. I found myself quite enjoying the writing in this article, and I realized that the author was a colleague of mine from college. Lila Guterman was a writer for the Harvard Science Review when I was its editor-in-chief. I particularly recall a bang-up article she wrote on naked mole rats. Glad to see she's keeping up the good work!