20 June 2007

Mathematics As A Mature Discipline

I was a mathematics major in college, and something of a mathematics prodigy before then. I finished vector calculus, linear algebra, discrete mathematics and a year of college physics before I graduated from high school. Thus, to fill out my hours to complete my math major, I had to take more than the usual share of upper level courses. But, there is almost nothing I studied in college (with the exception of a couple credit hours on fractals and chaos) that wasn't settled knowledge in the field of mathematics by the time Leohhard Euler died in 1783. The truth of the matter is that we could have gotten a man to the moon almost entirely using pre-Euler mathematics.

Statistics is a somewhat younger field, but only a little. William Gosset at Guiness Brewery in Dublin invented to t-test in 1908.

Scholarly work in mathematics tends to produce the shortest papers of any field, and a good tenured professor will be lucky to publish a dozen papers in a lifetime. For example, one institution, notable only for being so explicit, requires one published article, and a second significant scholarly work possibly short of a published article to grant tenure. Unlike most scientific fields, the number of papers in the leading mathematics journal has plummeted since the 1970s to just 11 per year, although many new journals have been established in this field as in others. The average mathematics journal article, while longer than 6 page average of 1970, is still under 27 pages.

In law, in contrast, articles of about 50-70 pages are the norm, and typically, and a productive scholar is expected to have published several of them before securing tenure, and to published several dozen of them in a career.

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