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Science on the Farther Shore

Brian Hayes

The method of least squares is a familiar and trusted implement in the toolkit of statistics, learned by generations of students in all the sciences. It is the usual procedure for fitting a line or a curve to a set of data points that may be subject to errors of measurement. The invention of the method is usually ascribed to Carl Friedrich Gauss, the superstar of German mathematics in the first half of the 19th century, but the French mathematician Adrien-Marie Legendre had a rival claim to priority. Several others also contributed to the development of the technique, most notably Pierre Simon de Laplace, who was Legendre's senior colleague in the French Academy. All of these names are still immediately recognized today; they are to be found inscribed on marble busts in the main rotunda of the mathematics hall of fame.

But the method of least squares was also invented by another mathematician of the same era, whose fame is more narrowly circumscribed. This lesser-known inventor was Robert Adrain, who published an account of the method—and also of the closely related bell-shaped curve we now know as the normal or Gaussian distribution—at roughly the same time as Gauss's own publication. Yet Gauss and Legendre and Laplace knew nothing of Adrain or his writings. The reason is that Adrain lived and worked and published in an out-of-the-way corner of the world, cut off from communication with the main centers of learning. He spent his career teaching at small institutions with names such as Columbia and Rutgers. He was a citizen of a developing country: the United States of America.

Adrain's story is already well known to historians of mathematics, and I have nothing new to add to the factual record. But the story is worth telling again, if only for what it has to say about the practice of science on the margins. One obvious fact is that it can be very hard to get noticed when you are standing on the farther shore of the ocean, no matter how vigorously you wave your arms. Another truth, even more bitter, is that it's also very hard in those circumstances to do anything worth noticing. And yet there is a more cheerful outlook, at least for those who can afford to be patient: The world turns, and eventually the farther shore may become the center.

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