Carl Friedrich Gauss

A retro review from January 26, 2004.

Review: Carl Friedrich Gauss, Tord Hall, translated by Albert Froderberg, 1970.Gauss

There are two audiences for this book. The first would be those steeped in math, who know the math of Gauss but not the man. The second would be those, like me, who have heard of the man but know little of his work or life.

This book may be thin fodder for the first. Like many intellectual giants, there was little externally interesting in Gauss’ life. His most vigorous physical activities were geodesic surveys in the summer and astronomical observations. But the mind, the thoughts …

Gauss, in the eyes of Hall, was the third greatest mathematician of all time, behind only Archimedes and Isaac Newton. The range of his scientific and mathematical accomplishments is great: plotting Ceres’ orbit — the first time that was ever done for an asteroid; pinning the Earth’s magnetic field as originating in its interior; introducing the statistical concepts of Gaussian (normal) distribution, error curves, and the least square fitting of data; establishing non-Euclidean geometry; conducting geodesic surveys; pioneering work on elliptic functions and hypergeometric series. Hall briefly puts these accomplishments in the greater context of scientific and mathematical history

But his protean intellect didn’t stop with math. He originally was interested in becoming a philologist and read Russian, Danish, classical Greek and Latin, and English (and was a fan of Sir Walter Scott). He also put his stastical and actuarial knowledge to practical use in investing. Besides student fees, he only earned 1,000 thalers a year as a professor but died with an estate worth 153,000 thaler.

As for the life of Gauss, we meet a child prodigy from a very humble background, estranged from a father whose coldness he would emulate towards his own sons. Duke Ferdinand of Braunschweig, was the royal patron who lifted him out of his common existence and encouraged him. The Duke’s death, from wounds sustained fighting Napoleon at the Battle of Auerstadt, made Gauss a lifetime political conservative. A blissful first marriage too soon ended with his wife’s death. Two of his six children emmigrated to Missouri and did well for themselves. One son, Eugene, always had strained relations with his father but was closest to possessing his gifts in languages and math. He could do elaborate calculations in his head and remember long figures well enough to catch them incorrectly dictated to him. He also helped compose a dictionary of a Sioux language for use by missionaries.

The words Hall uses most often to describe Gauss’ personality are “Olympian” and “cold”. His personal motto seems to have been “Few But Ripe.” when publishing his mathematical discoveries. He only considered a mathematical proposition finished when he could present in full form without the “scaffolding” showing of how he arrived at it. He also wanted his work to be of general significance, and he also didn’t want to argue his ideas with intellectual inferiors. A consequence of this was that several mathematicians were credited with first proposing ideas that were later shown, in his notebooks, to have been discovered earlier by Gauss. It was disconcerting for other mathematicians who wrote him of some new theorem or proof they had developed to have him write back that their ideas followed some he had already had, sometimes followed by a comment that they had saved him the work of polishing his ideas. This was not idle boasting. Gauss didn’t lie. However, in the case of Johann Bolyai, son of a mathematician friend of Gauss and developer of hyperbolic geometry, this lead to a strained relationship. When Gauss became aware of Bolyai’s invention of a non-Euclidean geometry, he didn’t praise the work because it followed his own discoveries of 30 years before. Gauss could not resolve the conflict of wanting to preserve the priority of his own work and yet also wanting to praise important work done independently.

The legacy of his mathematical work — as well as his physical studies — is secure. No less than Albert Einstein said that, without Gauss, there would have been no theory of relativity.

A good introduction to the signficance of Gauss and his work, but those who already know his work will no doubt want more about the man.

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