Carl Friedrich Gauss

Portrait of Carl Friedrich Gauss

Few, But Ripe · Mathematician & Astronomer · 1777–1855

The Göttingen mathematician who recovered a lost planet from forty-one days of readings that disagreed, and who built the systematic elimination that handles more equations than there are unknowns.

Who was Gauss?

Carl Friedrich Gauss was born at Brunswick in 1777 to a bricklayer's family, and his ability was noticed early enough that the Duke of Brunswick paid for his education. In 1801, at twenty-four, he published the Disquisitiones Arithmeticae, which turned the theory of numbers from a collection of curiosities into a subject with a structure. In the same year the small planet Ceres was discovered by Piazzi at Palermo, tracked for forty-one days, and then lost in the glare of the sun. Recovering it meant computing an orbit from a short arc of observations that were individually imprecise and mutually inconsistent. Gauss did it, said where the object would reappear, and it reappeared there. He was famous by the end of the year. The machinery behind that result was published in 1809 as the Theoria Motus. It contains a systematic elimination that reduces a system of equations by clearing one unknown at a time — an old idea made into a reliable procedure — and it applies that procedure to a situation the textbook case never mentions: more equations than unknowns, none of them exactly true, because each comes from a measurement. Gauss takes the values that make the disagreements collectively as small as possible. Legendre had published that principle first, in 1805, and disputed priority sharply when Gauss said he had been using it since 1795. Gauss published little and late. His motto was pauca sed matura — few, but ripe — and he withheld results he considered unfinished, including a geometry in which the parallels assumption fails; Bolyai and Lobachevsky published it independently and Gauss told Bolyai's father he had reached it years before, which was true and unkind. He directed the Göttingen observatory for nearly fifty years, ran the geodetic survey of Hanover, worked on terrestrial magnetism with Wilhelm Weber, and strung an electric telegraph across the town. The famous story that as a schoolboy he summed the numbers from one to a hundred instantly by pairing the ends was written down by his friend Sartorius von Waltershausen after his death, and is not documented earlier.

Major achievements

Life in brief

Explore the life of Gauss — five chapters

  1. Brunswick — The story about the schoolroom, and what to make of it
  2. The Lost Planet — Forty-one days of readings, and a prediction that held
  3. Few, But Ripe — What he knew and did not say
  4. The Disquisitiones — Numbers sorted by what they leave behind
  5. Fifty Years at Göttingen — Surveying, magnetism, and a telegraph across the town

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