I am taking a class on linear algebra at the moment, which means that I am breathing in matrices and Gaussian elimination on a daily basis. There is a footnote in our textbook where row reduction algorithms are discussed: "The algorithm here is a variant of what is commonly called Gaussian elimination. A similar elimination method for linear systems was used by Chinese mathematicians in about 250 B.C. The process was unknown in Western culture until the nineteenth century, when a famous German mathematician, Carl Friedrich Gauss, discovered it. A German engineer, Wilhelm Jordan, popularized the algorithm in an 1888 text on geodesy" (Linear Algebra and its Applications, 4th edition, by David C. Lay - 2012 - p. 12). Geodesy is mathematically determining the size and shape of the Earth. I remembered Gauss's name coming up in my statistics class; it turns out his contributions to both linear algebra and statistics were secondary byproducts of his interest in geodesy. I decided to look him up in my reference works and discovered that his contributions to mathematics and science, in general, were so great that Gaussian elimination isn't even mentioned.

Even though it was just published 32 years after Gauss's death, Johnson's Universal Cyclopaedia (1887) features a compact summary of his life and accomplishments: Gauss (Karl Friedrich), b. in Brunswick, Germany, Apr. 30, 1777; was educated at the expense of the duke of Brunswick, who had heard of his precocious mathematical talents; solved when eighteen years old the problem of the division of the circle into seventeen equal parts, and afterwards became famous for skill in the indeterminate analysis and in curious numerical questions; demonstrated Fermat's theorem; became in 1807 professor of astronomy at Göttingen and director of the observatory; received in 1810 the Lalande medal for calculating by a new method the orbits of Ceres and Pallas; was made in 1816 a court councillor, and in 1845 a privy councillor of Hanover; made after 1821 important improvements in geodetic methods and instruments; after 1831 devoted much attention to terrestrial magnetism. D. at Göttingen Feb 23, 1855. Gauss is regarded as one of the first mathematicians of this century (vol. 3, p. 403).

The 11th edition Encyclopaedia Britannica (1910) is a bit more thorough. The article on Gauss can be found in volume 11, beginning with the fact that he was "born of humble parents" (535). Some fun extracts (pp. 535-536):

In 1807 he was appointed director of the Göttingen observatory, an office which he retained to his death: it is said that he never slept away from under the roof of his observatory, except on one occasion, when he accepted an invitation from Baron von Humboldt to attend a meeting of natural philosophers in Berlin. [...] With [Wilhelm] Weber's assistance he erected in 1833 in Göttingen a magnetic observatory free from iron (as Humboldt and F. J. D. Arago had previously done on a smaller scale), where he made magnetic observations, and from this same observatory he sent telegraphic signals to the neighboring town, thus showing the practicality of an electromagnetic telegraph. [...] Running through these volumes in order, we have in the second the memoir, Summatio quarundam serierum singularium, the memoirs on the theory of biquadratic residues, in which the notion of complex numbers of the form a + bi was first introduced into the theory of numbers; and included in the Nachlass are some valuable tables. That for the conversion of a fraction into decimals (giving the complete period for all the prime numbers up to 997) is a specimen of the extraordinary love which Gauss had for long arithmetical calculations, and the amount of work gone through in the construction of the table of the number of the classes of binary quadratic forms must also have been tremendous.

A much longer entry on Gauss appears in the Macropaedia section of the 15th-edition Encyclopaedia Britannica (here the 1997 printing, volume 19, pp. 697-698). This article comments a little bit on his personal life outside of his mathematical discoveries, and also mentions his contributions to statistics (couched in the context of his interest in geodesy); here is a fraction of the details found within:

His own dictum, "Mathematics, queen of the sciences, and arithmetic, the queen of mathematics," aptly conveys his perception of the pivotal role of mathematics in science. [...] His first wife died in 1809, after a marriage of four years and soon after the birth of their third child. From his second marriage (1810-31) were born two sons and a daughter. [...] By introducing what is now known as the Gaussian error curve, he showed how probability could be represented by a bell-shaped curve, commonly called the normal curve of variation, which is basic to descriptions of statistically distributed data. [...] The most important result of their [Weber + Gauss's] work in electromagnetism was the development, by other workers, of electric telegraphy. Because their finances were limited, their experiments were on a small scale; Gauss was rather frightened at the thought of worldwide communication. [...] Teaching was his only aversion, and, thus, he had only a few students. Instead he effected the development of mathematics through his publications, about 155 titles, to which he devoted the greatest care. Three principles guided his work: "Pauca, sed matura" ("Few, but ripe"), his favourite saying; the motto "Ut nihil amplius desiderandum relictum sit" ("That nothing further remains to be done"); and his requirement of utmost rigour. It is evident from his posthumous works that there are extensive and important papers that he never published because, in his opinion, they did not satisfy one of these principles. He pursued a research topic in mathematics only when he might anticipate meaningful relationships of ideas and results that were commendable because of their elegance or generality.

A fun text in general for looking at the lives of great scientists and mathematicians comes from another prolific writer, Isaac Asimov, in Asimov's Biographical Encyclopedia of Science and Technology: The Lives & Achievements of 1195 Great Scientists from Ancient Times to the Present; I have the revised version from 1972. The entries in this book are arranged chronologically, but there is a handy alphabetical index at the front of the book, which helped me quickly locate the biography of Gauss on pages 249-251. My favorite quips:

At the age of three, he was already correcting his father's sums, and all his life he kept all sorts of numerical records, even useless ones such as the length of the lives of famous men, in days. He was virtually mad over numbers. [...] All of this was not without a price, for his intense concentration on the great work that poured form him withdrew him sometimes from contact with humanity. There is a story that when he was told, in 1807, that his wife was dying, he looked up from the problem that engaged him and muttered, "Tell her to wait a moment till I'm through." [...] His agile mind never seemed to cease. At the age of sixty-two he taught himself Russian. [...] Each of his two wives died young and only one of his six children survived him. His life was filled with personal tragedy, and though he died wealthy, he also died embittered.