The Archetypal Mathematician

Carl Friedrich Gauss (1777-1855), known as the Prince of Mathematics, is one of the most prolific mathematicians of all time. He joined the ranks of Sir Isaac Newton and Archimedes of Syracuse while living in Germany at a time where little mathematical progress was being made. His career included work in pure mathematics (arithmetic, number theory, geometry, algebra, and analysis), applied mathematics (probability, statistics, mechanics, and physics), as well as the mathematical sciences (astronomy, geodesy, magnetism, dioptics, actuarial science, and financial securities). He is credited with more than 300 publications, which represent just a fraction of the original ideas he developed (McElroy, 2005).

Portrait of Carl Friedrich Gauss by G. Biermann (1824-1908) (public domain).

Gauss had a hard start to life as he was born to a family on the edge of poverty. His mother was highly intelligent, but illiterate. In fact, after his birth, his mother never wrote down his birthday and could only recall that he was born on a Wednesday, eight days before Ascension Day (Bien, 2004). This missing knowledge about himself spurred Gauss to create an algorithm that would tell him the date of Easter in any given year (and in turn, Ascension Day and his birthday). He was ultimately successful in this endeavor (although he had to invent modular arithmetic to do it) and learned he was born April 30th (Gardner, 1981; Petrilli, 2012).

Despite Gauss’ mother’s illiteracy (or perhaps due to it), she was extremely supportive of her son’s education. Meanwhile, his father was practically minded and never valued his gifted son (McElroy, 2005). He worked as a gardener, laborer, foreman, assistant to a merchant, and treasurer of a small insurance fund in an effort to raise his family out of poverty. He did not understand the pull towards abstract mathematics and had a tenuous relationship with his son. Gauss described his father as “worthy of esteem,” but “domineering, uncouth, and unrefined” (Biographical, 1991, pg. 860).

Gauss’ talent was clear from a young age. It is said he learned to calculate before he could talk and began correcting mistakes in his father’s wage calculations by the age of 3 (something apparently unappreciated by his father). There is also the well-known story of Gauss’ arithmetic teacher who assigned him the task of adding together the first 100 integers. Rather than do this explicitly, Gauss found a pattern and grouped the integers into 50 pairs that each added to 101, quickly providing the answer of 5,050.

An illustration of Gauss’ method of adding the first 100 integers (Wilburne, 2014).

As for his personal life, Gauss married Johanna Osthoff in 1805 and with her had a son and a daughter. In 1809, Osthoff died while in childbirth and the child died soon after. The loss sparked a loneliness from which Gauss never recovered. He wrote that he had “closed the angel eyes in which for five years [he had] found a heaven” (Biographical, 1991, pg. 864). Less than a year later he married Minna Waldeck and had two sons and a daughter. However, the marriage was unhappy and Waldeck was often sick from tuberculosis (Young, 1998).

Gauss’ happiness in his first marriage is somewhat surprising as he spent most of his life as a recluse. Whether this is because there was no one at the time that he felt matched his intellect or because he was simply unwilling to work with others is unclear. He avoided teaching positions to the extent he could and never took anyone under his wing as one might have expected. The exceptions to this include correspondence with Eisenstein, Bernhard Riemann, and Sophie Germain. In general, he considered other mathematicians rivals and distractions. This even applied to his own family. The oldest son from his second marriage, Eugene, grew up as a prodigy like his father. Rather than mentor him, Gauss discouraged his son from a career in mathematics. Eugene took this to mean that his father feared he would soil their last name with subpar work (Biographical, 1991).

While Gauss was disinterested in people, he was especially fond of newspapers and magazines, a novelty in the 19th century. He was reportedly called the “newspaper tiger” in his university library for his penchant of staring down students who got to a new printing before he did (Young, 1998). While off putting for the people around him, this habit seems to have paid off for him. Motivated by his actuarial work, Gauss kept collections of statistics and observations from daily newspapers. This lead to financial speculations astute enough to create a net worth nearly 200 times his annual salary. Gauss had achieved the financial status his father had dreamt of, but without the “practical” career he had been told was necessary (Biographical, 1991).

Gauss lived in a time with no mathematical equals (a fact even they acknowledged). While the lack of collaborators and rivals may have discouraged most, Gauss was known for his solitary and reclusive attitude. Introspective and ambitious, Gauss represents the archetypal mathematician (McElroy, 2005). In our next few blog posts, we will dive deeper into the major accomplishments of this extraordinary mathematician.

References

Bien, R. (2004). Gauβ and beyond: The making of Easter algorithms. Archive for History of Exact Sciences, 58(5), 439-452.

Biographical dictionary of mathematicians : Reference biographies from the dictionary of scientific biography (Vol. 2). (1991). New York, NY: Charles Scribner’s Sons.

Gardner, M. (1981). Mathematical games. Scientific American, 244(2), 17-22.

McElroy, T. (2005). A to Z of mathematicians (Notable Scientists). New York, NY: Facts on 
File.

Petrilli, S. J. (2012). Servois' 1813 perpetual calendar, with an English translation - Gauss' calculation for the date of Easter. Retrieved from https://www.maa.org/press/periodicals/convergence/servois-1813-perpetual-calendar-with-an-english-translation-gauss-calculation-for-the-date-of-easter

Wilburne, J. M. (2014). [Sum of integers]. Retrieved from https://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/The-Story-of-Gauss/

Young, R. V. (Ed.). (1998). Notable mathematicians: From ancient times to the present. Detroit, MI: Gale Research.