Johann Karl Friedrich Gauss Biography

World of Mathematics on Johann Karl Friedrich Gauss

Gauss invites comparisons only to Isaac Newton or perhaps Johann Wolfgang von Goethe, being the sort of endlessly inventive mind that achieved results when put to any task. His contributions to the fields of pure and applied mathematics were all equally sensational in his day, and equally influential into the 20th century. Gauss' major discoveries reached back to Greek practices, either updating or employing them to novel use. His penchant for publishing only the most rigorous and polished proofs had set a standard for arguments in symbolic logic not seen before. Gauss' formulation of the complex number system advanced number theoryso that all possible operations could be performed on all possible numbers without needing to create new ones. His investigations into algebra and geometry paved the way for the modern disciplines of probability theory, topology, and vector analysis. Among Gauss' inventions and collaborations include the heliotrope(a trigonometric measuring device), a prototype of the electric telegraph, and the bifilar magnetometer. Gauss' interests also ran to crystallography, optics, mechanics, and capillarity.

Johann Friedrich Carl Gauss was the only son born to Gebhard Dietrich, a laborer and merchant, and Dorothea Benze Gauss, a servant. They made their home in Brunswick, capital of the Duchy of Braunschweig, Germany. As Gauss himself later calculated he was born on April 30, 1777, eight days after Ascension of that year as his mother always told him. His mother was a functional illiterate, a fact which lent a special poignancy to Gauss' later fame, which she could only ascertain by asking others, rather than experiencing direct proof of it herself.

An arithmetic prodigy, Gauss enjoyed telling the story of catching his father's addition mistake at the age of three. The most famous vignette related to his youth involved an obnoxious teacher who instructed his class to add all the integers from one to 100. By adding them in pairs the eight-year-old boiled them down to a smaller set of 101s, fifty to be exact, and calculated the sum from there to be 5050. "Ligget se!" was all he had to say to his teacher, and showed him his slate. The formula Gauss had arrived at is given by S = n(n+1)/2 and was actually in use during the days of Pythagoras. Such adroitness was initially disparaged by his father, but Gauss was eventually rewarded by a tutor's aid and admission to secondary school in 1788. He began his higher education at Caroline College in his hometown, which offered mathematical training and lessons in Latin and High German. From there, Gauss proceeded to the University of Göttingen in 1795.

Gauss never published a proof until it was airtight, but his interests ranged so far so early in his life that he preceded Bode's Law, Janos Bolyai and N.I. Lobachevsky 's non-Euclidean geometry, Karl Jacobi's double-period elliptic functions, Augustin-Louis Cauchy's functions of a complex variable and William Hamilton's quaternions. While still a teenager, Gauss constructed a with a ruler and compass a 17-sided polygon inscribed in a circle. This was the first true innovation in Euclidean geometry since the time of the ancient Greek mathematicians.

Gauss also discovered the law of quadratic reciprocity and the method of least squares. In 1799, he proved the fundamental theorem of algebra: that every polynomial equation has a root in the form of a complex number a+bi. His thesis, "Disquisitiones Arithmeticae," was completed in 1798 but not published until 1801.

The University of Helmstedt awarded Gauss a doctorate in 1799. A return to the University of Göttingen allowed for his early research and later career with the help of his benefactor, the Duke of Brunswick. He held a dual post of Professor of Mathematics and Director of Göttingen Observatory by 1807, though not before enduring a period of unemployment. His most famous work in applied mathematics, Theoria motus corporum celestium, followed just eight years after his first major publication. In 1801, Gauss had rediscovered the "lost" orbiting asteroid or minor planet, Ceres. He successfully calculated the object's orbit according to certain observations and predicted where it would next reappear--a triumph that secured his fame. This method was refined during his subsequent tenure at Göttingen Observatory into the book-length work. He was also retained by various governments to travel, making geodetic surveys at different locations. For this, Gauss invented a new measuring device, the heliotrope.

Such applied work inspired more pure mathematics, this time differential geometry of curved space and surfaces. Gauss' third major publication, Disquisitiones Generales Circa Superficies Curvas, was not published until 1827 because of the subject's far-reaching implications. What he called "intrinsic" geometry would pave the way for current differential geometry. Gauss entertained the idea of the curvature of all space, an idea that would be of central importance to Albert Einstein's formulation of space time as a geometric whole.

Gauss married twice, first to Johanna Osthoff on October 9, 1805. The union produced three children, the youngest of whom died soon after birth, followed by the mother. Though a recent widower, Gauss proposed to Friederica Wilhelmina Waldeck, the daughter of a fellow professor. They married August 4, 1810, and had three children before the second Mrs. Gauss died of tuberculosis. Eugene, the eldest boy from Gauss' second marriage, grew up with the same abilities as his illustrious father. However, for reasons that can only be speculated, Gauss prevented his son from following him into the mathematical field.

This reticence also held in Gauss' relationships with his students. Despite his encouragement of a protégéé named Eisenstein who died tragically young, and correspondence with the self-taught pioneer Sophie Germain, Gauss never really took anyone under his wing. To Gauss, lecturing would not improve a bad student nor impress a good one. He tended to consider fellow mathematicians as rivals or distractions. He was fond of newspapers and magazines, novelties of the early 19th century. Students in the university library called him the "newspaper tiger" for his habit of staring down anyone who tried to take any newspaper he wanted first.

Nearly seventy-five official honors came to Gauss throughout his life from various countries, though Gauss made light of their accompanied ceremonies, preferring instead to make curmudgeonly jokes at the speechmakers' expense. These recognitions included being installed as a Foreign Member of the Royal Society of England, but Gauss was content to be considered without question the greatest mathematician in the world and get on with his work. He was not intellectually isolated, however. At the age of 62, Gauss taught himself Russian so he could more easily read the works of Lobachevsky. Eventually his health failed, and the loss of friends and family members through death and estrangement took a toll. Gauss died February 23, 1855, of a heart attack after suffering from an enlarged heart for some time. He was buried in Göttingen next to the simple grave of his mother.

Throughout his career, Gauss repositioned pure inquiry as the ultimate test of logic, unbuttressed by geometric or theoretical assumptions and circular arguments. He considered mathematics as a science, with arithmetic as its most important subdiscipline. Gauss avoided trivialities by realizing that one cannot study a magnitude in isolation, for true mathematics lies in the study of relationships. Moreover, he envisioned new relationships to consider among infinite series, hypercycles, and pseudospheres, the sort of fanciful mathematical entities that populate the imaginations of contemporary theorists.