# Johann Karl Friedrich Gauss

Born April 30th, 1777, in Brunswick (Germany), Karl Friedrich Gauss was perhaps one of the most influential mathematical minds in history.

Sometimes called the “Prince of Mathematics”, he was noticed for his mathematical thinking at a very young age. At only 7 years old, he caught the eye of his schoolteacher, Buttner, with his ability to sum up the numbers from 1 to 100 in mere seconds. (What was his trick? See if you can find it on your own, then see the bottom of the page for the method.) At age 11, he began his formal education at the “Gymnasium” (senior secondary school in Germany), and went on to the Brunswick Collegium Carolinum at age 15 on a stipend from the Duke of Brunswick – his benefactor. Even at this age, Gauss – working on his own – was able to deduce some very important results in the field of Number Theory: Bode’s law, the binomial theorem, the prime number theorem, the arithmetic/geometric mean, and the law of quadratic reciprocity. He was later quoted as saying “Mathematics is the queen of the sciences, and number theory is the queen of mathematics”. (Want to hear more about some of these topics, and see how you measure up against Gauss? Check out the Number Theory courses.)

At age 18, Gauss began his studies at Gottingen University under Kastner. He left the school without his diploma, but along the way made the discovery of the construction of a regular 17-gon (called a “heptadecagon”) with only a compass and straight-edge. He later requested that this shape be imprinted on his gravestone! (To learn more about ruler and compass constructions and polygons, check out the class Math in Art, MATH 1020.) He completed his degree at the age of 22 in Brunswick, and followed it with a Doctorate at the University of Helmstedt, studying under Pfaff.

During this time, he discovered the Fundamental Theorem of Algebra, which states that every polynomial has a root of the form a+bi (he came up with 4 different proofs for this theorem!). (You can learn about the Fundamental Theorem of Algebra in Techniques of Classical and Linear Algebra, MATH 1210.) He also developed a method known as “Gaussian Elimination” and used it to solve least squares problems in celestial computations and later in computations to measure the earth and its surface (we use this method to solve systems of linear equations in Applied Finite Mathematics MATH 1010 , and Vector Geometry and Linear Algebra (and a few others)).

He published his first book, “Disquisitiones Arithmeticea”, and began his work in astronomy at the age of 24. An astronomer named Zach published several estimations for the orbital positions of a new “small planet” called Ceres. Gauss was one of those who had tried to predict its positions. His predictions varied greatly from all of the others, and turned out to be almost exactly correct! (He developed a method called “least-squares approximation” to make those predictions, and you can learn about this approximation method and others in Introduction to Mathematical Modelling, MATH 3820.) He also completed work on the Fundamental Theorem of Arithmetic, which states that every natural number can be represented as the product of primes in only one way (see the Number Theory courses). At age 27, he became a Fellow of the Royal Society, and one year later he married his wife, Johanna Ostoff (who died during childbirth 2 years later, after which he married her best friend, Minna).

At 30, he became director of the Gottingen Observatory after continuing his work on investigating the orbits of various celestial bodies (perhaps this is one of the reasons that a lunar crater has been named after him!).

He then published his second book, “Theoria motus corporum celestium in sectionibus conicus Solem ambientium”, which delved into the areas differential equations (you can too, see Ordinary Differential Equations, MATH 2800) conic sections (see Math in Art, MATH 1020 ), and elliptical orbits.

During his late 30’s and Early 40’s, he completed work on a new observatory, invented a machine called a “heliotrope” which reflected the sun’s rays over great distances to mark the position of participants in a land survey, published over 70 papers, became a Fellow of the Royal Society of Edinborogh, and pursued his interests in non-Euclidean Geometry (see Math in Art, MATH 1020).

This momentum did not slow in his 50’s, when he began working with Wilhelm Weber in the field of Physics, specifically, terrestrial magnetism. He used the Laplace Equation (see Engineering Mathematical Analysis, MATH 2132) to specify the location of the magnetic South Pole, and completed a new “magnetic observatory” (completed in 1833 – free of all magnetic metals). He also discovered Kirchhoff’s Law, developed a primitive telegraph machine (that could work over distances of 5000 feet), a magnetometer (which measures the strength and/or direction of the magnetic field in its vicinity), and worked with Weber on establishing a world-wide grid of magnetic observation points.

In his 60’s, he made his fortune in shrewd investments and bonds, and updated the Gottingen University’s widows’ fund. He also won the Royal Society Copley Medal.

He gave his Golden Jubilee lecture at the age of 72, and continued his practical work until his death on February 23rd, 1855, in Gottingen, Hanover.

 Since then, his work has been used in many different mathematical fields, and his memory has been honoured with various statues, monuments, and even on the 10 Deutsch Mark bill.

References:

J. J. O’Conner, E.F. Robertson,Johan Karl Friedrich Gauss:
Weisstein, Eric W, Gauss, Karl Friedrich (1777-1855):
A Brief History of Linear Algebra and Matrix Theory

Quotations by Gauss:

http://www-history.mcs.st-andrews.ac.uk/history/Quotations/Gauss.html

Summing the numbers from 1-100:

The trick is to spot the following pattern: