Construction of the regular heptadecagon with ruler and compass (1796)
First new constructible regular polygon since the Greeks; convinced him to become a mathematician
Science · Maths, astronomy, medicine & more
Carl Friedrich Gauss
1777–1855 · German
Mathematics — number theory, astronomy and geodesy
Carl Friedrich Gauss, a child prodigy from Brunswick who spent his career as director of the observatory at Göttingen, is often called the Prince of Mathematicians. His Disquisitiones Arithmeticae founded modern number theory, he showed the regular 17-sided polygon can be constructed with ruler and compass, and he rediscovered the dwarf planet Ceres by computing its orbit. He also made foundational contributions to statistics, differential geometry, geodesy and magnetism, where the CGS unit of magnetic flux density is named after him.
How to spot them
- ▸'Princeps mathematicorum' — the Prince of Mathematicians
- ▸Adding 1 to 100 as a schoolboy; the regular 17-gon
- ▸Disquisitiones Arithmeticae; quadratic reciprocity; the Gaussian (normal) distribution
- ▸Predicting Ceres; Göttingen observatory; telegraph with Wilhelm Weber
- ▸Theorema Egregium; the gauss unit; Measuring the World by Daniel Kehlmann
Key discoveries & works
Disquisitiones Arithmeticae (1801)
Founded modern number theory, introducing congruence (modular) arithmetic and proving quadratic reciprocity
Calculating the orbit of Ceres, allowing its rediscovery (1801)
Ceres had been lost behind the Sun; his prediction found it again and made him famous
Theoria motus corporum coelestium (1809)
On the motion of celestial bodies; includes the method of least squares
Theorema Egregium (the 'remarkable theorem') (1827)
The curvature of a surface can be determined by measurements within the surface itself
Electromagnetic telegraph at Göttingen, with Wilhelm Weber (1833)
Early working telegraph linking the observatory and physics institute
Doctoral proof of the fundamental theorem of algebra (1799)
Every polynomial equation has a root in the complex numbers
Key ideas
- Modular arithmetic and the congruence notation a ≡ b (mod n)
- Quadratic reciprocity, which he called the 'golden theorem' and proved several ways
- The normal or Gaussian distribution and the method of least squares
- Intrinsic differential geometry, later extended by his student Riemann
- Gauss's law relating electric flux to enclosed charge
Quick-fire facts
- •Born in Brunswick (Braunschweig) to a poor family; his education was funded by the Duke of Brunswick
- •As a schoolboy he reputedly summed the numbers 1 to 100 almost instantly by pairing them
- •Director of the Göttingen observatory from 1807 until his death
- •His motto was 'Pauca sed matura' ('few, but ripe'), reflecting his reluctance to publish
- •Invented the heliotrope for surveying the Kingdom of Hanover
- •The CGS unit of magnetic flux density, the gauss, is named after him
- •He corresponded with Sophie Germain, who wrote under the male pseudonym 'M. Le Blanc'
- •His portrait and the bell curve appeared on the German 10-mark note
- •Daniel Kehlmann's novel Measuring the World (2005) pairs him with Alexander von Humboldt
Drill it — 9 cards
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Sources
- MacTutor History of Mathematics, University of St Andrews — Carl Friedrich Gauss
- G. Waldo Dunnington — Carl Friedrich Gauss: Titan of Science