- Wrote
*Disquisitiones Arithmeticae,*a treatise on number theory that is considered a masterpiece in number theory.

- Proved that given an unmarked ruler and compass, you can construct a regular polygon of 17-sides. It was the first major discovery in that field, since the time of Euclid and the Greeks, i.e. since 2000 years. Gauss achieved this at the age of 18! His tombstone has a regular hepta-decagon (17-sided polygon) inscribed on it.

- Discovered the celebrated binomial theorem, arithmetic-geometric mean and prime number theorem (regarding the distribution of primes)

- Gave four different proofs of the Fundamental Theorem of Algebra (which asserts the existence of a root (possibly complex) of a polynomial in one variable).

- Astronomers lost track of a dwarf planet Ceres and it was considered a superhuman task to re-trace its orbit. Eminent mathematicians demanded several months’ time, Euler achieved using three days and the illustrious Gauss, using his own superior methods, located it in an hour!

- Consequently, he wrote a two volume treatise on motion of celestial bodies,
*Theoria motus corporum coelestium in sectionibus conicis Solem ambientium*.

- The Gaussian curve, Gaussian distribution, Gauss’ Divergence theorem and Gauss elimination method are known to every engineer, showing the wide range of his study.

- Gauss shrewdly managed his financial investments on his own. It is said that though he started with virtually nothing, he left an estate worth 100 times his average annual income.

- Gauss and Weber discovered Kirchoff’s laws and invented the world’s first telegraph (of range 5000 ft.)

- The CGS unit of magnetic field “Gauss” is named after him.

- Built the world’s first magnet-free laboratory with his friend Wilhelm Weber. Together, they specified a location of the South Pole.

- Famous mathematicians Richard Dedekind (he constructed real numbers), Bernhard Riemann (he rigorously invented the Riemann integration we study today), Moritz Cantor and Friedrich Bessel (Bessel’s inequality, Bessel’s equation) were among his notable doctorate students.

- Click here to view a list of topics named after Gauss.

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Some anecdotes about Gauss:

- Corrected a mistake in his father’s accounts at the age of 3!

- Gauss’ primary school teacher tried to occupy pupils by asking them to add numbers from 1 to 100. Gauss added the series 1+2+…+100 and 100+99+…+1 and came up with the answer in seconds!

- It was said, that Gauss hardly bothered to publish his results before they were made succinct and often, he would remove any trace of analysis by which he reached his result. He justified this by saying, that no architect would, after completing his building, leave the scaffolding in its place.

- Contemporary mathematicians didn’t know about Gauss’ unpublished results. It is said, that many a times, Jacobi would come to Gauss with a new discovery of his; but Gauss would take out a fifty year old notebook of his, and show him the same result (which was, of course, known to Gauss)!

- It is said, that Euler, Gauss and Cauchy were among the very few mathematicians who knew all the mathematics in their time.

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- Differential Equations: With Applications and Historical Notes by G F Simmons
- http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss
- http://www.geocities.com/RainForest/Vines/2977/gauss/quotes.html

## 2 comments

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December 9, 2008 at 22:49

Amar MainkarGreat post, but the sad part is, the German Deutche Mark has been replaced by the Euro, which means the bank note is not in circulation anymore. But the man does not need such honours. There are so many stories behind the anecdotes you have mentioned that speak of his legendary brilliance. Gauss had his fingers in every imaginable area of mathematics right since he was very young. I would put him right up there with the Newtons and Einsteins of physics.

December 11, 2008 at 07:16

shashankA very informative post. The following link displays a picture of the day for wikipedia.

http://en.wikipedia.org/wiki/Template:POTD/2008-12-08

Couldn’t make much sense out of it. Please post if anyone can.