Johann Carl Friedrich Gauss reportedly believed that there had been only three 'epoch-making' mathematicians: Archimedes, Newton, and one of his own students. While there is puzzlement as to why Gauss would accord this singular honor to his student, many would Gauss himself, sometimes referred to as the "prince of mathematics", the rightful third member of his list.

Gauss, a stickler for perfection, lived by the motto "pauca sed matura" (few but ripe). He published only a small portion of his work. It is from a scant 19 page diary, published only after Gauss's death, that many of the results he established during his lifetime were posthumously gleaned.

Gauss is portrayed with one of his most important results -- the refutation of Euclid's fifth postulate, the 'parallel postulate', which posited that parallel lines would never meet.

Gauss discovered that valid self-consistent geometries could be created in which the parallel postulate did not hold. These geometries came to be known as 'non-Euclidean geometries".

The parallel lines which begin in the portrait of Euclid, end and meet in the portrait of Gauss, the two portraits also sharing a common color palette.

Gauss chose not to publish his results in alternative geometries, and credit for the discovery of 'non-Euclidean geometry' was accorded to others (Bolyai, and Lobachevski) who arrived at similar results independently.

In the Gauss portrait, above the parallel lines which meet, what has come to be known as "Gauss's Equation" (for the second derivatives of the radius vector r), is inscribed.

Gauss did pioneering work on differential geometry (the specialized study of manifolds), which he did publish in Disquisition cica superticies curvas.

Overlying Gauss's portrait the Gaussian distribution curve is incised. This probability distribution curve is commonly referred to as the "normal distribution" by statisticians, and, because of its curved flaring shape, as the "bell curve" by social scientists. The Gaussian distribution has found wide application in numerous experimental situations, where it describes the deviations of repeated measurements from the mean. It has the characteristics that positive and negative deviations are equally likely, and small deviations are much more likely than large deviations.

Gauss is also known for Gaussian primes, Gaussian integers, Gaussian integration, and Gaussian elimination -- to name only a few of the achievements directly named after an individual who was, perhaps, the most gifted mathematician of all time.