Eukleides (Euclid of Alexandria), although little is known about his life, is likely the most famous teacher of mathematics of all time. His treatise on mathematics, The Elements, endured for two millennia as a principal text on geometry.
The Elements commences with definitions and five postulates. The first three postulates deal with geometrical construction, implicitly assuming points, lines, circles, and thence the other geometrical objects.
Postulate four asserts that all right angles are equal -- a concept that assumes a commonality to space, with geometrical constructs existing independent of the specific space or location they occupy.
Eukleides is pictured with what is perhaps his most famous postulate -- the fifth postulate, often cited as the "parallel postulate". The parallel postulate states that one, and only one, line can be drawn through a point parallel to a given line -- and it is from this postulate, and on this basis, that what has come to be known as "Euclidean geometry" proceeds.
It was not until the 19th century that Euclid's fifth postulate -- the "parallel postulate" was rigorously and successfully challenged.
The two parallel lines of Euclid meet and converge in the portrait of Johann Carl Friedrich Gauss -- whose work led to the emergence of non-Euclidean geometry, where Euclid's fifth postulate gave way to new mathematical universe, where 2 parallel lines could, in fact, meet.
The portrait of Gauss shares a common dominant color palette with the portrait of Euclid -- but two different conceptions of 'geometry'.
Pictured over Euclid's right shoulder is a small drawing which is taken from Euclid's proof of the right angled triangle which has come to be known as the theorem of Pythagoras. While very little is known about the lives of either Pythagoras or Eukleides, it is both plausible and likely that Euclid and Pythagoras independently discovered and "proved" this basic theorem. Euclid's proof of this theorem relies on most of his 46 theorems which preceded this proof.
Central to Euclid's portrait is a circle with its radius drawn. Euclid's geometry was one of construction, and the circle and radius were central elements to Euclid's constructions.