Hippocrates of Chios

[1] The major accomplishment of Hippocrates is that he was the first to write a systematically organized geometry textbook, called Elements (Στοιχεῖα, Stoicheia), that is, basic theorems, or building blocks of mathematical theory.

From then on, mathematicians from all over the ancient world could, at least in principle, build on a common framework of basic concepts, methods, and theorems, which stimulated the scientific progress of mathematics.

Only much later was it proven (by Ferdinand von Lindemann, in 1882) that this approach had no chance of success, because the side length of the square would have a transcendental ratio

In this way, Hippocrates' pioneering work laid the foundation for Euclid's Elements (c. 325 BC), which was to remain the standard geometry textbook for many centuries.

His ideas have not been handed down very clearly, but he probably thought both were optical illusions, the result of refraction of solar light by moisture that was exhaled by, respectively, a putative planet near the Sun, and the stars.