Major Greek contributions include astronomy, optics, and acoustics, along with major advances in mathematics. Science in ancient Greece was based on logical thinking and mathematics. The Greeks were very interested to know about the world, the heavens, and themselves. Greek geniuses were lucid thinkers and bold reasoners.

The Greek philosophers were very much drawn to mathematics. They invented its generality, analyzed its premises, and made notable discoveries of theorems by a rigid adherence to deductive reasoning. Geometry became the basic instrument for measuring all things. Plato examined the difference between the changing world of the senses and that of the permanent truths that could only be found through rational thought. The unchanging elements of geometry were the measures of this ideal, permanent thought-world. This union of logic with geometry laid the foundations of the Western way of life.

Euclid's "Elements," is a comprehensive treatise on geometry, proportions, and the theory of numbers and is the most long-lived of all mathematical works.

It includes the Pythagorean Theorem, which states that the square on the hypotenuse of a right triangle is equal to the sum of the square on the other two sides.

Pythagoras studied geometry, and discovered the general proof of the theorem about right-angled triangles. He insisted on generality in reasoning. He is said to have taught that the mathematical entities, such as numbers and shapes, were the ultimate stuff out of which the real entities that we perceive are constructed. He asked, "what is the status of mathematical entities, such as numbers for example, in the realm of things?" He discovered the importance of dealing with abstractions; and in particular directed the attention of number as characterizing the periodicity of notes of music. His followers made important contributions to medicine and astronomy and were among the first to teach...