The Influence of Euclid in Mathematics and Science

Euclid (fl. 300 BC) was a Greek mathematician and is considered as the “Father of Geometry”. He devised the modern process of abstract mathematical thinking, including the technique of proving theorems from propositions and axioms by deductive reasoning. He is mainly known for his 13-volume treatise entitled “The Elements”. This treatise established the foundation of geometry that dominated the field of mathematical teaching until the end of the nineteenth century, although it is still used in modern schools up to A-Level mathematics.

His “Elements” became the second most widely read book for over 2000 years, after the Bible. It deeply influenced the development of modern mathematics. The “Elements” was also instrumental in the development of the field of mechanics and applied physics, as well as projective geometry, including the construction of technical drawing in engineering and the development of steam engines during the Industrial Revolution.

In fact, Isaac Newton read Euclid’s Elements widely and he constructed his laws of motion using Euclidean geometry. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote many works on perspective, conic sections, spherical geometry, number theory and mathematical rigour. Furthermore, Euclid wrote a central early text on “Optics,” on the properties of light and works on “Data” and “Phenomena”.

His works on optics and Aristotle’s notion that light consisted of particles produced from a light source was translated by Early Arabic scholars from the classical Greek into Arabic, then eventually into the Latin-speaking world of modern European civilisation. Indeed, Isaac Newton’s work on optics and his theory of light being corpuscular (particle-like) was indirectly and directly influenced by both Euclid and Aristotle, including the notion of light exhibiting the properties of reflection, refraction and dispersion.

Unfortunately, Euclid is known to have written many other mathematical and scientific works that have since been lost. As with many classical Greek mathematicians, the details of Euclid’s life are mostly unknown, but he is believed to have lectured and taught in Alexandria at the prestigious Museum of Alexandria where the Greeks established a major research and teaching university in the field of science, mathematics and the humanities. It is also believed that Euclid founded a mathematical tradition in Alexandria. The city was founded by Alexander the Great in 331 BC. Ptolemy, Alexander the Great’s trusted general, sponsored, commissioned and constructed the massive museum and research institution. Ptolemy became the first Hellenic King of Egypt, Ptolemy I.

Euclid is speculated to have been $among the Museum’s first scholars. There are numerous anecdotal stories about Euclid, who was described in old age as “a kindly and gentle old man”. The best-known anecdote about Euclid is when Ptolemy I, who was tutored by Euclid, asked whether there was a quicker path to learning geometry than reading his “Elements”, upon which Euclid replied with “Oh king, there is no royal road to geometry”. This should be a lesson to us all when studying any subject, as if we try to find a short-cut to learning rather endeavouring to study it thoroughly, we place ourselves in danger of not fully understanding the subject in depth, and, consequently, learning it properly.

In conclusion, Euclid’s work not only provided a logical framework for geometry but also demonstrated the power of logical deduction and systematic organisation in mathematics and science. Indeed, his method of systematic and logical analysis has proved indispensable in the way the modern world practises both mathematics and the Scientific Method!