Archytas, a Mathematician, Scientist and Founder of Mathematical Mechanics

Archytas (428 BC-345BC) was an Ancient Greek mathematician, a music theorist, statesman and scientist from the ancient city of Taras (modern day Taranto), Southern Italy. He was also a philosopher, a friend of Plato, and affiliated with the Pythagorean School. He is now regarded as the founder of Mathematical Mechanics.

Only fragments of Archytas’ genuine work have survived, and we know that his original scientific and mathematical treatises were copied many times and throughout the Middle Ages. Archytas was the first to solve one of the most celebrated mathematical problems in antiquity, the duplication of the cube, and he proved the ratios in harmonical scales (now known as wavelengths) in musical theory.

He was the most sophisticated of the Pythagorean harmonic theorists, defined and identified four canonical sciences: logistic (arithmetic), geometry, astronomy and music. These became known as the quadrivium in the Middle Ages. He also contributed to the development of the science of optics and laid the mathematical foundations for the science of mechanics. He believed that the ultimate goal of the sciences is the description of phenomena in the cosmos in terms of equations that describe the ratio and proportion of scientific quantities that could be measured experimentally.

He gave definitions of quantities that took account of both their matter and their form. He also developed the most famous argument for the infinity of the universe. He also believed that rational calculations and an understanding of proportion, and the application of these in scientific phenomena were the master sciences through which humanity could begin to understand the universe. Although Archytas was a friend of Plato, there are many signs of disagreement between the two philosophers. 

However, he is known to have sent a ship to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361 BC (after Plato visited the dictator in a vain attempt to educate him into ruling justly). Archytas was also a dominant political figure in Taras, being elected general seven consecutive times, and was a good statesman and strategist. However, his work in mathematics and the sciences, especially mechanics, proved deeply influential during the Renaissance and Enlightenment Period, and therefore in the development of modern science.  

Indeed, his strong belief in the application of mathematics in understanding the universe and his development of mathematics in mechanics, together with Archimedes, influenced scientists during the Enlightenment period, including Galileo Galilei, Gottfried Wilhelm Leibniz, and Isaac Newton.