Ah Archimedes: Who I want to be When I Grow Up
“Give me a place to stand and I shall move the earth.” The previous statement will evoke laughter, scorn, and confusion out of most audiences, as only a madman or a visionary would construct such a grand statement. While ancient Greek society boasted a selection of mad philosophers, this much-adored Greek quote comes from none other than the polymath, genius, and indeed visionary that was Archimedes.
Many historians willingly cite Archimedes as the Einstein or Da Vinci of his time, however, it would be considerably more appropriate to pronounce Einstein or Da Vinci as the Archimedes of their eras. Archimedes, through his numerous advances in both theoretical and applied mathematics as well as in astronomy and engineering, catapulted Hellenistic-period Greece into the mathematical and scientific golden age whose legacy defined Greek culture for centuries afterward. Archimedes initiated the expansion and union of the sciences in the western world.
Archimedes, with his breakthroughs in physics, mathematics, and engineering prompted numerous Greek scientific revolutions and simultaneously superseded the discoveries of his notable intellectual predecessors like Pythagoras and Euclid. In particular, Archimedes’ mathematical footprint was so grand even during the Renaissance and Baroque era mathematicians like Gottfried Leibniz and Leonhard Euler deferred to the Greek’s ancient publications detailing the properties of the irrational number pi. Unlike many mathematicians before and after him, Archimedes of Syracuse saw no bounds with his mathematics, and thus he pursued both the theoretical and practical renditions of his work, particularly with his discovery of the volume of spheres and cylinders (“On the Sphere and Cylinder”). Another defining characteristic of Archimedes was his deliberate exclusion of all philosophy from his mathematics, a concept unknown to previous Greek intellectuals, who sought to study all the sciences as one.
Due to his indisputable mathematical prowess, Archimedes’ discoveries spoke for themselves, and thus he refrained from publicly appraising his findings like other Greek intellectuals who often were armed with dubious knowledge and superstition rather than facts. The mathematician unequivocally boasted the power of mathematics, always implementing the subject to tackle normally unsolvable problems. “Archimedes boasted in the third century BC that he could write a number larger than the number of grains of sand it would take to fill the universe.” This statement was one of many such speculations championed by Archimedes. Archimedes particularly extolled the powers of applied mathematics to solve practical problems to ingratiate himself to Greek politicians, who in turn supported the mathematician’s work. Archimedes of Syracuse was an intellectual who eschewed the boundaries separating astronomy, engineering, and mathematics, making him one of the most prodigious and competent scientists of both Hellenistic Greece and western civilization.
Some of Archimedes’ greatest contributions to Hellenistic culture were made during his astronomical career in which he pioneered topics and theories about the cosmos largely unknown to Europeans at the time. One such contribution was the invention of the Antikythera mechanism, the machine that augmented the capabilities of individual astronomers by accurately predicting solar and lunar cycles. “To assist in the study of astronomy, Archimedes invented and fabricated a pair of astronomical globes. One was apparently stationary; the other appears to have been mechanized and to have illustrated the movements of the heavens as Archimedes understood them”. In addition to automating the work of astronomers, Archimedes was the first Greek to estimate the size of the cosmos, in the oddest of units: grains of sand. His estimate, in scientific notation, stood at 8 x 10⁶³ grains of sand, now a minuscule approximation, but quite large in the 3rd century B.C.E. Astronomy was the blank canvas in which Archimedes painted abstract theories of the cosmos using the paintbrush of mathematics. Lastly, Astronomy prompted Archimedes’ pursuit of engineering, as many of the scientist’s initial inventions were geared towards his Astronomical research.
Like astronomy, Archimedes’ engineering endeavors were merely extensions of his applied mathematics. Levers and the applications of simple machines supremely intrigued Archimedes because of their relationship with geometric ratios. The force needed to lift a given load on the opposite end lever is entirely dependent on the distance of the lever fulcrum(pivot) from the load, which is expressed as a ratio. Archimedes’ work with levers was majorly successful as the Greeks enjoyed experimenting with geometric ratios to improve machines or produce aesthetically pleasing architecture. One of Archimedes’ most successful engineering enterprises was the Archimedes screw, a water raising device used up until the Renaissance period in Europe. “A friend and adviser of King Hieron II, Archimedes was famous for his inventions, which included the Archimedes screw, still used today for drawing a continuous flow of water upward.” Such was the success of the Archimedes screw that it was immediately commissioned by King Hieron II to aid Syracuse’s irrigation systems. In fact, it was principally the invention of the Archimedes screw that propelled its inventor into the Syracusan upper classes, and thus further legitimizing his work, as classism was still prevalent in Hellenistic Greece despite the presence of democratic city-states. However, Archimedes’ triumphant engineering projects were vastly eclipsed by his innovations in applied mathematics.
Archimedes’ applied mathematics not only enabled him to better immerse himself in astronomy and engineering but also to gain fame through feats only solvable through the art of practical mathematics:
But his best-remembered utterance concerns his discovery of the principle of specific gravity after he was asked by King Hieron to determine whether a golden crown had been adulterated by baser metal. Pondering the problem in his bath at the gymnasium (the story goes), Archimedes suddenly realized that he could compare the amount of water displaced by the crown with that displaced by an equal weight of pure gold. Delighted with his discovery, he ran naked through the street shouting “I have found it! — heureka!” (or, as we render it today, “Eureka”)
King Hieron’s crown dilemma is one of the myriad examples of Archimedes’ mathematical ingenuity quantitatively evaluating originally unsolvable problems.
As a proud Syracusan and Greek patriot, Archimedes readily weaponized his mathematical knowledge to develop deadly siege and projectile weapons to repel the Roman invasion of Syracuse of 213–211 B.C.E. His weapons decimated the heavy Roman cavalry as well as approaching Roman warships, earning Archimedes the respect of Greek and Roman military leaders alike. In particular, Archimedes’ concentrated light weapons not only demonstrated the mathematician’s brilliance and competence as a military scientist, but his devotion to his country. “When Hieron II died in 215, his alliance with Rome collapsed. Two years later, Marcellus attacked Syracuse, but his initial onslaught was repelled thanks to the genius and foresight of Archimedes, the famed mathematician, and inventor. Archimedes, in his capacity as military adviser to Hieron II, had thoroughly prepared the city for such an attack.” In fact, Archimedes met his death while developing a new geometric theorem during the siege of Syracuse of 212 B.C.E.
While Archimedes entertained the applications of his mathematics, he prized his theoretical discoveries above all else. “ Yet he dismissed engineering feats as pandering to a vulgar public and was prouder of his work in geometry, particularly his discovery that a sphere contained inside a cylinder will always have an area two-thirds that of the cylinder.”Archimedes’ loyalty to his pure mathematics continued throughout his life, as he utilized his applied mathematics begrudgingly only to gain the favor of Syracuse’s elite. Circles occupied most of Archimedes’ career, as he experimented with pi, spheres, and other related formulas, all avantgarde fields in the western world. Ratios were also the subject of Archimedes’ research, thus explaining his affinity for pi. Additionally, Archimedes’ fascination with pi was revolutionary in western mathematics, as Archimedes’ predecessors rejected the idea of an irrational constant. Though Archimedes’ applied mathematics contributions were more overt, his theoretical work had a much larger impact on western mathematics as a whole, as later mathematicians like Eratosthenes, Pacioli, and even Isaac Newton would build upon his work on circles.
Archimedes’ mathematical, astronomical, and engineering accomplishments imparted knowledge on both Greek society and European science as a whole. Archimedes’ mathematics jumpstarted western science and European theoretical mathematics, notably the fields of analytical geometry and number theory. Archimedes’ engineering facilitated military and industrial progress in Greece, in fact, the mathematician is often considered the father of engineering whose simple machines influenced even Newtonian physics of the 17th century. Archimedes, unlike most Greek mathematicians, was not bound by dogmas or tradition, which allowed him to see farther than his predecessors. As a gifted mathematician, ingenious engineer, and Greek patriot, Archimedes of Syracuse’s contributions to Greek society spoke for themselves as they supremely augmented and cemented Greece’s indisputable legacy as the birthplace of western culture and science.
References:
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