**Archimedes**

#### Archimedes (Syracuse, present-day Italy, h. 287 B.C. – id., 212 B.C.) Greek Mathematician. The great advances of Hellenistic mathematics and astronomy are due, to a large extent, to previous scientific advances and the legacy of Oriental knowledge, but also to the new opportunities offered by the Hellenistic world.

He and Newton could have understood each other perfectly, and it is quite possible that **Archimedes**, if he had been able to live up to a postgraduate course in Mathematics and Physics, would have understood Einstein, Bohr, Heisenberg and Dirac better than these have understood each other.

Of all the ancients, Archimedes is the only one whose thought enjoyed the freedom that the greatest mathematicians allow themselves today after 25 centuries have smoothed their way.

At the beginning of the Hellenistic era is situated Euclid, who bequeathed to posterity a prolific work of synthesis of the knowledge of his time that fortunately remained almost intact and became an almost indispensable reference until the Contemporary Age.

But the most famous and prestigious mathematician was Archimedes. His writings, a dozen of which have been preserved, are eloquent proof of the multifaceted nature of his scientific knowledge. Son of the astronomer Fidias, who probably introduced him to mathematics, he learned from his father the elements of that discipline in which he was destined to surpass all ancient mathematicians,

to the point of appearing as prodigious, «divine,» even to the founders of modern science.

His studies were perfected in that great center of Hellenistic culture that was the Alexandria of the Ptolomei, where Archimedes was, around 243 B.C., disciple of the astronomer and mathematician Conon of Samos, for whom he always had respect and admiration.

There, after learning the not insignificant mathematical culture of the school (the great Euclid had recently died), he became close friends with other great mathematicians, including Eratosthenes, with whom he always corresponded, even after his return to Sicily. Archimedes dedicated his Method to Eratosthenes, in which he exposed his brilliant application of mechanics to geometry, in which he imaginatively «weighed» unknown areas and volumes in order to determine their value. He then returned to Syracuse, where he devoted himself fully to scientific work.

Apparently, later he returned to Egypt for some time as Ptolemy’s «engineer», and there designed his first great invention, the «coclea», a kind of machine that served to raise the waters and thus irrigate regions not reached by the flood of the Nile.

But his mature activity as a scientist developed completely in Syracuse, where he enjoyed the favour of the tyrant Hierón II. There he alternated mechanical inventions with studies of theoretical mechanics and high mathematics, always imprinting on them his characteristic spirit, marvelous fusion of intuitive daring and methodical rigor.

His mechanical inventions are many, and even more those attributed to him by the legend (among the latter we must reject that of the ustorial mirrors, immense mirrors with which he would have set fire to the Roman fleet besieging Syracuse); but they are historical, besides the «coclea», numerous war machines destined to the military defense of the city, as well as a «sphere», great and ingenious mechanical planetary that, after the seizure of Syracuse, was taken to Rome as war booty, and there Cicero and perhaps Ovid still saw it.

**¡Eureka! ¡Eureka!**

**Archimedes’ biography** is more populated with tasty anecdotes than with facts such as those described above. The plot of a legendary figure was woven around him first by his fellow citizens and the Romans, then by the ancient writers and finally by the Arabs; Plutarch already attributed a **«superhuman intelligence» to this great mathematician and engineer**.

The most divulged of these anecdotes is the story of Vitruvius and refers to the method he used to check whether there was fraud in the making of a gold crown commissioned by Iron II, tyrant of Syracuse and protector of Archimedes, and perhaps even his relative.

It is said that the tyrant, suspecting that the jeweller had deceived him by putting silver inside the crown, asked Archimedes to determine the metals of which it was composed without breaking it.

Archimedes meditated for a long time on the difficult problem, until one day, finding himself in a bathing establishment, he noticed that the water overflowed from the bathtub as it was being introduced into it.

This observation inspired the idea that enabled him to resolve the question posed by the tyrant: if he immersed the crown in a container filled to the brim and measured the overflowing water, he would know its volume; then he could compare the volume of the crown with the volume of a gold object of the same weight and see if they were the same. It is said that, driven by joy, Archimedes ran naked through the streets of Syracuse towards his house shouting **«Eureka! Eureka!»**, that is to say, «I found it! I found it!

Archimedes’ idea is reflected in one of the initial propositions of his work On floating bodies, pioneer of hydrostatics, which would be carefully studied by the founders of modern science, among them Galileo.

It corresponds to Archimedes’ famous principle that **«every body submerged in a liquid experiences an upward thrust equal to the weight of the volume of water it dislodges»**, and, as explained there, by making use of it it it is possible to calculate the law of an alloy, which allowed him to discover that the goldsmith had committed fraud.

**Give me a foothold and I’ll move the world**

According to another famous anecdote, collected among others by Plutarch, Archimedes was so enthusiastic about the power he was able to obtain with his machines, capable of lifting large weights with relatively little effort, that he assured the tyrant that,** if given a point of support, he would be able to move the Earth**; it is believed that, exhorted by the king to put his assertion into practice, he managed without apparent effort, by means of a complicated system of pulleys, to set in motion a three-masted ship with its cargo.

Analogous mental concentration and abstraction in meditation demonstrates the episode of his death. It is said that the war inventions whose paternity is attributed to him by tradition allowed Syracuse to resist the Roman siege for three years, before falling into the hands of Marcellus’ troops.

While the soldiers of Marcellus were looting Syracuse, who had finally succeeded in expelling the city, the old mathematician was meditating, forgetting everything, on his geometrical problems.

Surprised by a soldier who asked him who he was, Archimedes did not answer him, or, according to another version, replied irritated that he did not bother him or spoil the drawings he had drawn in the sand; and the soldier, enraged, killed him.

Marcellus was very saddened to learn of this and ordered a monument to be erected for him, removing his figure from the treatise On the Sphere and the Cylinder. Many years later, Cicero recognized by this figure his forgotten tomb.

**This passion of Archimedes for erudition**, which caused his death, was also what, in life, it is said made him forget even to eat and that he used to entertain himself drawing geometric drawings in the ashes of the home or even, when he anointed himself, in the oils that covered his skin.

This image contrasts with that of the inventor of war machines spoken of by the historians Polibio and Tito Livio; but, as Plutarco points out, his interest in this machinery was based solely on the fact that he presented his design as mere intellectual entertainment.

Archimedes’ effort to turn statics into a rigorous body of doctrine is comparable to that made by Euclid for the same purpose with respect to geometry.

Such effort is reflected in a special way in two of his books; in the first of them, Equilibrios planos, he based the law of the lever, deducing it from a reduced number of postulates, and **determined the center of gravity of parallelograms, triangles, trapeziums and that of a segment of parabola**.

In his work On the **Sphere and the Cylinder**, he used the so-called exhaustion method, precedent of integral calculation, to determine the surface of a sphere and to establish **the relationship between a sphere and the cylinder circumscribed in it**.

This last result happened to be his favorite theorem, which by his express wish was engraved on his tomb, thanks to which Cicero was able to recover the figure of Archimedes when it had already been forgotten.

*Source: Biographies and lives | The Great Mathematicians of E.T Bell*