Eudoxus of Cnidus

Eudoxus of Cnidus

Boyer, in his "A History of Mathematics" gives a quote from Eudoxus that is quite self-descriptive of this genius, "Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size and its substance."

It is descriptive of the man from Cnidus because it shows us the mind of this genius, the curiosity he displayed during his lifetime and why he contributed so much, in particular, to the fields of mathematics and astronomy.

Unfortunately, all of his works are lost to history. We have snippets, pieces, basic facts about Eudoxus' life and work, and some words from others through the ages who have dug up what could be found and put it together in biographies and descriptions of his work.

Biography

We know that Eudoxus was born in Cnidus, Asia Minor (now Turkey). Actually, historical documents claim a birth sometime between 408 B.C. To 390 B.C. And his death at the age of 50 to 53 years old. Best guess is 408-355 B.C.

He is known for his revolutionary work as a mathematician, astronomer, and philosopher. However, at some point in his life he was also a theologian, meteorologist, doctor, and "http: geographer. He studied mathematics in Italy under the tutelage of Archytas, the Greek mathematician and philosopher. Many historians claim that Eudoxus worked with Plato in Athens, but others dispute whether there is enough data to support that and are unclear about this relationship between the two great intellectuals. (O'Connor & Robertson, 1999) Archytas and Plato were close friends, so it is possible that Eudoxus met Plato, and, perhaps, this too, could explain part of the confusion whether or not Plato and Eudoxus actually worked with each other.

It is somewhat clear from historical records that Eudoxus had little respect for Plato's analytic ability, but since Plato was not the mathematician that Eudoxus was, that is to be expected. It does not appear as if either had much influence on the other's work. (O'Connor & Robertson, 1999)

Diogenes Laertius, the Roman biographer of Greek philosophers, claims that Eudoxus did, indeed, study in Athens under Plato. However, some of Laertius' usually solid work has come under question by other scholars, and, since Laertius' lived in the third century A.D., we can't be certain he was correct, since, again, all of Eudoxus' work is lost. (Soylent Communications, 2008)

He traveled to Sicily where he studied medicine with Philiston. After that, we surmise, with the help of financial aid from friends, he went to Egypt to learn astronomy with the priests at Heliopolis, and made astronomical observations from an observatory located between Heliopolis and Cercesura. From there Eudoxus travelled to Cyzicus, in northwestern Asia Minor on the south shore of the Sea of Marmara. There he established his own school which proved to be quite popular. As a matter of historical record, it appears that Plato became somewhat jealous of Eudoxus' success with his school. Not much more is known about that, however. (O'Connor & Robertson, 1999)

After a second trip to Athens in about 368 B.C., Eudoxus returned to his native Cnidus and there was acclaimed by the people who put him into an significant role in the legislature. He continued his scholarly work, writing books and lecturing on theology, astronomy and meteorology. He had built an observatory on Cnidus and we know that from there he observed the star Canopus. (O'Connor & Robertson, 1999)

He died in Cnidus, an honored citizen.

Contribution to Discovery

The list of Eudoxus's accomplishments include: advancing number theory, giving the first systematic explanation of the motions of the sun, moon, and planets, and introducing geometry into science. In his spare time he built his observatory at Cnidus from which he made his astronomical observations. He invented a planetary system, which consisted of spheres, the earth being still at the center, and twenty-seven concentric spheres rotating around the earth.

Actually, most of his accomplishments are difficult to explain at all to the nonprofessional, since they involve the complicated fields of math and astronomy. But, for those who work in those areas, Eudoxus accomplishments are extraordinary. However, what his work does is make the work today so much easier. Those who labor in those fields know the practicalities, complexities, and almost impossibility of what Eudoxus did.

Eudoxus made important contributions to the theory of proportion, where he made a definition allowing possibly irrational lengths to be compared in a similar way to the method of cross multiplying used today. A major difficulty had arisen in mathematics by the time of Eudoxus, namely the fact that certain lengths were not comparable. The theory developed by Eudoxus is set out in Euclid's Elements Book V. Definition 4 in that Book is called the Axiom of Eudoxus. (Encyclopaedia Brittanica, 2008)

G.L. Huxley, writes, in his "Dictionary of Scientific Biography,"

It is difficult to exaggerate the significance of Eudoxus' theory, for it amounts to a rigorous definition of real number. Number theory was allowed to advance again, after the paralysis imposed on it by the Pythagorean discovery of irrationals, to the inestimable benefit of all subsequent mathematics."

Similarly, Eudoxus's theory of incommensurable magnitudes (magnitudes lacking a common measure) and the method of exhaustion (its modern name) influenced Books X and XII of the Elements. Eudoxus also contributed a solution to the problem of doubling the cube -- that is, the construction of a cube with twice the volume of a given cube. (Encyclopaedia Brittanica, 2008)