We're here with the ghost of the famous mathematician, Eudoxus of Cnidus. Responsible for many mathematical feats, he was also a famous astronomer and legislator.
Q. When were you born?
A. About 400 BC. My father was Aischimes.
Q. Where were you born?
A. Cnidus, on the Black Sea. It is located in Asia Minor, or current day Turkey.
Q. Did you receive any education?
A. First I studied under Archytas, a follower of Pythagoras, who influenced my math career. I later studied medicine with Philistium on Sicily. Then when I was twenty-three years old, I went to Plato's academy in Athens where I studied philosophy and rhetoric. I also studied astronomy in Egypt at Helopolis.
Q. After receiving your education, what did you do?
A. I established a school at Cyzicus, located in northwestern Asia Minor, on the shore of the Marmora Sea. I returned with my pupils to Athens in 365 BC. There, I became a colleague of Plato and a respected legislator.
Q. Were you close friends with Plato?
A. Actually, he was jealous of how popular my school was. So, as you can imagine, we weren't exactly great friends.
Q. When did you die?
A. I died in my home of Cnidos when I was fifty-three.
Q. During your lifetime, were you well known?
A. I was the most renowned astronomer and mathematician of the day for advancing number theory, giving the first systematic explanation of the motions of the sun, moon, and planets, and introducing geometry into science.
Q. You did not just focus on mathematics, then. Did you have any accomplishments in astronomy?
A. I built an observatory at Cnidus which aided my astronomical observations. I invented a planetary system. It consisted of spheres, the earth being still and at the center. Twenty-seven concentric spheres rotate around the earth. The stars are fixed and are carried by the exterior sphere. The remaining spheres are the sun, moon, and five planets. Each of the five planets has four spheres, the planet itself, the sun, and the moon.
Q. Well, your theory is imaginative but totally inaccurate.
A. Yes, in fifty years my theory had been entirely forsaken.
Q. What are your mathematical accomplishments?
A. Well, my theory of proportion, my concept of magnitude, the method of exhaustion, and other things.
Q. Would you mind explaining one of these accomplishments?
A. Of course. First of all, a magnitude is a number characteristic of a quantity that forms a basis for comparison with similar quantities such as length. My concept of magnitudes was a way of solving a problem discovered by the Pythagoreans. When using their Pythagorean Theorem, they realized that when you had a square whose sides were the length of one, the diagonal of the square would equal v2, an irrational number (this was calculated by using the Pythagorean theorem of a² + b²= c², a and b representing the two legs or sides of the triangle and c representing the hypotenuse of the triangle). No one had a way of dealing with irrational numbers as lengths. That is, until I came along. I realized that a way for comparing rationals and irrationals. My concept is that a:b and c:d are equal (even if they are irrational) if for any integers m and n;
If ma<nb, then mc< nd. If ma="nb" then mc="nd" If ma>nb then mc>nd.
This concept is stated in Book 5 Definition 5 of Euclid's Elements. This concept may seem trivial to you, but at the time, the Pythagorean discovery of the irrational had been a shock and I was able to get mathematics moving again.
Q. Did your influence carry over even after your death?
A. My planetary system was unused after
fifty years but Euclid did use many of my ideas in his Elements,
especially Books V and XII. I also influenced many future
mathematicians and scientists.
Before leaving, Eudoxus informed us that
his plans for the rest of eternity include discovering how far pi
goes and debates with other mathematical legends.
Allen, Don. Eudoxus of Cnidus. February 1997. 20 February 2002. www.math.tamu.edu/~don.allen/history/udoxus.html
This source was good for the biographic information.
Eudoxus of Cnidus: Encylcopedia Britanica. 1999 ed.
This source explained the math pretty clearly.
O'Connor, J. Eudoxus of Cnidus.
20 February 2002.
In most of the sources I looked at, the math was explained in too complicated a manner. It took a while to find sources that could explain the math clearly. There also was not a lot of biographic information.