Thales of Miletus

Father of Greek Mathematics

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Thales of MiletusBorn around 640 B.C.E.; died around 542 B.C.E.

(dates differ, many sources say only that he lived about 600 B.C.E.

Ruins in Miletus

Miletus is located in the modern country of Turkey.

The Rumors*traveled to Egypt and brought back Egyptian geometry

*predicted a solar eclipse (May 585 B.C.E.)

*proved several geometric theorems

*diverted a river to help an army cross

*made a fortune by cornering the market of olive presses

*was a political advisor

*developed a method for determining the distance of ships at sea

*measured the height of a pyramid

*founded an Ionian school of natural philosophy

*taught geometry to Anaximander

*fell down a well while looking at the stars

Geometric Theorems attributed to Thales

*a circle is bisected by its diameter

*the base angles of an isosceles triangle are equal

*when two lines intersect, vertically opposite angles are equal

*the angle-angle-side congruence

*the angle subtended by a diameter of a circle is a right angle

Thales “discovered many propositions, and disclosed the underlying principles of many others to his successors, in case his method being more general, in others more empirical.”

--Eudemus, via Proclus

The Witnesses

None.

No works written by Thales survive. No history about Thales that was written either during his lifetime or within 100 years of his life exists.

The EvidenceHerodotus

(about 150 years after Thales

-engineer

-astronomer

-political advisor

Plato

(about 210 years after Thales

-astronomer

-falls in a well

Aristotle

(about 260 years after Thales)

-astronomer

-made a fortune

Proclus (Eudemus, 280 years after)

(about 1050 years after Thales)

-geometric proofs

-history

Diogenes Laertius

(at least 800 years after Thales)

Plutarch

(about 690 years after Thales)

Measuring the Pyramid*used concept of similar triangles

(may have had knowledge of contents of Rhind Papyrus)0

*compared shadow of known object (like a person) with the pyramid shadow

The Spirit of the Times

600 B.C.E. to 300 B.C.E.*Greeks began to ask “Why?”

-development of the proof

-Euclid’s Elements (about 300 B.C.E.)

*mathematics became a separate field of study

*rational methods for science

The Verdict

--We don’t know--

“There is no Proof!”

BibliographyHerodotus. The History of Herodotus. Great Books of the Western World, Vol. 6. Chicago: Encyclopeaedia Britannica, Inc., 1952.

Plato. Theaetetus. Great Books of the Western World, Vol. 7. Chicago: Encyclopeaedia Britannica, Inc., 1952.

Aristotle. Politics, Book 11. Great Books of the Western World, Vol. 9. Chicago: Encyclopeaedia Britannica, Inc., 1952.

Katz, Victor J. A History of Mathematics: An Introduction, Second Edition. New York: Addison Wesley Longman, 1998.

Struik, Dirk J. A Concise History of Mathematics, Fourth Revised Edition. New York, Dover Publications, 1987.

Cuomo, Serafina. Ancient Mathematics. NewYork: Routledge, 2001.

Diamandopoulous, P. The Encyclopedia of Philosophy, Vol. 7. New York: Macmillan Publishing Co., Inc. and The Free Press, 1967.

Heath, Sir Thomas L. A Manual of Greek Mathematics. New York: Dover Publications, Inc., 1963.

Anglin, W.S. and J. Lambek. The Heritage of Thales. Undergraduate Texts in Mathematics. New York: Springer-Verlag, 1995.

Gow, James. A Short History of Greek Mathematics. New York, Chelsea Publishing Company, 1968.

http://www-groups.mcs.st-andrews.ac.uk/Extras/Proclus_history_geometry.htmlMac Tutor History of Mathematics/Additional Material Index/Proclus and the history of geometry as far as Euclid.

Plutarch. The Lives of Noble Grecians and Romans. Great Books of the Western World, Vol. 14. Chicago: Encyclopeaedia Britannica, Inc., 1952. www.classicpersuasion.org/pw/diogenes/dlthales.htm Diogenes Laertius. The Lives and Opinions of Eminent Philosophers. London: Henry G. Bohn, 1853.

Neyman, Jerzey and Niccolo Zucchi. Biographical Dictionary of Mathematicians, Vol. 4. New York: Simon & Schuster Macmillan, 1991.

Young, Robyn V., editor. Notable Mathematicians: From Ancient Times to the Present. New York: Gale Research, 1997. Burnet, John. Early Greek Philosophy. http://faculty.evansville.edu/+62courses/phil211/burnet/ch1.htm

Euclid. The Elements. Great Books of the Western World, Vol.11. Chicago: Encyclopeaedia Britannica, Inc., 1952.

The Problem of “Everyone Knows”

You write in your diary, “I had cereal for breakfast this morning. I sure do love that Cap’n Crunch.”

Fast forward 500 years. An archeologist finds your diary and reads the entry. How does the archeologist interpret the entry?

*strolled out to a local field and picked cereal grains and ate them?

*you did this in the company of a military officer with a funny name

The Problem of “Everyone Knows”What we know about that cereal that the future archeologist may not know:

*the cereal was a processed product

*the cereal contained non-cereal ingredients like sugar and preservatives

*it came in a box or a bag

*you bought it from a grocery store

*you put it in a bowl

*you poured milk over it

*you ate it with a spoon

*Cap’n Crunch is one of many varieties of cereal available

Every culture makes assumptions about what “everyone knows.” The ancient Greeks are no exception.