B.C. (approximate dates
to 976 B.C.)
 50,000 counting
 25,000 Geometric design Paleolithic
 3,000 Hieroglyphic numerals Egypt
 2,800 Great Pyramid 1/2
octahedron form
 2,400 Positional Mesopotamia
 600 Babylonian Art Star
Pentagon
 500 Discovery near Padua
of an Etruscan Dodecahedron stone

Dawn
of Greek Classical Geometry (Mathematics) 
585
Thales of Miletus deductive geometry; logic traveled
to Egypt introduced "rope pulling" to the Greeks;
Egyptian practice of measuring the land after annual Nile
floods.
Thales elevated measurements from practical to philosophical
logic
"not what we know, but how we know it" (scientific
method).
Mathematics defined "that which is learned".

540
Pythagorean arithmetic and geometry (Italian coast) Harmonics/Music.
Pythagoreans were secretive and cultish.
Motto: "All is number".
Discovered theory of proportions and constructed the "cosmic
figures" or Regular Polyhedra.
They were partially interested in the pentagon and pentagram
or the star pentagon which describes the "golden mean".
They knew of the cube and octahedron (seen in minerals and crystals)
and pentagonal dodecahedron. Did not know of the tetrahedron
or icosahedron. 
427
Birth of Plato.
Plato was not a mathematician but had the Academy in Athens
and encouraged mathematics discoveries. Elevated math to "pure
intelligence" and discouraged practical applications. Academy
motto "Let no one ignorant of geometry enter here".
Restricted geometric construction to the use of a straight
edge and compass; the Academy originated the basic "liberal"
education: arithmetic, music, geometry, astronomy (quadravium). 
414
Theltetus, friend of Plato and student of the Academy
who developed the theorems of the Five Platonic Solids. Proved
there are only five possible.
The theorems appear in Euclid's Elements 
388
Plato visited the Pythagoreans and returned to Athens
where the five regular polygons were developed and associated
with natural elements: Tetrahedron=Fire, Octahedron=Air, Cuboctahedron=Earth,
Icosahedron=Water, Dodecahedron=Universe.
"God used it for the Whole" Written down in
the Timeaus Platonic Dialogue. 
370
Aristotle: Greatest scholar of all time and started the
Lyceum School. He was astudent of Plato and tutor of Alexander
the Great. 
332
Euclid of Alexandrea in 300 B.C. produced the greatest
math book of all times called The Elements. Thirteen
Books in all. The last book contains the "Cosmic Figures"
(Platonic Solids) and describes how they can be constructed
within spheres. This would later inspire Kepler's cosmology. 
306
Ptolemy: Started the School of Alexandria also called
The Museum or The Library located in Alexandria Egypt (Part
of Greece at the time). The seat of Greek learning for
the next nine hundred years. 
287
Archimedes: Considered the greatest mathematician of Antiquity.
Killed by Roman soldier 212B.C. He was called on to invent
defensive weapons against Rome. He preferred pure
mathematics to practical invention. Discovered the 13(?) semiregular
polyhedra: convex polyhedron whose
faces are all regular polygons but not the same. Finite
set. Many of Archimedes' works are lost. The Method,
which included the theorems for the Archimedes Solids are lost
from approx. 11th Century to 1906 when it was discovered in
Constantinopal. 
44
Death of Julius Ceaser. 