Greek Philosophers, Mathematicians and Scientists

Thales of Miletus (ca. 640-ca. 546 B.C.)
  demonstrative mathematics

Pythagoras of Samos (ca. 572-ca. 495 B.C.)

Zeno of Elea (ca. 490-ca. 430 B.C.)
  Zeno's paradoxes

Hippasus
 irrational number

Hippocrates of Chios (ca. 470-ca. 410 B.C.)
 quadrature of the lune

Socrates (ca. 469-399 B.C.)

Plato (427-347 B.C.)
 Five regular polygon

Eudoxus of Cnidus (ca. 408-355 B.C.)
 theory of proportion
 method of exhaustion

Aristotle (384-322 B.C.)

Euclid of Alexandria (ca. 300 B.C.)
 the Elements

Achimedes of Syracuse (287-212 B.C.)
 Archimedean screw
 lever and pulley
 On Floating Bodies
 Measurement of Circle
 On the Sphere and the Cylinder


Eratosthenes of Cyrene (ca. 276-ca. 195 B.C.)
 The Sieve of finding prime numbers
 On the Measurement of the Eearth

Eratosthenes sieve. Animation by Sebastian Koppehel

Syene is close to the tropic of cancer

Apollonius of Cyrene (ca. 262-ca. 190 B.C.)
 Conics

Note on Probability Theory: The Logic of Science by E. T. Jaynes

Chapter 1 Plausible reasoning
Boolean algebra

Chapter 2 Quantitative rules
product rule
sum rule
principle of indifference

Chapter 3 Sampling theory

Chapter 4 Hypothesis testing
4.1
X = prior information
H = hypothesis to be tested
D = data

P(H|X): prior probability
P(H|DX) : posterior probability
L(H) = P(D|HX)/P(D/X): likelihood, where P(D|HX) is the sampling distribution

P(H|DX)  = P(H|X)P(D|HX)/P(D/X)

4.2 binary hypothesis with binary data

Weber-Fechner law: intuitive human sensations tend to be logarithmic functions of the stimulus.

sequential inference