Egypt

Egypt

Egypt

Greece: Early Period

Thales of Miletus

- 3 sections: Early, Plato and Aristotle's Academy, Alexandria
- Hardly any primary sources - Papyrus
- Rely entirely on comments and later versions : Proclus and Islamic scholars

Greece: Early Period

600 BC?

Believed to be responsible for a theorem about right angles.

Greece: Athens

Greece: Athens

Greece: Athens

Niomachean Ethics

Metaphysics

Greece: Athens

Mentions that the origin of money was barter

Greece: Alexandria

Greece: Alexandria

Greece: Alexandria

Greece: Alexandria

Greece: Alexandria

Wrote about numbers satisfying x^{2} + y^{2} = z^{2}

method to divide a square number into two squares

Greece: Alexandria

Greece: Alexandria

Magic square on a tortoise

Text 2

Sunzi Suanjing

Chinese remainder theorem

Classic Island of the Sun

pi: 3072 sides

pi: 24576 sides

Islamic scholar: arithmetic, algebra

Kitab al-jabr w'al muqabalah

Algorithmi de numero Indorum

Astronomical tables, treatise on astrolabe

Arithmetic introduced the Indian number system to the Islamic world

study of optics

invention of the pinhole camera and the camera obscura

Kitab al-Manazir (Book of optics) - Alhazen's problem

Tried to prove Euclid's parallel postulate

Solving equations

Money was circulating in Lydia by the end of 1700 BC, whose last king Croesus is proverbial for his wealth

Found in North Britain

- Trained in Catalona
- Introduced Hindu-Arabic numerals to Christian Europe
- Revival of interest in mathematics began with him
- Teacher of Quadrivium subjects
- Reintroduced the armillary sphere
- Pope Sylvester II

- Son of Bonaccio
- Born in Pisa, travelled the Mediterranean
- Popularise the Hindu-Arabic numerals
- Critical in bringing the Arabic mathematics to wider recognition Europe

(Book of Calculation)

4 main areas : calculations, business math, recreational math, roots and geometry

- Not much known about him
- Pioneer of symbolic algebra
- Author of at least 6 mathematical texts
- Not much influential

Oxford: Merton School

- Doctorate in Theology
- Translation of the works of Aristotle (on the request of King Charles V)
- Infinite series, proposition work on mechanics and representation of data in graphical form
- Opposed to many of Aristotle’s ideas of weight and planetary motion

Spoke about barter being the origin of money

Octagonal Cupola of a cathedral in Florence, perspective painting

The first duty of a painter is to know geometry

Madonna and Child with Saints

- Probably greatest astronomer of 15th century
- Founded his own printing press, one of the first publishers of mathematical and scientific work for commercial use

Fermat's last theorem

Arithmetica Infinitorum

October

Translated by Jacqueline Stedall

Bernoulli Family

John Wallis

2nd brother - Bernoulli family

- Second generation of Bernoullis, Jakob Bernoulli’s son
- Mathematician and physicist
- Studied mathematics and medicine at University of Basel
- Was the first to apply mathematical analysis to the problem of movement of bodies
- Utility theory
- Marginal Utility
- Poor man lottery ticket
- logarithmic curve represents utility

Proven impossible by Euler

Euler's treatise on the dynamics of a particle

By Daniel Bernoulli

- Utility theory

- A poor man vs rich man with a lottery ticket analogy

- Marginal Utility

- Logarithmic curve represents utility

Translated by Louise Sommer 1954

Euler joined Berlin Academy

Euler's Introduction to the analysis of the infinite

Euler's equations of motion, moments of inertia

Euler proved that any rotation of a rigid body about a point is equivalent to a rotation about a line through that point.

1928: Minimax theorem

- There is a `rational’ outcome for any two-person zero-sum game. There is a kind of equilibrium. Both players are satisfied that they cannot do any better. (Pareto efficiency)

The Theory of Games and Economic Behaviour (1944) written with Morgenstern

Hungarian and Jewish by birth, von Neumann emigrated from Europe

Institute of Advanced Sciences, close to Princeton University in the US.

The Theory of Games and Economic Behaviour (1944) written with Morgenstern

There is a `rational’ outcome for any two-person zero-sum game. There is a kind of equilibrium. Both players are satisfied that they cannot do any better. (Pareto efficiency)

John von Neumann and Oskar Morgenstern

- Official title of Chancellor of Oxford in 1214
- Founded the tradition of scientific thought in Oxford
- Geometry and optics

Bishop Grosseteste given the title of Chancellor of Oxford

- Most famous Grossetestes’s admirer
- Franciscian friar
- Came to oxford very young
- Took holy orders at 19
- Dr. Mirabilis (known as)
- Money on scientific manuscripts and instruments and wrote on scientific issues
- Conflict with the Church in Rome, imprisoned for his views

- Most important of the Merton scholars
- Books on arithmetic, algebra, velocities and logic
- Called ‘Dr. Profundus’ because his discourses - learned
- Greatest English mathematician of the 14th century
- Archbishop of Canterbury

- Interested in mathematical instruments
- treatise of the astrolabe - one of the earliest scientific books

Book by Geoffrey Chaucer

One of the earliest Science books to appear in English

Brownian motion

E=mc2

- Member of the Academy of Sciences
- Mathematical Physics, scientific improvements
- one of the spirits of the French Revolution
- How best to combine individual preferences
- resolving single preference anamoly
- Assigning marks: Borda count
- Conducting the election in Rounds

Condorcet

- Professor of math at University of Lyon
- Wrote about mathematics and economics
- Used differential calculus to discuss maximising profit
- Law of Demand
- Demand is a function of price D = F(p)
- Maximizing revenue pF(p) by optimisation

Written by Antoine Cournot

- Used differential calculus to discuss maximising profit

- Law of Demand

- Demand is a function of price D = F(p)

- Maximizing revenue pF(p) by optimisation

Louis Bachelier

- Mathematical model of asset prices

- Doctoral thesis - foundation of financial mathematics

- dS/S = Adt + Bdx

Cubic Equations

- Found a general method for solving cubic equations
- Mathematics lecturer
- Taught at University of Bologna Italy

- Niccolo of Brescia
- Solved cubic equations
- Won problem-solving competition against Fior

Wrote about mathematics, medicine, physics, probability

- Ars Magna

Cardano