History of Math

Egypt

Egypt

2700 BC - 1600 BC

Pyramids of Saqqara and Giza

2600 BC - 1600 BC

Egypt

The Moscow Papyrus

1850 BC

Egypt

The Rhind Papyrus

Approx. 1650 BC

Egypt

Mesopotamia

Mesopotamia

2000 BC - 1600 BC

Greece

Thales

624 BC - 547 BC

Greece: Early Period
Thales of Miletus

Greece

600 BC - 500 AD
  • 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

Pythagoras

520 BC

Greece: Early Period
600 BC?
Believed to be responsible for a theorem about right angles.

Plato

387 BC

Greece: Athens

Plato's Academy Founded

387 B.C.

Greece: Athens

Aristotle

384 BC - 322 BC

Greece: Athens
Niomachean Ethics
Metaphysics

Eudoxus

370 BC

Greece: Athens

Niomachean Ethics - Aristotle

350 BC

Mentions that the origin of money was barter

Archimedes

250 BC

Greece: Alexandria

Euclid

Approx. 250 BC

Greece: Alexandria

Apollonius

220 BC

Greece: Alexandria

Ptolemy

150 AD

Greece: Alexandria

Diophantus

Approx. 250 AD

Greece: Alexandria
Wrote about numbers satisfying x2 + y2 = z2
method to divide a square number into two squares

Pappus

320 AD

Greece: Alexandria

Hypatia

400 AD

Greece: Alexandria

China

Emperor Yu

Approx. 2000 BC

Magic square on a tortoise

China

300 BC - 1400 AD

Han Dynasty

206 BC - 220 AD

Jiuzhang Suanshu

200 BC

Text 2

Sun Zi

250 AD

Sunzi Suanjing
Chinese remainder theorem

Liu Hui

263 AD

Classic Island of the Sun
pi: 3072 sides

Zu Chongzhi

500 AD

pi: 24576 sides

India

King Ashoka's edicts

250 BC

India

400 AD - 1200 AD

Mayan

Mayan

500 AD - 1000 AD

Islamic/Arabic

Islamic/Arabic

750 AD - 1400 AD

Al-Khwarizmi

783 AD - 850 AD

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

Al-Haitham

965 AD - 1039 AD

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

Omar Khayyam

1048 - 1131

Solving equations

Money and Measurement

Money invented : Lydia

1700 BC

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

Vindolanda tablets

Approx. 100 AD

Found in North Britain

Roman coins in England

300 AD

Romans left Britain

Approx. 410 AD

Europe

Dark Ages

500 - 1000

Gerbert of Aurillac

938 - 1003
  • 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

Fibonacci

1170 - 1240
  • Son of Bonaccio
  • Born in Pisa, travelled the Mediterranean
  • Popularise the Hindu-Arabic numerals
  • Critical in bringing the Arabic mathematics to wider recognition Europe

Liber Abaci

1202

(Book of Calculation)
4 main areas : calculations, business math, recreational math, roots and geometry

Jordanus de Nemore

Approx. 1220
  • Not much known about him
  • Pioneer of symbolic algebra
  • Author of at least 6 mathematical texts
  • Not much influential

Richard of Wellingford

1292 - 1336

Oxford: Merton School

Nicole Oresme

1323 - 1382
  • 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

De Moneta by Nicole Oresme

1360

Spoke about barter being the origin of money

Filipo Brunelleschi

1377 - 1446

Octagonal Cupola of a cathedral in Florence, perspective painting

Leon Battista Alberti

1404 - 1472

The first duty of a painter is to know geometry

Piero Della Francesca

1415 - 1492

Madonna and Child with Saints

Johannes Regiomontanus

1436 - 1476
  • Probably greatest astronomer of 15th century
  • Founded his own printing press, one of the first publishers of mathematical and scientific work for commercial use

Bungus's compilation of perfect numbers

1584

Fermat

1601 - 1665

Fermat's last theorem

John Wallis

1616 - 1703

Arithmetica Infinitorum

Fermat's letter to Mersenne about his little theorem

1640

October
Translated by Jacqueline Stedall

Isaac Newton

1642 - 1727

Mersenne on testing for primes

1644

Jacob Bernoulli

1654 - 1705

Bernoulli Family

Arithmetica Infinitorum

1656

John Wallis

Johann Bernouli

1667 - 1748

2nd brother - Bernoulli family

Daniel Bernoulli

1700 - 1782
  • 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

Leonhard Euler

1707 - 1783

Konigsberg problem

1735

Proven impossible by Euler

Mechanica

1736

Euler's treatise on the dynamics of a particle

Exposition of new theory on the measurement of risk

1738

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 in Berlin

1741 - 1766

Euler joined Berlin Academy

Introductio in Analysin Infinitorum

1748

Euler's Introduction to the analysis of the infinite

Euler on motion of a rigid body

1750

Euler's equations of motion, moments of inertia

Theorem on the rotation of a body about a point

1776

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

Mathematical Psychics

1881

Investigations in currency and finance Stanley Jevons

1884

Sir T.L Heath's The Works of Archimedes

1897

John Von Neumann

1903 - 1956
  • 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

John von Neumann proves minimax theorem

1928

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)

Theory of Games and Economic Behavior

1944

John von Neumann and Oskar Morgenstern

Great Britain

Bishop Robert Grosseteste

1175 - 1253
  • Official title of Chancellor of Oxford in 1214
  • Founded the tradition of scientific thought in Oxford
  • Geometry and optics

Oxford University

Approx. 1214

Bishop Grosseteste given the title of Chancellor of Oxford

Roger Bacon

1214 AD - 1294 AD
  • 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

Thomas Bradwardine

1290 - 1349
  • 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

Geoffrey Chaucer

1342 - 1400
  • Interested in mathematical instruments
  • treatise of the astrolabe - one of the earliest scientific books

Treatise of the Astrolabe

1343

Book by Geoffrey Chaucer
One of the earliest Science books to appear in English

The Merton School

Approx. 1400

Germany

Carl Friedrich Gauss

1777 - 1885

Mobius

1790 - 1868

Einstein's miraculous year

1905

Brownian motion
E=mc2

France

Marin Mersenne

1588 - 1648

Montmorth

1678 - 1719

Jean-Charles de Borda

1733 - 1799
  • 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

Gaspard Monge

1746 - 1818

Joseph Georgenne

1771 - 1859

Essai

1785

Condorcet

Jean-Victor Poncelet

1788 - 1867

Ecole Polytechnique founded

1794

Antoine Cournot

1801 - 1877
  • 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

Researches into the Mathematical Principles of the Theory of Wealth

1838

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

Theory of Speculation

1900

Louis Bachelier
- Mathematical model of asset prices
- Doctoral thesis - foundation of financial mathematics
- dS/S = Adt + Bdx

Italy

Cubic Equations

Luca Pacioli

Approx. 1465 AD - 1526 AD

Scipione del Ferro

1465 - 1526
  • Found a general method for solving cubic equations
  • Mathematics lecturer
  • Taught at University of Bologna Italy

Tartaglia

1500 - 1557
  • Niccolo of Brescia
  • Solved cubic equations
  • Won problem-solving competition against Fior

Gerolamo Cardano

1501 - 1576

Wrote about mathematics, medicine, physics, probability
- Ars Magna

Ars Magna

1545

Cardano