History of mathematics I

general courses

The lecture dynamically presents the history of mathematical ideas and thinking. The focus is on relations between mathematics and the course of political and social history, civilisation, culture and the entirety of science. The scope of the lecture ranges between the neolithic revolution up to our times. In principle, mathematical knowledge at school level is sufficient to follow the course. However, greater knowledge of mathematics may help in a deeper understanding of some facts.

The course is widely accessible. However, it contains historically important examples of mathematical reasoning.

Linguistic sources on the prehistory of mathematical notions. The ideas of Piaget and New Maths.

Mathematics in empirical methodologies. Babilon. Egypt.

The revolution of the 18th century b.C. Thales and his school. The postulate of certain knowledge.

The conceptual revolution of the 6th century b.C. The Pythagoreans. Beginnings of deduction.

Plato's Academy. The numerical crisis. Creation of real numbers. Eudoxos and Theaetetus.

Euclid's "Elements" and other works.

Archimedes. Ptolemy, Diophantos. Historians and epigons.

Mathematics out of Europe in the antiquity and in the Middle Ages.

Mathematics as a game.

Gerbert. Universities. Fibonacci. Solution of equations of degree 3 and 4. The status of complex numbers.

Getting rid of computational problems. Logarithms.

Copernicus and Kepler. Pantheism.

Galileo Galilei. Descartes's "Discourse on the method". Academies of Science.

Beginnins of mathematical analysis. Newton, Leibniz, Huygens. The Bernoulli family.

The state of knowledge by the end of the 17th century.

Extended lecture notes:

M. Kordos, Wykłady z historii matematyki, WSiP 1994, Script 2005

In Polish:

D.J. Struik, Krótki zarys historii matematyki do końca XIX wieku, PWN 1963

Historia matematyki, pod red. A.P. Juszkiewicza, PWN 1978-1985

N. Bourbaki, Elementy historii matematyki, PWN 1980

S. Kulczycki, Z dziejów matematyki greckiej, PWN 1973

J. Mioduszewski, Ciągłość. Szkice z historii matematyki, WSiP 1996

Filozofia matematyki: antologia tekstów klasycznych, wyb. i opr. R. Murawski, Wyd. Naukowe UAM 1986

R. Murawski, Filozofia matematyki, PWN 1995

In other languages:

M. Kline, Mathematical Thought from Ancient to Modern Times, Oxford UP 1972

M. Kline, Mathematics, The Loss of Certainty, Oxford UP 1980

M. Kline, Mathematics in Western Culture, Oxford UP, 1958

A. Dahan-Dalmedico, J. Peiffer, Routes et dedales, Etudes Vivantes 1982 (French)

F. Klein, Vorlesungen uber die Entwicklung der Mathematik im 19.Jahrhundert, Springer 1926 (German)

(a series) Matematika XX wieka, red. A.N. Kolmogorov, A.P. Yushlevich, Nauka, 1978-1990 (Russian)

S.G. Gindikin, Rasskazy o fizikah i matematikah, Nauka 1981 (Russian)

(a selection of texts) Ob osnovanyah geometrii, Nauka 1988 (Russian)