MA0024 lecture 1
History of mathematics
History of mathematics:
internalist, externalist, social, cultural
Helena Durnová
20 February 2025
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Purpose of this lecture
● Inspiration for your book presentations next week
● Talking about books you probably will not read, because they are in
German, French, and Russian (in translation)
● Different authors: also fiction writers
● Different styles:
– Compendium, Handbook, Monograph,
– Textbook, Popular book
● Different readerships:
– Historians of mathematics, mathematicians
– Children, Students, the Public
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Hans Wussing (1927-2011)
● German historian of mathematics
● Worked in the GDR (Eastern
Germany)
● Famous for writing about
Mathematicians on postage stamps
● Mathematics in the Antiquity
● Lectures on History of Mathematics
(for future maths teachers)
● Biographies of significant
mathematicians
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Biographical dictionaries
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Dictionary of Scientific Biography
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Une Histoire des Mathématiques.
Routes at dédales. (1982)
● Authors: Amy Dahan-Dalmedico,
Jeanne Pfeiffer
● Translation into Russian: 1986
● Criticism in the Russian edition:
weird choice of topics, missing
information about Russian and
Soviet scientists, etc.
● 8 chapters: Panorama; Greece;
Figures and geometry; Classical
Algebra; Big changes; The notion of
a function; Between algebra and
geometry; New objects.
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Egmont Colerus (1888-1939)
● German edition: 1940
● Translated into Italian (1941) as
Piccola Storia Della Matematica
● Pythagoras; Euklid; Archimedes;
Apollonios von Perga. Diophantos;
Alchwarizmi; Leonardo von Pisa;
Nicole von Oresme; Vieta; Jost
Bürgi; Descartes; Jean Victor
Poncelet; Evariste Galois; Carl
Friedrich Gauss; Bernhard
Riemann; David Hilbert
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A Concise history of mathematics
(Dirk Jan Struik)
● Beginnings
● Ancient Orient
● Greece
● Beginnings – western Europe
● 17th
century
● 18th
century
● 19th
century
● Main periods in history of
mathematics
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Math through the Ages:
A Gentle History for Teachers and Others
● Beginnings
● Greek Mathematics
● Meanwhile in India
● Arabic Mathematics
● Medieval Europe
● The 15th
and 16th
centuries
● Algebra comes of age
● Calculus and Applied Mathematics
● Rigor and Professionalism
● Abstraction. Computers...
● Mathematics Today
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Turning points in the history of
mathematics (Grant & Kleiner 2015)
● Axiomatics – Euclid and Hilbert
● Solution by radicals
● Analytic geometry
● Probability (games to theory)
● Calculus
● Gaussian integers
● Noneuclidean geometry
● Hypercomplex numbers
● The Infinite
● Philosophy of mathematics
● Some further turning points
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Writing history of mathematics essay
● Topic and question
– Your own question, but may be on an “old” topic
– How did it happen? What is the story?
● Sources
– GOOD: but what is a good source? Paper vs. Internet is not the right distinction
– For your essay, they should be easily available
● Advice?
– Get the chronology right
– Do not use words like “naturally”, “obviously”, etc., nor superlatives
– Explain why you would like to know about the particular topic
– Use footnotes: History floats on footnotes.