MA0024 lecture 2
History of mathematics
Babylonian mathematics
as seen by a mathematician
and by a historian
Helena Durnová
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Tablet YCB 7289
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Square root and the diagonal
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Mesopotamian mathematics
● Eleanor Robson, 2009, Mathematics in
Ancient Iraq: A Social History (Princeton
University Press)
● The region of modern-day Iraq is uniquely rich in evidence for
ancient mathematics because its prehistoric inhabitants wrote
on clay tablets, many hundreds of thousands of which have
been archaeologically excavated, deciphered, and translated.
Drawing from these and a wealth of other textual and
archaeological evidence, Robson gives an extraordinarily
detailed picture of how mathematical ideas and practices were
conceived, used, and taught during this period. She challenges
the prevailing view that they were merely the simplistic
precursors of classical Greek mathematics, and explains how the
prevailing view came to be. Robson reveals the true
sophistication and beauty of ancient Middle Eastern
mathematics as it evolved over three thousand years, from the
earliest beginnings of recorded accounting to complex
mathematical astronomy. Every chapter provides detailed
information on sources, and the book includes an appendix on
all mathematical cuneiform tablets published before 2007.
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Donald Knuth (*1938)
● Programmer? Mathematician?
Physicist?
● Honorary doctorate, MU
● TeX typesetting system
● The Art of Computer
Programming (1997 and on, in
notes before)
● John von Neumann (1902-1957)
and Donald Knuth
● ACM Turing Prize, 1974
(Who was Alan Turing?)
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Honorary doctorate at MU Brno, 1996
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Jens Hoyrup (*1943)
● Danish … mathematician? physicist?
historian of mathematics?
● Studied mathematics and physics
(1962-1969)
● Later turned to history of
mathematics and science
● Specialisation: Babylonian
(Mesopotamian) mathematics
● A historian of mathematics should
know more languages (Latin
German, French and the old scripts
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50 F 1
● The contents of the storehouse
of grain was distributed among
men and consequently, 45, 42,
51 rations (together 164571)
were distributed, while 3 sila
were left over.
● What is the size of the granary?
Either standard, or known to the
pupil (scribe).
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671 R and 671 F
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Tablet 50: top
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Tablet 50: from the side
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Tablet 671: from the bottom
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Tablet 671: from the top
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Tablet 671: from the side
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… actually, a formal division problem
● Why is it interesting? Unlike other traditions, it uses reciprocals.
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Some numerals in Mesopotamia
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Capacity (volume) units
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Algorithm?
● What is an algorithm? - Al Khwarizmi, 8th
century
● Can Ancient Babylonian procedures be called algorithms?
● Purpose of Knuth's paper: trace history of informatics as far back as
possible.
● Purpose of history of mathematics – similar.
● History of calculating / computing, history of geometry, history of
book keeping, history of table making, ...
● Which one do we want?
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Implications for the course
● Both versions present “out there”
● If “it's history, it cannot be new”, then what about historians?
● Euclid: a well-known figure, but do we know anything?
– Vincenzo de Risi, “polycephalic Euclid”
● Egyptian fractions
– repeated in textbooks often with looking down on the ancients
– Unit fractions: fictional reason, “they were UNABLE to work
● Giving ancient concepts modern names
– Sabetai Unguru