Book of the Month: Famous Problems in Mathematics

JUngelösteProblemeanuary’s Book of the Month is Famous Problems in Mathematics by Heinrich Tietze, first published in German in 1959, and republished in 1990 by DTV. An English translation published by Graylock Press in 1964. The preface contains a beautiful metaphor and explanation of the nature of mathematical learning.

The original work is entitled Gelöste und ungelöste mathematische Probleme aus alter und neuer Zeit.
The full English translation has the title Famous Problems of Mathematics: Solved and Unsolved Mathematical Problems from Antiquity to Modern Times.

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Site of the Month: Famous Problems in the History of Mathematics

HistoryOfMathJanuary’s Site of the Month is Famous Problems in the History of Mathematics.

This site is part of NCTM’s MathForum and continues the problems theme of recent Sites and Books of the Month.

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Hilbert’s Problems

hilbertDecember’s Site of the Month is Hilbert’s 2000 Lecture.
At the International Congress of Mathematicians in 1900, David Hilbert presented ten important unsolved problems. When his lecture was published it contained 23 problems, several of which have now been solved (see the Wikipedia site for more historical information).
This month’s site is a copy of the published lecture–it was presented in the Mathematics Education part of the congress, and so is addressed to teachers of mathematics.

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+Plus Magazine

plusNovember’s Site of the Month is +Plus.
+Plus is an internet magazine from Cambridge University that is now connected to the Millenium Mathematics Project which “aims to help people of all ages and abilities share in the excitement of mathematics and understand the enormous range and importance of its applications to science and commerce”.
Several links from last month’s site are to articles in +Plus.

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Applications of Mathematics

applicationmathOctober’s Site of the Month is Applications of Mathematics.
This is part of the Mathigon website, directed at resources for schools. However the Applications of Mathematics section has links to several references for each application where the reader can access the mathematics behind the application.

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The Pythagorean Theorem

pythagoreantheoremDecember’s Book of the Month is The Pythagorean Theorem: A 4000-year History by Eli Moar, published in 2007 by Princeton Science Library.

This is the third book that celebrates a famous equation, in this case one that is so well known that it needs little introduction. However, its history pre-dates Pythagoras by over 1000 years, and traces through many cultures.

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Euler’s Gem: The Polyhedron Formula and the Birth of Topology

eulersgemNovember’s Book of the Month is Euler’s Gem: The Polyhedron Formula and the Birth of Topology by David Richeson, published in 2008 by Princeton University Press.
(Adapted from the Amazon description)
Leonhard Euler’s polyhedron formula describes the structure of many objects–from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the formula’s far-reaching impact on topology, the study of shapes. David Richeson tells how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope for use with higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula.

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E = mc^2: A Biography of the World’s Most Famous Equation

emc2October’s Book of the Month is E = mc^2: A Biography of the World’s Most Famous Equation by David Bodanis. First published in 2003 by Walker and Company, paperback published 2001 by Berkley.
(Adapted from the Amazon description)
Beginning by introducing each of the equation’s letters and symbols, Bodanis brings it to life historically, making clear the astonishing array of discoveries and consequences it made possible. It would prove to be a beacon throughout the twentieth century, coming to inform our daily lives, governing everything from the atomic bomb to the carbon dating of prehistoric paintings.

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Gamma – Exploring Euler’s constant

gammaThe September Book of the Month adds to the collection of books on particular “numbers” from last month:
Gamma: Exploring Euler’s constant by Julian Havil, published in 2003 by Princeton Science Library
and
Brief History of Infinity: The quest to think the unthinkable by Brian Clegg, published in 2003 by Constable and Robinson.

If readers of this blog know of other titles that would fit in this list of “Books about Numbers” please email b.barton@auckland.ac.nz. Please note that the Book of the Month is only used for books that have been in print for at least ten years.

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mathoverflow

appli_grouptheoryAugust Site of the Month is about applications of advanced mathematics: mathoverflow

The site is a thread of MathOverflow, a site for professional mathematicians.
This thread, however, simply collects all the applications of different areas of research mathematics.
Scroll down and enjoy.

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