March Site of the Month: The Wolfram MathWorld List of Unsolved Problems

This updated list explains the most famous unsolved problems in mathematics and progress made on each, with references for further reading.

Connecting mathematical worlds

March Site of the Month: The Wolfram MathWorld List of Unsolved Problems

This updated list explains the most famous unsolved problems in mathematics and progress made on each, with references for further reading.

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January’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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January’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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December’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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November’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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October’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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December’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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November’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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October’s Book of the Month is *: 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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The 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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