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Math Horizons Contents—September 2013

In the September issue of Math Horizons, Jordan Ellenberg explains recent progress on the twin primes conjecture; Tommy Ratliff reports from the courtroom, where he finds pi on trial and an illegal prime number; and, in keeping with the Mathematics of Planet Earth 2013 theme, Glen Van Brummelen explores the nuances of finding the qibla, and George Heine explains just how we came to know that the Earth is not quite a perfect sphere. —Stephen Abbott and Bruce Torrence

Volume 21, Issue 1


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The Beauty of Bounded Gaps: A Huge Discovery about Prime Numbers and What It Means for the Future of Mathematics

Jordan Ellenberg

Important in its own right, a recent breakthrough by University of New Hampshire professor Tom Zhang represents a major step toward proving one of the most famous mathematical conjectures of all time.

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Of Camels, Inheritance, and Unit Fractions

Paul K. Stockmeyer

Proportional division problems are more than 3,500 years old, but they continue to charm and challenge new generations of problem-solvers.

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THE VIEW FROM HERE: Budapest Semesters in Mathematics: A Study Abroad Utopia

Gregory Michel

Our student author reports on his transformative semester abroad in the city of Paul Erdős.

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Seeking the Divine on Earth: The Direction of Prayer in Islam

Glen Van Brummelen

The widely practiced Muslim ritual of facing Mecca to pray turns out to involve the less widely practiced tools of spherical trigonometry.

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Pi on Trial and Other Prime Suspects

Tommy Ratliff

Is π a copyrightable fact? Can a prime number be illegal? Real court cases about real numbers can be real strange. (pdf)

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ALUMNI PROFILES: Not Your Father's Ad Agency

Ben Liang

A recent math major exits the slow-moving traffic on Wall Street for the fast-paced world of digital advertising.

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Beading the Seven-Color Map Theorem

Susan Goldstine, Sophie Sommer, and Ellie Baker

A decorative bracelet illustrating the seven-color theorem makes the four-color theorem seem plane boring.

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Euler and the Flattening of the Earth

George Heine

In the early 18th century, questions about the precise shape of the world sent mathematicians to the ends of the earth searching for an answer.

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The Math Horizons problem section, edited by Derek Smith and Gary Gordon


AFTERMATH: $$i$$ Can't Stand It Anymore

Travis Kowalski

Did Euler’s choice of notation doom complex numbers to reside in an imaginary world?