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In: 2026, Algebra and Number Theory, Bill Casselman, History of mathematics
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This is not obviously a difficult problem. But in over two hundred years since Carl Friedrich Gauss first posed it, there has been remarkably little progress... Another Look at Circles and Squares Bill Casselman University of British Columbia Another look at circles and squares One of the most intriguing unsolvedRead More →
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In: 2026, Algebra and Number Theory, History of mathematics, Ursula Whitcher
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Though the chart starts out in alphabetical order, there's a break in the pattern that offers a clue... Puzzling Like the Seventeenth Century Ursula Whitcher Mathematical Reviews (AMS) The following chart is taken from the second edition of a German-language arithmetic textbook by Anton Schultze. It was published in LiegnitzRead More →

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In: 2026, Discrete Math and Combinatorics, History of mathematics, Joseph Malkevitch
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Every time some mathematical question is answered, it generates new mathematical issues to think about.... Does Mathematics Progress? Joe Malkevitch York College (CUNY) Introduction With the beginning of a New Year—2026 in one system of counting, though not all societies use the same calendar—many people take the opportunity to examineRead More →
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In: 2025, Algebra and Number Theory, Bill Casselman, History of mathematics
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The Greeks were wary of infinities of any kind, and nothing like an exact definition of 'ratio' was possible for them... Irrationality Tamed Bill Casselman University of British Columbia Not so long ago, the internet magazine Quanta posted an article titled "How the square root of two became a number".Read More →

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In: 2024, History of mathematics, Joseph Malkevitch, Math and Technology
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A variety of experiments related to the Turing test have been carried out, and there are now computer programs that can systematically convince many humans that they are conversing with another human... People and Computers Compared Joe Malkevitch York College (CUNY) Introduction Humans—homo sapiens—often compare themselves to other species suchRead More →
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In: 2024, Anil Venkatesh, History of mathematics, Math and Arts/Humanities
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We see a distinct preference for denying the premise of the measurement rather than accepting a measured value of zero… Much Ado About Zero Anil Venkatesh Adelphi University Act NULLA1 It happened at the peak of remote instruction. I had just finished a Zoom session with my calculus students fromRead More →

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In: 2023, Algebra and Number Theory, Courtney Gibbons, History of mathematics
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Polynomials, it turns out, are useful for more than just input-output assignments! Perspectives on Polynomials (it’s a witch!) Courtney Gibbons Hamilton College It was a dark and stormy night… Okay, it was probably more like 3:30 in the afternoon on a crisp fall day back when I was teaching CalcRead More →

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In: 2021, Adam A. Smith, History of mathematics, Math and Technology, Real and Complex Analysis
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Alan Turing and the Countability of Computable Numbers Turing's methodology was unique: he imagined hypothetical machines that could perform complicated mathematical tasks in a deterministic manner, in the way computers do today. In this way, he inadvertently kickstarted the entire field of modern computer science... Adam A. Smith University ofRead More →

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The Battle of Numbers Our topic is the game called rithmomachia or rithmomachy—literally, the battle of numbers... Ursula Whitcher AMS | Mathematical Reviews, Ann Arbor, Michigan This month, we're going to explore a very old—indeed, medieval—educational game and correct a mathematical error in a sixteenth-century game manual. But before weRead More →

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The Once and Future Feature Column We’re going to look back at the Column’s history, revisit some of our favorite columns, and talk about what comes next. Spoiler alert: We’re recruiting new columnists! Ursula Whitcher AMS | Mathematical Reviews, Ann Arbor, Michigan The number 24 has many charming properties. ForRead More →