Pythagoras as a mathematician

The mathematician as a formalist

A Mathematician Reads

New York University mathematical physicist Alan Sokal published in the postmodern humanities journal Social Text a parody entitled “Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity” [1]. His point in doing so was to test whether the field of “cultural studies of science” was seriously lacking in “intellectual standards”. His article is nonsense from start to...

Beyond Pythagoras

This paper discusses the new harmonic possibilities enabled through the implementation of Sethares’ theory of the dissonance curve in Max/MSP and its use in a live electronic composition by two of the authors.

Relieving and Readjusting Pythagoras

Bill James invented the Pythagorean expectation in the late 70’s to predict a baseball team’s winning percentage knowing just their runs scored and allowed. His original formula estimates a winning percentage of RS/(RS+RA), where RS stands for runs scored and RA for runs allowed; later versions found better agreement with data by replacing the exponent 2 with numbers near 1.83. Miller and his c...

Pythagoras Numbers of Fields

The study of sums of squares in a ring or a field is a classic topic in algebra and number theory. In this context, several questions arise naturally. For example, which elements can be represented as sums of squares, and if an element can be written as a sum of squares, how many squares are actually needed ? For instance, for an integer n to be a sum of squares of integers, we must obviously h...