It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question. In June 1978, the ...

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2024. Analytic combinatorics in several variables estimates coefficients ...

Rational functions are fundamental in mathematics, particularly in calculus and algebra, serving as building blocks for more complex mathematical models and analyses. Understanding what constitutes a ...