The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: ...

Fuzzy number approximations provide a robust framework for representing and managing uncertainty in quantitative analyses. By generating simplified yet accurate representations of fuzzy ...

Earlier this summer, we posted about a study that revealed that monkeys could listen to a series of beeps and then equate it to a visual representation of the same number. One of the researchers ...

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer. The ...

Around 250 B.C., the Greek mathematician Archimedes calculated the ratio of a circle's circumference to its diameter. A precise determination of pi, as we know this ratio today, had long been of ...

Pi Approximation Day falls on July 22 (written as 22/7 in the day/month date format). It commemorates the common approximation of the mathematical constant π as 22⁄7, which dates back to Archimedes ...

The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field.

In this paper, we reveal a new connection between approximation numbers of periodic Sobolev type spaces, where the smoothness weights on the Fourier coefficients are ...