More than 100 years ago Hungarian-born mathematician George Pólya found himself trapped in a loop of social awkwardness. A professor at the Swiss Federal Institute of Technology Zurich, he enjoyed ...

Abstract: In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters.

Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...

Convolution is a remarkable property of the Fourier transform, often cited in the literature as the “faltung theorem”. Convolution is a remarkable property of the Fourier transform, often cited in the ...

For decades, Hindi dominated India’s film industry — the largest in the world. Then some underdog filmmakers from the south released a movie that would change everything. By Vishal Menon “Pan Indian” ...

A windowed sinc function can implement a low-pass filter, and a two-dimensional convolutional filter can blur or sharpen images. In part 3 of this series, we introduced a low-pass filter based on the ...

A moving-average filter can address white noise in the time domain but performs poorly in the frequency domain. Figure 1. The convolution engine calculates y(tn) for n=6 (a) and then goes on to ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...