News, Views & Insights
The Erdős unit distance problem asks for the largest possible number u(n) of unit distances among n points in the plane. This is equivalent to finding maximally dense unit-distance graphs. A recent OpenAI announcement concerns the asymptotic problem: the old n^(1+o(1)) expectation is false.
Every semester or two, students ask me about the implications of re-compression, especially of JPEG files. Compression comes in two main kinds—Lossless, which is completely invertible, meaning you get exactly what you put in when you decompress, and Lossy which ‘throws out’ things deemed unimportant in some way, so that when you decompress, you get […]
I am writing a novel. It’s a historical fiction thing. Apparently, that means I need to do a lot of research on what life was like in the 1920s. My problem last night was, my character moves to Boston from Chicago, and in order to give the city texture, we need to introduce characters, […]
“The cat’s out of the bag,” said the mathematician Andrew Granville, reflecting on the rapid improvement of AI systems. His phrase captures the mood of the moment: by 2025-26, large language models (LLMs) had become powerful enough to move from impressive demonstrations to serious mathematical and scientific use. AI systems reached gold-medal level at the […]
This tutorial is a follow-up to a recent post by the author herself about archeoastronomical modeling of Central European Neolithic Circular Ditches [1], or roundels, with Wolfram 3D graphical primitives. Here, the focus will be instead on the use of mesh-based primitives from computational geometry to build a realistic 3D model of a roundel recently […]
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard […]
Wolfram Language is a multi-paradigm programming language designed for functional programming. It is mainly used in Wolfram|Alpha and Mathematica. This year, Texas Tech University organized a HACKATHON with the purpose of detecting and classifying breast cancer using Wolfram Language. This competition aims to introduce girls from Colegios Científicos to programming, promote female participation in […]
It was a great pleasure to present this demo at APS 2026 alongside 2025 Nobel Laureate in Physics John Martinis, CTO of Qolab, and my good friend Paul Buttles from Qolab.
A pure qubit state lives on the Bloch sphere—a unit sphere whose poles are |0〉and |1〉and whose equator holds the superposition states. This document builds the complete computational machinery for rotating the Bloch vector from the north pole to any target point, then measuring that state through the dispersive readout chain that a real cQED experiment uses. Every formula is immediately verified with TransmonLab code: if we cannot compute it, we cannot claim to understand it.
I am pleased to announce that the Wolfram Notebook version of Essentials of Complex Analysis: A Computational Approach was published by Wolfram Media on December 16, 2025, ISBN-13: 978-1-57955-096-7. You can get your free copy of the e-book here: https://www.wolfram-media.com/products/essentials-of-complex-analysis
This e-book is the companion to the free course on complex analysis on Wolfram U, and is an introduction to the subject for a first undergraduate course.