News, Views & Insights
“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.
On April 1, 2026, NASA will launch the first crewed space mission around the Moon since the Apollo era. Known as Artemis II, the mission will not land on the Moon, nor will it orbit the Moon, but will undergo a free-return trajectory that whips the crew around the Moon and back along an asymmetric […]
Every sound you hear in a movie, a song or a phone call, has been shaped by audio effects—filters that cut unwanted noise, reverb that simulates the acoustics of a concert hall, pitch shifts that raise or lower a voice. In this post, we’ll build all of these from scratch using Wolfram Language, turning a […]
This study presents a comprehensive numerical investigation of magnetohydrodynamic (MHD) convection in a conductive fluid subjected to a rotating magnetic field within a rectangular cavity. The model incorporates a convective flow induced by differential heating of opposing vertical walls under adiabatic conditions. The governing equations are derived based on Maxwell’s equations and the incompressible Navier–Stokes equations, with the magnetic forcing term, averaged over time under low magnetic Reynolds number conditions. A high-resolution numerical algorithm is employed to analyze the stability and transition to turbulence as the magnetic Taylor number (Ta) and Rayleigh number (Ra) increase. The results are consistent with prior experimental observations of flow destabilization at critical values of Ta. Furthermore, the study investigates the emergence of large-scale, nonstationary structures in the turbulent regime, quantifying the finite-time blow-up of solutions as a function of Pr, Ra, and Ta. Attractor formation in velocity space is examined to distinguish deterministic non-periodic solutions from fully developed turbulence. By computing over 104 parameter points, phase diagrams are constructed to illustrate regions of flow stability, deterministic chaos, and turbulence. These results offer novel insights into the interplay between electromagnetic forcing and convective instability, with potential applications in metallurgy, electrochemistry, and crystal growth processes.