News, Views & Insights
June 23, 1988 is when we launched Version 1.0 of Mathematica. Todayāalmost 38 years laterāweāre launching Version 15 of whatāin recognition of how far itās expanded beyond āmathāāwe now call Wolfram Language. Itās an impressive release, with a lot of new core functionality. It might perhaps seem surprising that after 38 years thereād still be […]
LLMs donātāand canātādo everything. What they do is very impressiveāand useful. Itās broad. And in many ways itās human-like. But itās not precise. And in the end itās not about deep computation.
So how can we supplement LLM foundation models? We need a foundation tool: a tool thatās broad and general and does what LLMs themselves donāt: provides deep computation and precise knowledge.
And, conveniently enough, thatās exactly what Iāve been building for the past 40 years! My goal with Wolfram Language has always been to make everything we can about the world computable. To bring together in a coherent and unified way the algorithms, the methods and the data to do precise computation whenever itās possible. Itās been a huge undertaking, but I think itās fair to say itās been a hugely successful oneāthatās fueled countless discoveries and inventions (including my own) across a remarkable range of areas of science, technology and beyond.
The ErdÅs 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 kindsāLossless, which is completely invertible, meaning you get exactly what you put in when you decompress, and Lossy which āthrows outā things deemed unimportant in some way, so that when you decompress, you get […]
I am writing a novel. Itās a historical fiction thing. Apparently, that means I need to do a lot of research on what life was like in the 1920s. ā 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, […]
āThe catās out of the bag,ā 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 […]
