Wolfram Blog

• OpenAI Disproves Erdős Unit Distance Conjecture

  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.

• Theory Meets Practice: 8 Books to Start Your Career in Astrophysics, Geography, Civil Engineering and More

  In or out of school, the opportunities to learn and grow in your career are endless, and Wolfram is proud to bolster those with educational resources, from courses to textbooks. We are happy to share conversations with two authors whose books cover applications of Wolfram technology in astrophysics and geography, as well as highlight a […]

• Compression and Recompression of JPEG: Stability, Artifacts and Iterative Image Collapse

  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 […]

• A Data Adventure in Boston, 1929: Historical Census Corpus Analysis

  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, […]

• LLMs, Symbolic Computation and the Future of Mathematical Discovery

  “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 […]

• Computational Geometry Modeling of the Neolithic Circular Ditch in Vinoř, Prague

  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 Modern eTextbook on Laplace Transforms for Engineering, Science and More

  The Laplace transform is such an effective tool for solving problems in the fields of science and engineering—it’s one of the main tools available for solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). I’m excited to announce that the notebook version of Laplace Transforms in Theory and Practice: A Computational Approach by Hrachya Khachatryan […]

• All Elementary Functions from a Single Binary Operator

  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 […]

• A Computational Approach to Early Breast Cancer Detection Using Wolfram

  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 […]