Wolfram BlogWolfram Blog – News, Views and Insights from Wolfram - Digest Feed https://blog.wolfram.com News, Views and Insights from Wolfram Tue, 16 Jun 2026 19:14:22 +0000 hourly 1 https://wordpress.org/?v=4.7.2 OpenAI Disproves Erdős Unit Distance Conjecture https://blog.wolfram.com/2026/06/02/openai-disproves-erdos-unit-distance-conjecture/ Tue, 02 Jun 2026 15:01:18 +0000 Wolfram Blog Team https://blog.wolfram.com/?p=94295 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.]]> 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. (more…)

]]> Theory Meets Practice: 8 Books to Start Your Career in Astrophysics, Geography, Civil Engineering and More https://blog.wolfram.com/2026/05/28/theory-meets-practice-8-books-to-start-your-career-in-astrophysics-geography-civil-engineering-and-more/ Thu, 28 May 2026 15:09:47 +0000 Treyton Jansen https://blog.wolfram.com/?p=94243 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 few other recent book releases featuring Wolfram Language. Whether you’re building your summer reading list or prepping to wow interviewers, these titles are essential insights for real-world, computational STEM operations. (more…)

]]> Compression and Recompression of JPEG: Stability, Artifacts and Iterative Image Collapse https://blog.wolfram.com/2026/05/26/compression-and-recompression-of-jpeg-stability-artifacts-and-iterative-image-collapse/ Tue, 26 May 2026 16:53:01 +0000 Wolfram Blog Team https://blog.wolfram.com/?p=94286 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 something that is almost the same and is usually good enough. (more…)

]]> A Data Adventure in Boston, 1929: Historical Census Corpus Analysis https://blog.wolfram.com/2026/05/22/a-data-adventure-in-boston-1929-historical-census-corpus-analysis/ Fri, 22 May 2026 18:24:13 +0000 Wolfram Blog Team https://blog.wolfram.com/?p=94281 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.
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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, buildings, streets and so on in a way that feels real. The thing about Boston, especially the West End where he goes, is that it’s changed dramatically in the last 100 years. There was a massive urban revitalization project in the 50s and 60s which essentially bulldozed the entire area. So none of the streets or buildings are even remotely similar on a map now to what my character would see walking around. (more…)

]]> LLMs, Symbolic Computation and the Future of Mathematical Discovery https://blog.wolfram.com/2026/05/18/llms-symbolic-computation-and-the-future-of-mathematical-discovery/ Mon, 18 May 2026 17:05:38 +0000 Wolfram Blog Team https://blog.wolfram.com/?p=94239 “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 International Mathematical Olympiad, while newer research workflows began using LLMs together with symbolic tools to explore large mathematical spaces and even help resolve some open problems [1-5]. Many mathematicians now see this as a turning point: AI is becoming ready for “prime time” as a research companion in mathematics, physics, and related sciences – helping researchers test ideas rapidly and discover connections that might otherwise remain hidden. (more…)

]]> Computational Geometry Modeling of the Neolithic Circular Ditch in Vinoř, Prague https://blog.wolfram.com/2026/05/15/computational-geometry-modeling-of-the-neolithic-circular-ditch-in-vinor-prague/ Fri, 15 May 2026 14:20:31 +0000 Wolfram Blog Team https://blog.wolfram.com/?p=94234 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 excavated in Vinoř, a northeastern outskirt of Prague (Czech Republic). This roundel has a diameter of 55 m, with ditches 3.2 m wide and 1.7 m deep and three entrances, which is quite unusual for Central European ditches [2].

]]> A Modern eTextbook on Laplace Transforms for Engineering, Science and More https://blog.wolfram.com/2026/05/11/a-modern-etextbook-on-laplace-transforms-for-engineering-science-and-more/ Mon, 11 May 2026 21:28:14 +0000 Juan Ortiz https://blog.wolfram.com/?p=94209 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 is now available as a free download from Wolfram Media for all the world to learn this beautiful subject. (more…)

]]> All Elementary Functions from a Single Binary Operator https://blog.wolfram.com/2026/05/04/all-elementary-functions-from-a-single-binary-operator/ Mon, 04 May 2026 17:41:01 +0000 Wolfram Blog Team https://blog.wolfram.com/?p=94218 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 repertoire of a scientific calculator. This includes constants such as e, pi and i; arithmetic operations including addition, subtraction, multiplication, division and exponentiation as well as the usual transcendental and algebraic functions. (more…)

]]> A Computational Approach to Early Breast Cancer Detection Using Wolfram https://blog.wolfram.com/2026/04/29/a-computational-approach-to-early-breast-cancer-detection-using-wolfram/ Wed, 29 Apr 2026 16:25:00 +0000 Wolfram Blog Team https://blog.wolfram.com/?p=94205 Wolfram Language is a multi-paradigm programming language designed for functional programming. It is mainly used in Wolfram|Alpha and Mathematica.
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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 STEAM fields, and support the development of future professionals in a growing country such as Costa Rica.
The competition focuses on participants demonstrating the skills and knowledge acquired during their preparation. They analyze a code provided by the organizers to identify possible errors and correct them appropriately. (more…)

]]> Checkmate! Dominate the Competition by Learning Game Theory with Wolfram Language https://blog.wolfram.com/2026/04/22/checkmate-dominate-the-competition-by-learning-game-theory-with-wolfram-language/ Wed, 22 Apr 2026 19:42:11 +0000 Marc Vicuna https://blog.wolfram.com/?p=94173 Checkmate! Dominate the Competition by Learning Game Theory with Wolfram Language

“‘Tis better to have loved and lost than never to have loved at all.’ In other words, love is a dominant strategy.” ― Avinash K. Dixit, Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life

How do people make decisions? How close can mathematics imitate complex decision-making scenarios? What is rationality, really? What are the payoffs of war, marriage or revolution? What does mathematics have to say about making life-changing decisions? The answers to these questions require an understanding of game theory, which is otherwise known as the mathematics of decision making. An understanding of game theory is required for professionals in an increasing number of fields, such as economics, business, political science, psychology and computer science. (more…)

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