Using Mathematica implementations of machine learning algorithms
The Jacobian conjecture was (very) recently disproved by a counterexample found by Anthropic's Fable 5. This blog post demonstrates that counterexample using some of the built-in Wolfram Language (WL) functions and entries in Wolfram Function Repository (WFR). We show how to use WL's FindInstance to find three different points which the counterexample polynomial 3-dimensional (3D) transformation…
This document has a complete usage example of a thin Model Context Protocol (MCP) client of the Wolfram Language paclet "MCPClient". The MCP server is run in Docker -- see "Docker MCP Toolkit". "MCPClient" provides a set of functions for using MCP server's methods by converting them to LLMTool objects. Those objects can be used with Wolfram Language's Large Language Model (LLM) framework.
"Chatnik" is a Wolfram Language paclet that provides Command Line Interface (CLI) scripts for conversing with multiple, persistent Large Language Model (LLM) personas. Files of the host operating system are used to maintain persistence.
Happy Pi Day! Today (3/14) we celebrate the most famous mathematical constant: π ≈ 3.141592653589793... π is irrational and transcendental, appears in circles, waves, probability, physics, and even random walks. Wolfram Language (with its built-in π constant, excellent rational support, symbolic programming, and vast collection of Number Theory functions) makes experimenting with π especially easy…
This document describes three ways of making mazes (or labyrinths) using graphs. The first two are based on rectangular grids; the third on a hexagonal grid. All computational graph features discussed here are provided by the Graph functionalities of Wolfram Language.
This document explores the properties and relationships of the integer 2026 in number theory. The number 2026 is classified as a semiprime and a happy number, with 365 serving as one of its primitive roots. While 2026 may not be especially significant in the field of Number theory, it offers an opportunity to create various elaborate visualizations that highlight some intriguing aspects of the…
This document discusses different combinations of Grammar-Based Parser-Interpreters and Large Language Models (LLMs) to generate executable code from Natural Language Computational Specifications.
In this blog post (notebook) we show how to make neat chord plots of primitive roots generation sequences. Primitive roots a generators of cyclic multiplicative integer groups modulo . See the built-in Wolfram Language functions PrimitiveRoot and PrimitiveRootList.
Parsing, plotting, or otherwise processing the Doomsday Clock settings and statements are excellent didactic subjects for textual analysis (or parsing) and temporal data visualization. The visualization could serve educational purposes or provide insights into historical trends of global threats as perceived by experts.
This presentation discusses techniques for harnessing LLMs in a more robust and effective manner. (Because LLMs are unreliable and slow.)