The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those from Hilbert geometry, Peano arithmetic, or ZFC - we offer a new way to visualize, compare, and analyze mathematical knowledge. This vector-based formalism not only captures the logical foundation of theorems but also enables quantitative similarity metrics - such as cosine distance - between mathematical results, offering a new analytic layer for structural comparison. Using heatmaps, vector clustering, and AI-assisted modeling, this atlas enables the grouping of theorems by logical structure, not just by mathematical domain. We also introduce a prototype assistant (Atlas-GPT) that interprets natural language theorems and suggests likely proof vectors, supporting future applications in automated reasoning, mathematical education, and formal verification. This direction is partially inspired by Terence Tao's recent reflections on the convergence of symbolic and structural mathematics. The Axiom-Based Atlas aims to provide a scalable, interpretable model of mathematical reasoning that is both human-readable and AI-compatible, contributing to the future landscape of formal mathematical systems.

Computation is central to contemporary mathematics. Many accept that we can acquire genuine mathematical knowledge of the Four Color Theorem from Appel and Haken's program insofar as it is simply a repetitive application of human forms of mathematical reasoning. Modern LLMs / DNNs are, by contrast, opaque to us in significant ways, and this creates obstacles in obtaining mathematical knowledge from them. We argue, however, that if a proof-checker automating human forms of proof-checking is attached to such machines, then we can obtain apriori mathematical knowledge from them, even though the original machines are entirely opaque to us and the proofs they output are not human-surveyable.

Although pre-trained language models~(PLMs) have recently advanced the research progress in mathematical reasoning, they are not specially designed as a capable multi-task solver, suffering from high cost for multi-task deployment (\eg a model copy for a task) and inferior performance on complex mathematical problems in practical applications. To address these issues, in this paper, we propose \textbf{JiuZhang~2.0}, a unified Chinese PLM specially for multi-task mathematical problem solving. Our idea is to maintain a moderate-sized model and employ the \emph{cross-task knowledge sharing} to improve the model capacity in a multi-task setting. Specially, we construct a Mixture-of-Experts~(MoE) architecture for modeling mathematical text, so as to capture the common mathematical knowledge across tasks. For optimizing the MoE architecture, we design \emph{multi-task continual pre-training} and \emph{multi-task fine-tuning} strategies for multi-task adaptation. These training strategies can effectively decompose the knowledge from the task data and establish the cross-task sharing via expert networks. In order to further improve the general capacity of solving different complex tasks, we leverage large language models~(LLMs) as complementary models to iteratively refine the generated solution by our PLM, via in-context learning. Extensive experiments have demonstrated the effectiveness of our model.

This article is part of Demystifying AI, a series of posts that (try to) disambiguate the jargon and myths surrounding AI. ChatGPT and other large language models (LLM) have proven to be useful for tasks other than generating text. However, in some fields, their performance is confusing. One such area is math, where LLMs can sometimes provide correct solutions to difficult problems while at the same time failing at trivial ones. There is a body of research that explores the capabilities and limits of LLMs in mathematics.

AI is the future, we all know that. But the robot uses it's brain to do a certain task, and that brain will be powered by neural networks. Let's learn how neural networks work from scratch (no mathematical knowledge required). This story will walk us through the foundation of neural networks. A neural network is a network of neurons that are connected and learn from what it's been trained on, then it applies that knowledge.

Educational technology is the use of both physical hardware, software, and educational theoretic to facilitate learning and improve performance by creating, using, and managing appropriate technological processes and resources. In EdTech, the most significant uses of AI are in content recommendation, AI-powered teaching assistants such as chat-bots performing specific tasks and accessibility functions such as text to speech and voice recognition. When used effectively, these tools are empowering teachers. Continual, formative assessment data is used as input for adaptive algorithms that power an output that is a work programme. This data can also be shared with the teacher, saving them hours in manually collecting the data and giving them eyes on the strengths and weaknesses of students.

Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards "big mathematics", its relation to human cognition, and how machine support for big math can be organized. The central contribution of this position paper is an information model for "doing mathematics", which posits that humans very efficiently integrate four aspects: inference, computation, tabulation, and narration around a well-organized core of mathematical knowledge. The challenge for mathematical software systems is that these four aspects need to be integrated as well. We briefly survey the state of the art.

If you want to carve out a career in machine learning then knowing where to start can be daunting. Not only is the technology built on college-level math, jobs in the field typically ask for a Master's degree in a related technical field. Yet if you're willing to work at it, it's never been easier to learn about machine learning, and getting started doesn't even require much mathematical knowledge. Here's five tips for breaking into the field from senior data scientists and machine-learning engineers, speaking to TechRepublic at the AI Conference presented by O'Reilly and Intel AI. If you plan to start tweaking the machine-learning models used then you'll need need a reasonably deep knowledge of math, spanning linear algebra, calculus and statistics.

We would like to talk to you a little bit about deep learning. Some experts are predicting the dawn of a new era, which will also lead to the development of a wholly new set of software. What do you think of such predictions? What would this software 2.0 be like? Uwe Friedrichsen: I think that right now the magic crystal ball is still very cloudy; a prognosis is still difficult to make from my point of view.

There are many books that provide an introduction to the field of linear algebra. Most are textbooks targeted at undergraduate students and are full of theoretical digressions that are barely relevant and mostly distracting to a beginner or practitioner to the field. In this post, you will discover the book "No bullshit guide to linear algebra" that provides a gentle introduction to the field of linear algebra and assumes no prior mathematical knowledge. No Bullshit Guide To Linear Algebra Review Photo by Ralf Kayser, some rights reserved. The book provides an introduction to linear algebra, comparable to an undergraduate university course on the subject.