Practical math for the working programmer.
Exploring the interplay between AI and human logic in mathematical problem-solving
This paper investigates the dynamic interplay between Artificial Intelligence (AI) and human logic in the domain of mathematical problem-solving. By critically examining a series of case studies, we compare the efficacy of AI-generated solutions, particularly those offered by ChatGPT, against traditional human problem-solving methods. The study employs various mathematical challenges, ranging from abstract logical puzzles to applied numerical problems, to evaluate AI's problem-solving approach and alignment with human cognitive processes. Our analysis highlights instances where AI's computational strategies complement or diverge from human reasoning, shedding light on AI's potential and limitations in deciphering mathematical problems. Furthermore, we explore the implications of integrating AI tools in educational contexts, specifically their role in enhancing students' mathematical problem-solving skills. The paper aims to contribute to the ongoing discourse on the optimal utilization of AI in education, proposing a balanced approach that leverages AI's computational power while fostering the depth and creativity of human logic. Through this comparative study, we advocate for a collaborative model where AI and human reasoning merge to enrich the educational landscape, particularly in the teaching and learning of mathematics.
Formalising mathematics: an introduction.
An introduction to the TCC course “Formalising Mathematics”
J Notation as a Tool of Thought
Kenneth Iverson’s 1964 language, APL, won him the Turing Award. His award lecture, Notation as a Tool of Thought, argued that better notations would lead people to deeper insights about mathematics. He provided a number of examples ranging across linear algebra, arithmetic, probability, and logic. Unfortunately, most of the mathematics he covers isn’t relevant to programming. However, his core idea still applies, and changing how we describe programs changes how we think about them.
Brilliant | Your Personal Tutor for Math and Coding
Visual, interactive tutoring in math and coding, from 5th grade through college. Master concepts in algebra, calculus, Python, computer science, and more.
Mathematics in the age of AI
An essay, based on a public lecture delivered at the 2026 International Congress of Mathematicians, on how the mathematical community might respond to the arrival of artificial intelligence tools that are capable of performing research-level mathematical tasks. Rather than debating the capabilities of such tools, we condition on the hypothesis that these capabilities will arrive, and examine instead a question that is orthogonal to it: what the goals and values of mathematical research actually are. The problem-solving component of mathematics is used as a case study.
Embracing AI and formalization: Experimenting with tomorrow’s mathematical tools
Embracing AI and formalization: Experimenting with tomorrow’s mathematical tools. By Jarod Alper
Mathematical Beauty, Truth and Proof in the Age of AI | Quanta Magazine
Mathematicians have started to prepare for a profound shift in what it means to do mathematics.
Introduction to Higher-Order Categorical Logic (Cambridge Studies in Advanced Mathematics)
Introduction to higher order catagorical logic by J. Lambek, March 25, 1988, Cambridge University Press edition, Paperback in English
math.r — Brain Building Game
Mathr is a brain building game to improve your math calculation skills. Practice arithmetic and level up!
Learnable Programming
Here's a trick question: How do we get people to understand programming?
GATlab: Modeling and Programming with Generalized Algebraic Theories
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a domain-specific language for algebraic specification embedded in a technical programming language. GATlab is based on generalized algebraic theories (GATs), a logical system extending algebraic theories with dependent types so as to encompass category theory. Using GATlab, the programmer can specify generalized algebraic theories and their models, including both free models, based on symbolic expressions, and computational models, defined by arbitrary code in the host language. Moreover, the programmer can define maps between theories and use them to declaratively migrate models of one theory to models of another. In short, GATlab aims to provide a unified environment for both computer algebra and software interface design with generalized algebraic theories. In this paper, we describe the design, implementation, and applications of GATlab.
About - Project Euler
A website dedicated to the fascinating world of mathematics and programming
Mathematics in type theory.
An explanation of how to set up mathematics using universes, types, and terms
Category Theory for Programmers: The Preface
Table of Contents Part One Category: The Essence of Composition Types and Functions Categories Great and Small Kleisli Categories Products and Coproducts Simple Algebraic Data Types Functors Functo…
Motivating Adult Learners by Introducing Programming Concepts with Scratch
Novice programmers usually fail to combine abstract concepts and knowledge into program design, even though they know the syntax and semantics of individual statement. Adult novice programmers with little computer background knowledge might face more ...
When A.I. Comes for Your Purpose in Life
In the span of just a few months, A.I. systems have solved some of the biggest outstanding problems in math — adding mathematicians to the list of those terrified of losing their job to the technology.
