Mathematical discovery in the age of artificial intelligence

In this comment, we consider how artificial intelligence tools are reshaping the way mathematical research is conducted and discuss how future developments of this technology will transform mathematical practice.

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.

The AI Revolution in Math Has Arrived | Quanta Magazine

AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

Embracing AI and formalization: Experimenting with tomorrow’s mathematical tools

Embracing AI and formalization: Experimenting with tomorrow’s mathematical tools. By Jarod Alper

Terence Tao – Kepler, Newton, and the true nature of mathematical discovery

“And what those stories teach us about how AI will revolutionize math”

The fall of the theorem economy

How AI could destroy mathematics and barely touch it

The fall of the theorem economy

How AI could destroy mathematics and barely touch it

Artificial intelligence in mathematics education: The good, the bad, and the ugly

Integrating Artificial Intelligence [AI] into mathematics education offers promising advancements and potential pitfalls. Striking a balance between AI-driven developments and preserving core pedagogical principles is critical in the teaching and learning environment. AI has emerged as a transformative force in various fields, including education. In the realm of mathematics education, AI technologies offer a spectrum of potential benefits (including personalize instruction, adaptive assessment, interactive learning environments, and real-time feedback, among others) and challenges (such as lack of creativity and problem-solving skills, inability to explain reasoning, bias in data and algorithms, absence of emotional intelligence and data privacy and security concern etc). This conceptual study used autoethnography as the methodology and qualitative content approach to analyze data. The study discussed historical background of AI and considered ethical issues around AI. It was concluded that the journey to harness the full potential of AI in mathematics education requires careful navigation of the good, the bad, and the ugly aspects inherent in this technological evolution.

Daron Acemoglu on Twitter / X

I recommend Columbia mathematician Michael Harris’s wide-ranging, informative and thought-provoking essay in Boston Review on AI and mathematics:https://t.co/txwAd8ri4xHarris rightly worries about the possible negative effects of AI-generated proofs and mathematics on…— Daron Acemoglu (@DAcemogluMIT) June 16, 2026

Mathematical methods and human thought in the age of AI

Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the...

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.

The Technological Turn in Mathematics

Quickly evolving technologies, such as Interactive Theorem Provers (ITPs), Automated Theorem Provers (ATPs), and Large Language Models (LLMs), all falling under the general heading 'AI for mathematics,' are transforming mathematical practice in profound ways. This chapter explores the implications of these innovations, focusing on their impact on how mathematical knowledge is created and shared. It also discusses how they are reshaping the social dimension of mathematics, altering collaboration dynamics, trust relationships, and the collective production of knowledge. For instance, tools like ITPs facilitate large-scale collaborations and make new types of teamwork possible, where trust is not a necessary ingredient. ITPs also help us mitigate our human fallibility, yet they raise questions about the nature of formalization and the relationship between traditional and formal mathematics. Technologies such as LLMs are reshaping the division of epistemic labour between humans and machines and urge philosophers of mathematics to ask questions about the value of their work.

Mathematicians are grappling with the possibility that AI might eclipse them

I talked to 20 mathematicians about rapid AI progress in their field.