Artificial Intelligence in Mathematics

From Transformers to Large Language Model Assistants
Erscheinungsjahr 2027
ISBN: 978-3-032-39138-4
Verlag: Springer

Buch, Englisch, 342 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Springer Series in the Data Sciences

Artificial Intelligence is rapidly transforming mathematics, reshaping how problems are explored, solved, verified, and even discovered. In , Miquel Noguer i Alonso and Daniel Bloch provide a comprehensive and forward-looking examination of this emerging frontier.

Bridging the worlds of modern AI and mathematical reasoning, the book explores how transformer architectures, large language models, neural-symbolic systems, and formal verification tools are changing the practice of mathematics. Readers will discover how AI can tackle symbolic computation, theorem proving, differential equations, linear algebra, optimization, geometric reasoning, scientific machine learning, and mathematical discovery.

Moving beyond headlines and hype, the authors present a rigorous framework for understanding the strengths, limitations, and reliability of AI-powered mathematical systems. They introduce a verification-centered approach in which generation, search, and pattern recognition are combined with formal proof, symbolic validation, and computational certification to produce trustworthy mathematical results.

Drawing on the latest developments in large language models, reinforcement learning, theorem provers, and AI-assisted discovery systems, this book offers both conceptual foundations and practical methodologies for researchers, educators, students, quantitative professionals, and anyone interested in the future of mathematical intelligence.

At the intersection of mathematics, computer science, and artificial intelligence, this timely volume reveals how machines are evolving from computational tools into collaborative partners in mathematical reasoning and discovery.

Zielgruppe

Research

Autoren/Hrsg.

Noguer i Alonso, Miquel

Bloch, Daniel

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken

Inhaltsverzeichnis

Preface.- The Verification-Centered Thesis.- Part 1. Foundations and Reasoning Architectures.- Symbolic, Statistical, and Transformer Paradigms.- Large Language Models and Inference-Time Mathematical Reasoning.- Verifiable Reinforcement Learning and Self-Improving
Mathematical Agents.- Part 2. Computational Mathematics and Discovery.- Neural-Symbolic Mathematics and Algebraic Computation.- Linear Algebra, Matrix Computation, and Transformer-Based Numerical Reasoning.- Mathematical Discovery, Symbolic Regression, and Algorithmic
Invention.- AlphaEvolve and Evaluator-Gated Algorithmic Discovery.- Geometry, Olympiad Reasoning, and Synthetic Proof Search.- Advanced Mathematical Computation and Scientific Machine Learning.- Mathematical Proofs with Transformers and Neural Theorem
Proving.- Lean, Autoformalization, and Formal Mathematical Libraries.- Olympiad Formal Reasoning: AlphaProof, DeepSeek-Prover, and Program-Synthesis Proof Systems.- The AI Mathematician Stack: Prompt, Retrieval, Formalization, and Verification.- A Geometric Theory of AI Mathematical Reasoning.- Part 3. Evaluation, Limits, and Research Governance.- Reliability, Benchmarks, Interpretability, and Epistemic Limits.- Advanced Domains: Verification Protocols and Representation Invariance.- Future Directions, Laboratory Practice, and Verification Protocols.- References.- Index.

Über Autor(innen)

Miquel Noguer i Alonso is a financial professional and academic with over thirty years of experience in the industry. He is the Founder of the Artificial Intelligence Finance Institute, Head of AI at Captide, and Head of Development at Global AI; his previous roles include Executive Director at UBS AG and CIO at Andbank, and he served for a decade on the European Investment Committee at UBS. He sits on the advisory boards of the FDP Institute and the CFA Society New York. As an academic, he teaches artificial intelligence, big data, and fintech at institutions including the NYU Courant Institute, NYU Tandon, Columbia University, and ESADE, and in 2017 he pioneered the first fintech and big-data course at London Business School. He holds an MBA and a degree in business administration from ESADE and a PhD in quantitative finance from UNED, along with further professional certifications. His research interests span asset allocation, machine learning, algorithmic trading, and fintech, and he is the author of one hundred papers on artificial intelligence, as well as the books (Risk Books) and (Wiley).

Daniel Bloch  is a researcher and lecturer in Artificial Intelligence and Mathematical Finance. He is a Distinguished Visiting Professor at VinUniversity, where he leads Q1-level research, supervises students, and contributes to research programmes in AI applied to finance, and a lecturer at Université Paris 1 Panthéon-Sorbonne, where he teaches Systematic and Algorithmic Trading, as well as at the Certificate in Quantitative Finance (CQF), where he teaches Reinforcement Learning. His research focuses on applied mathematics, stochastic modelling, derivatives pricing, portfolio optimisation, and reinforcement learning for decision-making under uncertainty, with publications in leading quantitative finance journals.