Mathematics by Experiment: Plausible Reasoning in the 21st Century by Jonathan Borwein – A Guide to Computational Discov

Introduction

Mathematics is often taught as a finished product—a collection of rigid theorems and proofs handed down from the past. But what if you could watch mathematics being discovered in real time, using computers to explore, guess, and then prove? Mathematics by Experiment: Plausible Reasoning in the 21st Century by Jonathan Borwein flips the script, showing how modern computational tools can turn mathematical exploration into an experimental science. This revised second edition brings the excitement of discovery directly into your hands, making it an essential read for Indian students, researchers, and anyone curious about the future of mathematics.

Book Overview

This hardcover volume is a comprehensive guide to experimental mathematics—the art of using computers to generate examples, test conjectures, and uncover patterns before formal proof. The book demonstrates how numerical experiments, visualisation, and symbolic computation can lead to deep mathematical insights. It covers topics from number theory and analysis to combinatorics and special functions, all while emphasising the interplay between computation and rigorous reasoning. The new chapter, 'Recent Experiences', offers fresh case studies that highlight discoveries made since the first edition, ensuring the content remains cutting-edge.

Key Highlights

• Second Edition with New Content: Includes a brand-new chapter on recent experimental discoveries, keeping the material current for today’s learners.
• Hands-On Approach: Encourages readers to replicate experiments using software like Maple or Mathematica, bridging theory and practice.
• Real-World Examples: Features problems from number theory, calculus, and probability that demonstrate the power of experimental methods.
• Companion Volume: Pairs perfectly with Experimentation in Mathematics: Computational Paths to Discovery for deeper exploration.

Inside the Book

Open the cover and you’ll find a treasure trove of mathematical experiments. The book begins with foundational ideas—why experiment in mathematics?—and then dives into specific techniques: high-precision computation, integer relation algorithms, and visualisation of complex functions. Each chapter presents a problem, walks through computational experiments, and then connects the results to formal proofs. The writing is clear and accessible, with plenty of code snippets and output examples. The final chapter, 'Recent Experiences', shares stories of how experimental methods led to new theorems in fields like continued fractions and modular forms.

Key Topics

• Experimental number theory and prime patterns
• Symbolic computation and algebraic manipulation
• High-precision arithmetic and its applications
• Visualisation of mathematical objects
• Integer relation algorithms (e.g., PSLQ)
• Probabilistic and heuristic reasoning in proofs

Reader Benefits

This book transforms how you think about mathematics. Instead of passively learning theorems, you’ll actively participate in the discovery process. You’ll gain practical skills in computational exploration that are invaluable for research, teaching, or independent study. The experimental mindset helps you develop intuition, avoid dead ends, and find elegant solutions to tough problems. For Indian students preparing for competitive exams or research careers, this book offers a unique edge—showing how to harness technology to push mathematical boundaries.

Learning Outcomes

By the end of this book, you will be able to: design computational experiments to test conjectures; interpret numerical results to form plausible hypotheses; use software tools to explore advanced mathematical concepts; connect experimental findings with rigorous proof techniques; and appreciate the evolving role of computers in mathematical research. These skills are directly applicable to coursework, projects, and real-world problem-solving.

Who Should Read

This book is perfect for undergraduate and postgraduate students in mathematics, computer science, and engineering. It’s also ideal for teachers who want to bring discovery-based learning into their classrooms, and for self-learners who love exploring maths beyond the syllabus. Researchers in pure and applied mathematics will find fresh perspectives on their own work. No advanced programming experience is required—just curiosity and a willingness to experiment.

About the Author

Jonathan Borwein was a world-renowned mathematician and a pioneer of experimental mathematics. He served as a professor at Simon Fraser University and the University of Newcastle, Australia, and co-authored numerous influential books and papers. His work emphasised the beauty of computational discovery and its power to deepen mathematical understanding. Borwein’s legacy continues to inspire a generation of mathematicians who believe that computers are partners, not just tools, in the quest for knowledge.

About the Publisher

A K Peters/CRC Press is a leading publisher of high-quality books in mathematics, computer science, and engineering. Known for their rigorous yet accessible titles, they bring together cutting-edge research and clear exposition. This partnership ensures that Mathematics by Experiment meets the highest standards of accuracy and readability, making complex ideas available to a wide audience in India and around the world.

Conclusion

Mathematics by Experiment: Plausible Reasoning in the 21st Century is not just a book—it’s an invitation to join the adventure of mathematical discovery. Whether you’re a student looking to deepen your understanding, a teacher seeking innovative methods, or a researcher exploring new frontiers, this hardcover edition will become a trusted companion. Order your copy from Bookshops.in today and start experimenting with the language of the universe.