100 books like Ingenious Mathematical Problems and Methods

Peter Winkler is famous for his collections of counterintuitive puzzles. Thousands of people, including me, have spent many sleepless nights trying to understand the mysteries in these puzzles, for which, I am forever grateful.

Haunting puzzles in the book include hats and infinity, all right or all wrong, comparing numbers version 1/2, wild guess, laser gun, precarious picture, names in boxes, sleeping beauty, and dot-town exodus.

Most puzzle books exclude counterintuitive puzzles for unknown reasons. So, many people incorrectly assume that counterintuitive puzzles are majorly found in paradoxes. Peter Winkler in this book shows that counterintuition can come from either puzzles or solutions or both, and they need not come from paradoxes alone.

Finally, reading Winkler's statements is an absolute delight due to its enjoyable and entertaining nature.

Anany Levitin introduced me to algorithmics – my second love (my first love is mathematics), through his legendary algorithmics textbook. He was one of my superheroes in my young adult life and he got me addicted to algorithms. His book is my favorite because it is beautifully organized based on design techniques, well-written, and uses nice puzzles to teach algorithms.

Levitin went much deeper and wrote this book on algorithmic puzzles. This book is the first mainstream book in the puzzle literature that taught beautiful algorithmic puzzles via various algorithm technique techniques. Levitin claimed several mathematical puzzles as algorithmic focusing on aspects of the solutions that are automatable.

Elegant puzzles (with extensive references) in this book that I have enjoyed include missionaries and cannibals, bridge crossing, circle of lights, MU puzzle, turning on a light bulb, chameleons, poisoned wine, game of life, twelve coins, fifteen puzzle, hats with numbers, and… show more.

If you want a mathematical high, then the special theory of relativity is your cannabis. This out-of-the-world book by Tatsu Takeuchi gives us the key to the gateway to the heavens. This book beautifully teaches the special theory of relativity using hundreds of pleasing diagrams.

The special theory of relativity leads to the most counterintuitive concept that there is no "now". A's now can be the past of B's now and the future of C's now. This and several other counterintuitive ideas arise out of the fact that light travels at a finite speed. This book does an amazing job of teaching the mathematical theory that deals with time, space, and motion.

In many world religions there is a concept of heaven that is reachable after death. For puzzle addicts like me, the puzzle world itself is heaven, and I have been there an unlimited number of times when I… show more.

This book is full of beautiful puzzles on a mathematical topic called pursuit evasion. Its author Paul Nahin has written tens of books in physics and mathematics.

Nahin's writing can be described as a captivating reading experience pulling readers into his world like a whirlpool. His appreciation of mathematics, physics, and the people who discover them is unmatchable. It seems like the physics of motion and the mathematics of calculus is inseparable, as can be witnessed in the book.

The calculus used in this book is heavy. Nevertheless, Nahin makes his readers fall in love with this big beast. Almost every puzzle in this book is aesthetically beautiful and gives readers a deep sense of satisfaction. My favorites include Lady in the Lake, and Lion and Man.

It is fair to say that many people—even those who loved mathematics as students—view mathematics as having always existed. The idea that definitions and theorems that fill our school textbooks were created or discovered by human beings is something that has never crossed their mind. In fact, mathematics has a long, fascinating, and rich history, and William Dunham’s Journey Through Genius is a perfect introduction to the topic. Dunham expertly writes about the history of topics like geometry, number theory, set theory, and calculus in a way that is entertaining, understandable, and rigorous. After finishing Journey Through Genius, readers will not think about mathematics in the same way, and they will be eager to learn about the history of other mathematical topics, people, and cultures.

This book profoundly shaped my life. I discovered Eleftherios through my astrology community; he’s an expert in mystical connections between number theory, the Pythagorean theorem, and life on Earth. After one consultation, I knew I wanted to explore gematria and its hidden wonders.

What I love most about Eleftherios’ ancient approach is how he effortlessly connects the significance of gematria to various aspects of human knowledge. Eleftherios skillfully reveals the relevance of ideas, historical events, and philosophy through numbers.

I’ve read this book at least 20 times—and plan to revisit it again—and highly recommend it to anyone seeking deeper meanings and correlation between seemingly unrelated concepts by numbers.

Mathematicians are constantly baffled by the public’s lack of awareness, not just of what mathematics does, but what it is. Today’s technological society functions only because of a vast range of mathematical concepts, techniques, and discoveries, which go far beyond elementary arithmetic and algebra. This was one of the first books to tackle these misunderstandings head on. It does so by examining not just the math and what it’s used for, but the social structures, the ‘conditions of civilization’ that have brought us to this curious state: utterly dependent on math, almost universally unaware that we are. 

This book provides a systematic account of how to understand and structure mathematical proofs. Its approach is almost entirely syntactic, which is the opposite of how I naturally think – I tend to generate arguments based on examples, diagrams, and conceptual understanding. But that difference, for me, is precisely what makes this book so valuable. Solow gives a no-nonsense, practical, almost algorithmic approach to interpreting logical language and to tackling the associated reasoning. His book thereby provides the best answer I know of to the “How do I start?” problem so often encountered when students begin constructing proofs.  

As I write these lines, artificial intelligence (AI) is getting a lot of attention.

This is largely due to ChatGpt recently bursting onto the scene. But even before ChatGpt began making its mark, AI was often in the news. Some have expressed worry that it will take our jobs, others that it will reinforce systemic oppression by making racially or otherwise discriminatory decisions, and some have even voiced concerns that one day a superintelligent AI might pose an existential threat to humanity.

In the midst of all this, what might get lost is what AI is, what it's capable of doing, and what its limitations are. Wenger's book is intended to address all of these questions. It manages to do so in a way which goes into some of the mathematics of AI systems and yet remain accessible to a lay audience.

After laying out the technical aspects of AI,… show more.

Far too many math books are written in a style so terse and ungenerous that all but the most mathematically gifted readers hardly have a fair chance of understanding.

On the other hand, the discursive style of much philosophy of mathematics gains readability at the expense of formal rigor. Button and Walsh strike the perfect balance in this exceptionally rich introduction to model theory from a distinctively philosophical perspective.

There’s no getting around the fact that the mathematics of model theory is hard going. But this book works through all the relevant proofs in clear and detailed terms (no lazy “we leave this as an exercise for the reader”), and the authors are always careful to motivate each section with well-chosen philosophical concerns right up front.

An Everest, but worth it.