The best math books

This beautiful homage to a father from “The Greatest Generation” reads like a sermon with several urgent messages: To be kind, timely, and disciplined. Make helping a regular part of life, do every job right, listen and learn. Be a person of impeccable character, and stand strong even when times are tough.

Data visualizations are a cross between art, programming, and storytelling.

I've always been fascinated by the process creators go through to bring something from their imagination into existence. What amazed me was how the journey isn't a clear path from idea to finished product. I loved how Nadieh and Shirley documented their thought process – bringing me along and sharing why they made each decision.

Each chapter is a breakdown of a different data visualization. I laughed at how many of them were nerdy interests I loved: Dance Dance Revolution, Card Captor Sakura, and Lord of the Rings, to name a few. It reminded me that if I have fun, that'll show up in the finished product.

When I signed up for an introductory statistics course in college, I expected it would cover exactly what this book addresses. At that time, newspaper articles sometimes referred to the book that inspired this one, Darrell Huff’s How to Lie with Statistics.

I was excited to learn how to avoid getting snared by inadvertent and intentional flaws in public opinion polls, medical studies, and investment research. In a highly readable, entertaining style, Charles Wheelan arms his readers against all those pitfalls.

The somewhat abstruse quantitative methods actually taught emphasized in the statistics course proved to be helpful professionally. But Wheelan’s statistical malpractice stories are both accessible to readers unfamiliar with the underlying math and informative to those who are.

I remember being very surprised when I discovered that this book was written so long ago. It’s a social satire that is sadly still relevant. More importantly, it’s also a story constructed to point towards a transcendent reality. I love stories that are a springboard for the reader to journey into a deeper world. It is something I do in my own writing. Flatland is a book that can be used to flex the imagination; active imagination is the bedrock of my writing but is also vital in so many aspects of life. I think Flatland would be a great book to help kids take control of their own minds. 

The Four Color Problem was one of the most baffling questions in mathematics for over 120 years. First posed in 1852, it asks whether every map can be colored with four colors, or fewer, so that regions adjacent along a boundary have different colors. The answer (yes) was finally obtained in 1976, with massive computer assistance. This method was initially controversial, but the result is now firmly established. This highly readable account, with full-color illustrations, opens up the history and the personalities who tackled this topological enigma, as well as making the mathematics comprehensible. The path to the final solution is littered with blunders and mistakes, but also illustrates how mathematicians can join forces across the generations to chip away at a problem until it cracks wide open. 

John Urschel is an African-American mathematician specializing in graph theory, who recently completed his Ph.D. in mathematics at MIT. But he is better known for his football career, as a starting offensive lineman for the Baltimore Ravens. Six of Urschel’s papers were completed while he was still in the National Football League.

Mind and Matter is John Urschel’s memoir, co-authored with his wife Louisa Thomas. Each chapter alternates between football and mathematics, and how his success on the field translated to success in the classroom, and vice-versa. I loved how accessible the book is, for readers of all ages, and I fully agree with the author’s perspective that mathematics gives us a way of making sense of the world, and helping us see past the confusion of everyday life.

My first pick is the one most directly about Alan Turing himself. After 1950 his attention turned mainly to his new theory of mathematical biology, but his death in 1954 left most of this work unpublished.  His ideas were 20 or more years ahead of their time and few people could assess them. Jonathan Swinton is a leading expert in this field, and has been studying Turing’s manuscripts for 30 years. But his book has a much broader range: he adds so much on the culture of Manchester and its region, with a particular focus on women both as protagonists and observers. He has also illustrated his story with a wealth of pictures.

History isn’t just “what happened.” Trillions of things happened. History is about the patterns to be found among those trillions of facts. Getting at such patterns means following deep themes, and what could be deeper than ideas? Watson explores when, where, how, and why significant ideas emerged in history, how ideas led to more ideas, to inventions, to cultural changes…we witness the emergence of a soul as a concept, we’re there to see Freud construct his tripartite model of the human psyche… Every idea is part of a thread and this book is woven of many threads. 

This fictional interpretation of the creation of Alice’s Adventures is seen from the viewpoint of a constant, yet largely unremarked, fixture during these critical years: the Liddell family governess, Mary Prickett. The Oxford context of the time is convincingly depicted, and some of the burning issues of the day – Darwinism and Nonconformism, for instance – are interwoven with the more immediate tensions within the Liddell household, interpreted by an author who has more right than anyone to comment because Tait is the great-granddaughter of the real Alice herself. To sustain the pace she condenses the real events of 1857 to 1863 into a single fictionalised year, drawing on many well-known facts and suppositions – including Carroll’s rumoured amorous interest in Miss Prickett – and some lesser known details from her own family’s archives.

Love + Math is a delightful math book that transforms kids' perception of math from boring to enjoyable.

With engaging examples and colorful illustrations, it shows how math is present in everyday life, making it relatable and fun. This book helps kids see the beauty of math and replaces "I hate math" with "I love math."

It's a fantastic resource to instill a positive attitude towards math and encourage young minds to embrace the subject's possibilities. Get ready to witness a delightful transformation as kids discover the joy of math all around them!

In this classic book, the author gives numerous examples of how statistics is misused by the corporate world, government agencies, journalists, politicians, and even educational institutions.

While the book is somewhat lighthearted and somewhat lacking in rigor, it gives the reader a critical understanding of logical fallacies. I’ve recommended this book to math phobic friends who all tell me they came away with good awareness of when data is unreliable and how data can be exploited and misapplied to force certain conclusions.

In terms of conveying how to convey information (not just data) visually, Tufte is the undoubted master. 

This book is full of pithy examples, with clear insights about what works, what doesn’t, and why. I came across it when I was trying to understand why I was disgruntled with so many graphical representations – and Tufte provided useful clarity about my niggles.

(N.B. I had to pick just one of his titles for this list – but I’d recommend his other books as well.)

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.

The book is a well-curated collection of the essential mathematical concepts that form ML. You may experience a cultural shock jumping to this book from the previous one, because the writing in this book is a bit formal. However, it is the missing but necessary piece for building solid foundations for practical ML. You will find it more valuable combining the intuition behind ML that you gained previously. And the explanations in the book are succinct and from the ML perspectives. For instance, partial derivatives are explained in terms of neural network weight optimization. I wish the concepts in Linear Algebra, Vector Calculus, and Probability courses back in college were introduced this way so I understand better how they are applied.  

This book is a nonfiction history of the concept of Spherics – the idea that music and astronomy are intimately connected. It starts by talking about Pathagorous and works our way chronologically up to Einstein. There are a lot of books on the topic of Music of the Spheres (and a Coldplay album), but this is the best book I’ve found to fully understand the concept. 

This book might as well be called Introduction to machine learning, and it is probably one of the only books truly deserving of the title. Did you know neural networks have been used for decades to scan checks at the bank? They are called Boltzman Machine. Have you ever heard of how decision trees were used in old-school data mining? You could only get them from proprietary software packages from the early 2000s.

In quant trading, you will constantly face compute power constraints, so it is invaluable to understand the mathematical foundations of the most old-school machine learning methods out there. Researchers 20 years ago used to do a lot of impressive work with a lot less computing power.

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.

The number Pi, of course, has no history; like any other number, it is what it is and exists outside of time and space. But the human understanding of Pi has a rich history indeed, beginning with the discovery that the circumference of a circle is more than three times, but less than four times, its radius. The centuries brought better estimates, better ways of discovering new estimates, the discovery that Pi is irrational, the recognition that it has a habit of popping up in areas of mathematics that appear to have nothing to do with circles, and a slew of curious and beautiful formulas like this one.

Of course, a lot of other things were happening during those centuries, not all of them mathematical. Beckmann has not failed to notice this. His fascination with pretty much everything comes alive as he uses the history of Pi as a… show more.

For Gintis, morality is the result of social evolution.

Humans are meant to cooperate and behave morally because of the evolutionary history of our societies. If humans are social animals, then it follows, they must be moral animals as well.

Gintis, unlike the previous authors in the list, focuses on the social, rather than the individual, to also argue for a moral theory that does not depend on or stem from individual moral character, or moral constraints on behavior.

This is an important argument because it highlights, at least implicitly, that we have a lot in common with social animals and as such, we can learn a lot from animal societies, as well as from early human societies.