### Let’s teleport into the world of numbers

Mathematics runs our lives.

Some like it less than others but no one can deny its importance.

The following mathematics books can be enjoyed by everyone. But you can’t simply afford to miss them if you are a mathematician.

They will acquaint you with many bright minds as well as with the history of many mathematical concepts.

Let’s have a look at them.

Mathematics, complete or incomplete?

Kurt Gödel is a famous logician, mathematician, and philosopher.

He is well known for his Incompleteness Theorems. These theorems state that within every formal arithmetic system, certain things are assumed to be true. These cannot be proven.

This book explores Göedel’s life and his incompleteness theorems.

The writer gives us her explanation of his theorems as well as their proofs. She does a great job because even those who haven’t done advanced mathematics can get the jist of them.

“All truths — even those that had seemed so certain as to be immune to the very possibility of revision — are essentially manufactured.”

The book has many interesting anecdotes about Göedel’s life. Goldstein also explores Göedel’s relationship with his fellows including Einstein.

The author also touches on the mathematical philosophy environment that existed at that time.

All in all, it is an interesting book that acquaints us with a brilliant mind.

Crazy or dedicated, which one was he?

When you read this book, it almost feels as if Paul Erdős is an eccentric fictional character invented by the writer.

Only he isn’t.

Paul Erdős is a world-renowned Hungarian mathematician. The author of this book spent 10 years with Erdős in order to write this book.

“Mathematician need only peace of mind and occasionally, paper and pencil.”

The writer sets the scenes perfectly with his exceptional storytelling skills. We get to see Erdős for who he is.

A man running on coffee and drugs, who wants to do nothing else but math. He doesn’t care about marrying or having kids. Math is his bride.

“When the interests of Erdős’s colleagues drifted away from pure mathematics, he made no secret of his disapproval.”

The book covers the opinions and thoughts of Erdős’s friends and colleagues as well. This gives the reader a chance to paint a complex and dynamic picture of Erdős.

Does math always need to be practical?

G H Hardy is an accomplished British Mathematician. This book is his 1940 essay written in defense of math.

Hardy wants everyone to know that math has value even if it can’t be applied practically.

“Real mathematics must be justified as art if it can be justified at all.”

When reading this book, you’ll realize that Hardy is just like a lover describing his beloved (math), singing praises of her beauty and elegance. In that sense, parts of the book are just poetic.

The book also covers Hardy’s own life and struggles.

“If a man has any genuine talent he should be ready to make almost any sacrifice in order to cultivate it to the full.”

Hardy vehemently sides with high-level mathematics which he calls pure mathematics.

This book will help you get to know one of the brightest math minds of all time.

Enter the world of cryptanalysis.

In this book, Simon Singh discusses the history and effect of secret codes.

Much like the secret language that we created as kids, the author tells us about transposition and substitution, the two branches of cryptography.

He discusses the role of ciphers in wars and dynasties. Singh also makes us see the importance of ciphers in today’s world.

“Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics.”

The writer discusses the Enigma machine and how Germans encrypted their wartime messages during World War 2.

The Allies worked hard to crack its code. The team switched to mathematicians instead of linguists. Ultimately, the Allies were able to understand German communications.

“Previous experience… tells us that every so-called unbreakable cipher has, sooner or later, succumbed to cryptanalysis…”

By the end, the author predicts the future of cryptanalysis belonging to physicists.

From being shunned to being adopted, the story of zero.

Instead of a biography of a mathematical scholar, this book gives us the biography of a number.

Not just any number, but the number which stands for nothing. Zero.

“Zero and infinity are eternally locked in a struggle to engulf all the numbers.”

The interesting fact is that initially, zero wasn’t a part of counting. The writer takes us to ancient times when counters didn’t use zero.

Going forward, we meet the people who invented it. We also see how it spread across the world.

“Christianity initially rejected zero, but trade would soon demand it.”

The civilizations that adopted it were able to make great strides in mathematics. Those who rejected the idea of zero had to accept it sooner or later.

The most interesting piece of information that Seife gives us is that the Mayan calendar has a zero in it, unlike the Western calendar. Because we don’t have zero, we argue about whether 2000 or 2001 is the start of the next century.

This book is a pure pleasure for anyone who loves math.

Calculus in nature.

Steven Strogatz calls calculus the ‘language of the universe’.

He shows us how it exists all around us. Even in the guitar strings.

“In mathematical modeling, as in all of science, we always have to make choices about what to stress and what to ignore.”

This book explores calculus from its infancy to its modern-day applications. Indeed, we wouldn’t have the technology we have today, if it weren’t for calculus.

Strigatz also discusses chaos theory.

He tells us that math isn’t for classrooms only. In fact, it can help us solve the many mysteries hidden in the universe.

“This unexpected link between music (the harmony of this world) and numbers (the harmony of an imagined world) led the Pythagoreans to the mystical belief that all is number.”

Did you know that the Pythagoreans believe that even the planets’ orbits have music? Isn’t that poetic?

I am sure that those with even a little appreciation for mathematical intellect would have a blast reading this book.

Even if you are not a seasoned mathematician, this book will help you understand difficult concepts through everyday examples.

Discover the math that exists around you!

This book is a relatively easy one. Those even with a basic math foundation can appreciate the writing and benefit from it.

Strogatz tells us about the ripples on a pond, the ridges on the sand dune, and the stripes of the zebra, all in his bid to make us see the occurrence of sine waves around us.

“Nature … somehow knows calculus”

The author has divided the book into 6 chapters:

Numbers

Relationships

Shapes

Change

Data

Frontiers

In each of them, he takes us by hand and teaches us mathematical concepts. His style of teaching is clear and understandable.

I feel like the writer is talking about me when he says:

“I have a friend who gets a tremendous kick out of science, even though he’s an artist.”

Even though I am not a scientist, ever since childhood I have enjoyed learning and expanding my knowledge of science. I used to devour science sections of online newspapers.

Not to brag, but in high school, I was pretty good at mathematical theorems too.

Although I don’t have an appetite for advanced math, I appreciate math and science in all its glory. This book invites all of us to do the same.

#### 8. Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem by Simon Singh

The story of a quest that spanned 300 years.

Simon Singh is a BBC science journalist with PhD in particle physics.

He tells us the story of Fermat’s last theorem.

Pierre de Fermat was a 17th-century mathematician. He created a theorem in the margin of a book he was reading. It states that one cannot find three numbers such that xn + yn = zn, where n is greater than 2.

“God exists since mathematics is consistent, and the Devil exists since we cannot prove it.”

This theorem became the stuff of nightmares for mathematicians. They tried and failed to solve it.

A 10-year-old boy learned about it and dedicated himself to it. He was finally able to solve it when he was around 40 years old.

“Maths is one of the purest forms of thought, and to outsiders mathematicians may seem almost other-worldly.”

For a mathematician, this book is like an adventure novel where everyone is trying to find the hidden treasure. All but one fail.

When a mathematician’s mind betrays him.

John Nash Jr was a brilliant man.

His most important contribution is the expansion of John Neuman’s Game Theory. He also gave the concept of Nash Equilibrium.

“People look to the order of numbers when the world falls apart.”

Despite his genius, his mind betrayed him. He became increasingly paranoid and erratic. His wife, Alicia committed him to a psychiatric institute where was diagnosed with paranoid schizophrenia.

He lost his wife (they divorced) and other relationships in his life. Not only this, he no longer had a source of income.

“A profound dislike for merely absorbing knowledge and a strong compulsion to learn by doing is one of the most reliable signs of genius.”

Miraculously, Nash started getting better.

He recovered, started teaching again, remarried Alicia, and…. Won the Nobel Prize for his contribution to Game Theory.

The life of a man who played a pivotal role in World War 2.

Hodges explores the life and contributions of Alan Turing.

Some biographies jump back and forth in time. This book thankfully doesn’t. It is organized chronologically.

Alan Turing is well known for breaking the code of German Enigma machines, making the Allies win World War 2. The book discusses this and many of his other achievements.

It also sheds light on the maltreatment that Alan endured because of being gay.

“Despite all he had done in the war, and all the struggles with stupidity, he still did not think of intellectuals or scientists as forming a superior class.”

In 1936, Turing proposed the idea of a universal machine. Later on, he was able to put his idea into action by creating the ‘Turing Machine’.

In 1950, Turing wrote a paper on artificial intelligence under the name, ‘Computing Machinery and Intelligence’. This shows that Turing was way ahead of time.

One might wonder, if he was alive today, what would he say?

Alan Turing’s work is referred to in computer science books and courses around the world.

“Online search engines, which work with such astonishing speed and power, are algorithms, and so equivalent to Turing machines.”

The 2014 film, ‘The Imitation Games’ is loosely based on this book.

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