The area of mathematics known as number theory is essentially concerned with counting numbers. The prime numbers, or “building blocks” of our number system, are very significant. The topic has been studied for many years due to its age—it dates back more than two millennia to the ancient Greeks—and inherent beauty and elegance, not least because some of its difficulties are so simple to describe that anyone can comprehend them but have never been solved.
The security of your credit card, as well as the defense of the country, relies on a prime number result from the 18th century, but number theory has also recently gained significant practical significance in the field of cryptography. Other noteworthy advances in recent years include Andrew Wiles’s demonstration of “Fermat’s final theorem” (which had remained unproven for more than 250 years) and some fascinating work on prime numbers. Robin Wilson covers classical and contemporary number theory fundamentals in this Very Short Introduction. He places some of the most intriguing and innovative challenges in the field in the perspective of history by drawing on the work of many of the greatest mathematicians in history, including Euclid, Fermat, Euler, and Gauss.