Mathematics has long been a specialty of the Press, and mathematicians have been the subjects of many of our biographies. Julian Havil’s John Napier: Life, Logarithms and Legacy describes the life and thought of the inventor of logarithms. Napier’s work on logarithms, first published in 1614, established the efficient method of calculation that remained in widespread use until the development of computers over three hundred years later. Napier lived in an age when the boundaries between mathematics, science, religion and the occult were less clearly drawn: he attempted to predict the Apocalypse on the basis of the Book of Revelations and the Sibylline oracles, and was even alleged to be an alchemist and a necromancer.

A century later Leonhard Euler continued development of logarithms, but for Euler this was only one among dozens of mathematical innovations over the course of a brilliant and prolific career. Ronald Calinger’s Leonhard Euler: Mathematical Genius in the Enlightenment is the first full-scale biography of one of the great figures in mathematics. His tireless devotion to his work while at the court of Frederick the Great earned him the mockery of Voltaire, but his collected writings on topics ranging from calculus, number theory, and geometry to astronomy and optics are an extraordinary treasure trove of ideas. Despite near total blindness in the last two decades of his life, Euler’s prodigious memory and skill at mental calculation allowed him to continue working to his death, dictating to a team of scribes. He remains the only mathematician to have given his name to two numbers: the transcendental number (and base of natural logarithms) e, known as Euler’s number, and the Euler-Mascheroni constant.

Theoretical ability doesn’t always translate into practical applications, and Frederick the Great was unimpressed with Euler as an engineer. By contrast, Henri Poincaré worked in the French Corps des Mines throughout his life, eventually attaining the rank of Inspector General, while continuing to pursue his work in multiple fields in mathematics, physics and philosophy. Jeremy Gray’s Henri Poincaré: A Scientific Biography analyzes the lasting influence of a man that some argue was the true discoverer of relativity. Poincaré did not shy away from involvement in public affairs, acting as an expert witness to counter spurious claims by the prosecution in the Dreyfus trials that convulsed France.

Unusually for brilliant theoreticians, Euler and Poincaré also wrote for a popular audience – *Letters of Euler on Different Subjects in Natural Philosophy Addressed to a German Princess* was a bestseller in its time. In Undiluted Hocus-Pocus one of the great popularizers of our time, Martin Gardner, writes with characteristic wit about his own life. Gardner’s column in *Scientific American*, Mathematical Games, ran for 25 years – Cambridge University Press are currently working on a new edition of the fifteen volumes of the collected columns. No stranger to controversy, Gardner devoted much energy to combating pseudo-science, but is perhaps best known for the Annotated Alice, in which he explained in detail the mathematical trickery and literary wordplay of Lewis Carroll’s classic Alice books.