Books like The Poincaré conjecture by Donal O'Shea

Stephen Hawking explains the fundamental physics of the universe—space, time, cosmology, black holes, and the Big Bang—in clear, accessible language.

An accessible guide to mathematics designed for beginners, students, teachers, philosophers, and engineers, offering systematic exposition and practical insights into the mathematical world.

An encyclopedic reference edited by Fields Medalist Timothy Gowers, the Princeton Companion to Mathematics offers nearly 200 essays by leading mathematicians, covering key concepts, historical development, and interdisciplinary impact of modern mathematics.

In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincare developed the Poincare Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. Th e problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.

An approachable survey of two‑ and three‑dimensional geometry and topology that connects mathematical concepts with modern cosmological observations, including new chapters on the universe’s shape and galactic patterns.

Develops world contributions to mathematics, from the inception of numbers and geometry to modern probability and Bourbaki's mathematics.

From the simple elegance of the Pythagorean theorem to the looking-glass world of Russell's Paradox and the summed infinities of integral calculus, experience the beauty and majesty of the mathematical universe. William Dunham, author of the popular Journey Through Genius, will give you a rare sampling of its joys. Writing in his trademark razor-sharp style, Dunham introduces a tantalizing selection of the great proofs, notorious disputes, and intriguing unsolved mysteries. Subjects range from the golden age of Greek geometry to the furthest frontier of infinite series. In chapters spanning the field from A to Z, discover the marvels of the Monte Carlo Method and the ancient riddle of Dido's Problem. Scale the heights of the Himalayas with famed surveyor Sir George Everest and puzzle over the fascinating conundrum of Fermat's Last Theorem. Dunham explores more than five thousand years of mathematical history, digging into the earliest records in Egypt, Babylon, India, and China, and turning up surprising tales and tidbits from modern times. . All along the way, Dunham portrays the great masters of math at their work. In colorful anecdotes, the brilliant - often eccentric - luminaries chart the course of mathematical progress. Among them are the battling Bernoulli brothers, Jakob and Johann, who worked tirelessly to one-up each other's theorems; the famed Isaac Newton and largely forgotten Gottfried Wilhelm Leibniz, who independently and virtually simultaneously discovered "the calculus"; and the exceptionally determined genius Sofia Kovalevskaia, who discovered the rules of trigonometry for herself when she was left without instruction. Your passport to rich rewards, The Mathematical Universe is accessible to any reader with a basic knowledge of algebra and geometry. You will come away from this exhilarating book with a keen sense of the power and splendor of the magical mathematical world.