Philosophy Of Mathematics

Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised, and the great minds behind them, with this original, graphic-led book. Applying the Big Ideas series' trademark combination of authoritative, accessible text and bold graphics to ch...art the development of maths through history, the book explores and explains subjects that range from ancient mathematical ideas and inventions, such as prehistoric tally bones and Sumerian multiplication tables, through to the developments in mathematics during medieval and Renaissance Europe, to the rise of game and group theory more recently Tracing maths through the scientific revolution to its 21st-century use in computers, the internet, and AI, The Maths Book uses an innovative graphic-led approach to make the subject accessible to everyone.
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Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use - from our computers and cars, to our kitchen gadgets and home appliances. This title examines the history of Boole's ideas, and considers how they led to Shannon's work o...n electrical relay circuits and information theory.
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Dazzling popular maths for the curious reader...from Britain's cleverest schoolboy!

A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the so-called problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, the...se compass and straightedge problems-squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle-have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately, their proofs-demonstrating the impossibility of solving them using only a compass and straightedge-depended upon and resulted in the growth of mathematics. Richeson explores how celebrated luminaries, including Euclid, Archimedes, Viete, Descartes, Newton, and Gauss labored to understand the problems of antiquity, and how many major mathematical discoveries were related to these explorations. Though the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. A little-known mathematician named Pierre Wantzel and Ferdinand von Lindemann, through his work on , finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana legislature passed a bill setting an incorrect value for , and how Leonardo da Vinci made elegant contributions to the puzzles. Taking readers from the classical period to the present, Tales of Impossibility demonstrates how four unsolvable problems captivated mathematical thinking for centuries.
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Uncertainty is everywhere. It lurks in every consideration of the future - the weather, the economy, the sex of an unborn child - even quantities we think that we know such as populations or the transit of the planets contain the possibility of error. It's no wonder that, through...out that history, we have attempted to produce rigidly defined areas of uncertainty - we prefer the surprise party to the surprise asteroid. We began our quest to make certain an uncertain world by reading omens in livers, tea leaves, and the stars. However, over the centuries, driven by curiosity, competition, and a desire be better gamblers, pioneering mathematicians and scientists began to reduce wild uncertainties to tame distributions of probability and statistical inferences. But, even as unknown unknowns became known unknowns, our pessimism made us believe that some problems were unsolvable and our intuition misled us. Worse, as we realized how omnipresent and varied uncertainty is, we encountered chaos, quantum mechanics, and the limitations of our predictive power. Bestselling author Professor Ian Stewart explores the history and mathematics of uncertainty. Touching on gambling, probability, statistics, financial and weather forecasts, censuses, medical studies, chaos, quantum physics, and climate, he makes one thing clear: a reasonable probability is the only certainty.
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