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Elwes R: The Story of Huge Numbers / LF

The Story of Huge Numbers

Elements in the Philosophy of Mathematics

Husserl's Philosophy of Mathematical Practice explores the applicability of the phenomenological method to philosophy of mathematical practice. The first section elaborates on Husserl's own understanding of the method of radical sense-investigation (Besinnung), with which he thought the mathematics of his time should be approached. The second section shows how Husserl himself practiced it, tracking both constructive and platonistic features in mathematical practice. Finally, the third section situates Husserlian phenomenology within the contemporary philosophy of mathematical practice, where the examined styles are more diverse. Husserl's phenomenology is presented as a method, not a fixed doctrine, applicable to study and unify philosophy of mathematical practice and the metaphysics implied in it. In so doing, this Element develops Husserl's philosophy of mathematical practice as a species of Kantian critical philosophy and asks after the conditions of possibility of social and self-critical mathematical practices.

Husserl's Philosophy of Mathematical Practice

This Element provides a framework for studying mathematical notations, aimed at researchers and students in philosophy, history, cognitive science, and mathematics education. It discusses the characteristics of mathematical notations, their language, cognitive resources, tasks, material basis, and historical context.

Mathematical Notations

'WHAT TO READ IN 2025' FINANCIAL TIMESMany artists are unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, but what if we're wrong?

How mathematics shapes creativity

Blueprints

A fascinating intellectual history that takes a comparatively little-known but important idea and shows how it affects huge areas of our lives

How Bayes' Remarkable Theorem Explains the World

Everything Is Predictable

A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work.

Elements of Purity

This volume brings together twelve essays exploring the history of theories of definition and essence in Western philosophy from Aristotle to Kant. Its broad historical sweep also facilitates comparisons between different figures.

Definition and Essence from Aristotle to Kant

Routledge Studies in the History of Economics

John Maynard Keynes is best known for his contributions to economics, yet he spent nearly two decades exploring the concept of probability. His extensive work culminated in the Treatise on Probability (1921), where he developed a unique notion of probability that continues to divide scholars regarding its relevance to economic theory.

The Influence of Locke, Leibniz, and Hume

J.M. Keynes and the History of Probability

Abstractionism

"An interdisciplinary history of trigonometry from the mid-sixteenth century through to the early twentieth century The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms"--

A History of Modern Trigonometry

The Doctrine of Triangles

"Galileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one. In dozens of lively and informative entries, Raâul Rojas shows how today's mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwarizmi, Renâe Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time. An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning"--

The Stories behind the Symbols

The Language of Mathematics

The Story of Huge Numbers

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