History of infinitesimals5/3/2023 ![]() "He thought the only way to re-establish order was much like the Jesuits: Just wipe off any possibility of dissent. Thomas Hobbes, remembered today for his works of political philosophy like Leviathan, was also acknowledged at the time as a mathematician. The aristocracy and propertied classes were desperate to hold onto their traditional power while lower class dissent fermented underneath. Meanwhile a similar situation was playing out in England, where civil war was also threatening upheaval. That was a sharp contrast with the dependable outcomes of geometry. ![]() But in the 17th century, those questions didn't yet have satisfying answers - and worse, the results of early calculus were sometimes wrong, Alexander tells NPR's Arun Rath. Today, mathematicians have found ways to answer that question so that modern calculus is rigorous and reliable. The fight over how to resolve it had a surprisingly large role in the wars and disputes that produced modern Europe, according to a new book called Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by UCLA historian Amir Alexander. That's the paradox lurking behind calculus. And if they're zero, well, then no matter how many parts there are, the length of the line would still be zero. But how long are those parts? If they're anything greater than zero, then the line would seem to be infinitely long. You can keep on dividing forever, so every line has an infinite amount of parts. Just how many parts can you make? A hundred? A billion? Why not more? Then you can cut those lines in half, then cut those lines in half again. Here's a stumper: How many parts can you divide a line into? Your purchase helps support NPR programming. Gray & Libby Knott).Close overlay Buy Featured Book Title Infinitesimal Subtitle How a Dangerous Mathematical Theory Shaped the Modern World Author Amir Alexander Part III, History of Mathematics in Mathematics Education, contains: (12) Classifying the arguments and methodological schemes for integrating history in mathematics education (Constantinos Tzanakis & Yannis Thomaidis) (13) A first attempt to identify and classify empirical studies on history in mathematics education (Uffe Thomas Jankvist) (14) Reflections on and benefits of uses of history in mathematics education exemplified by two types of student work in upper secondary school (Tinne Hoff Kjeldsen) and (15) Adversarial and friendly interactions: Progress in 17th century mathematics (Shirley B. Fried) (9) Book X of The Elements: Ordering Irrationals (Jade Roskam) (10) The Origins of the Genus Concept in Binary Quadratic Forms (Mark Beintema & Azar Khosravani) and (11) Where are the Plans: A socio-critical and architectural survey of early Egyptian Mathematics (Gabriel Johnson, Bharath Sriraman & Rachel Saltzstein). Part II, Topics in the History and Didactics of Geometry and Number, contains: (8) Euclid's Book on the Regular Solids: Its Place in the Elements and Its Educational Value (Michael N. Part I, Topics in History and Didactics of Calculus and Analysis, contains: (1) A note on the institutionalization of mathematical knowledge or "What was and is the Fundamental Theorem of Calculus, really?" (Eva Jablonka & Anna Klisinska) (2) Transitioning students to calculus: Using history as a guide (Nicolas Haverhals & Matt Roscoe) (3) The tension between intuitive infinitesimals and formal mathematical analysis (Mikhail Katz & David Tall) (4) The didactical nature of some lesser known historical examples in mathematics (Kajsa Brating, Nicholas Kallem & Bharath Sriraman) (5) The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem (Jeff Babb & James Currie) (6) Chopping Logs: A Look at the History and Uses of Logarithms (Rafael Villarreal-Calderon) and (7) The history of mathematics as a pedagogical tool: Teaching the integral of the secant via Mercator's projection (Nicolas Haverhals & Matt Roscoe). The book is meant to serve as a source of enrichment for undergraduate mathematics majors and for mathematics education courses aimed at teachers. In this monograph, the chapters cover topics such as the development of Calculus through the actuarial sciences and map making, logarithms, the people and practices behind real world mathematics, and fruitful ways in which the history of mathematics informs mathematics education. However there is little systematization or consolidation of the existing literature aimed at undergraduate mathematics education, particularly in the teaching and learning of the history of mathematics and other undergraduate topics. ![]() Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry.
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