Book contents
- Frontmatter
- Table of Contents
- Preface
- 1 Connecting Modernities: A Global Update
- Part I Modernity as We Know It: Narratives of Modernity across the Disciplines
- Part II Modernity under Fire: Critiques, Challenges, and Revisions
- Part III In the Shadow of the Pandemic
- Part IV Imagining New Global Frameworks: Democracy and Modernity-to-Come
- Index
3 - Math and Modernity: Critical Reflections
Published online by Cambridge University Press: 30 April 2022
- Frontmatter
- Table of Contents
- Preface
- 1 Connecting Modernities: A Global Update
- Part I Modernity as We Know It: Narratives of Modernity across the Disciplines
- Part II Modernity under Fire: Critiques, Challenges, and Revisions
- Part III In the Shadow of the Pandemic
- Part IV Imagining New Global Frameworks: Democracy and Modernity-to-Come
- Index
Summary
Abstract
Besides the birth of new revolutionary concepts and methods, and of new areas of research, mathematicians, logicians, and philosophers have put into question the foundations of the discipline itself and the whole meaning of “mathematical truth.” Before then, at the end of the eighteenth century, mathematics was mainly concerned with explaining the “real world” and its laws. At the beginning of the “modern era” things started to change, sometimes slowly, other times abruptly. Abstract mathematics was no longer intimately related to the real world and its description. This abstract approach, both on research and on mathematical education, generated critical reactions in the mathematical community, and some “modern” ideas were rejected or neglected after several decades of experimentation.
Keywords: math modernism; new math; Bourbaki approach; abstract Mathematics
Science is the captain and application is the soldier.
‒ Leonardo da VinciNeglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world.
‒ Roger BaconMathematics has always been part of Western history and tradition, and it has always been closely linked to its culture and its philosophy. We shouldn't forget Plato's Republic, for instance, where it is strongly suggested that philosophers study mathematics in order fully understand the ever changing world. In the sixteenth century, the Tuscan polymath Galileo Galilei claimed that “the book of nature is written in the language of mathematics; without its help it is impossible to comprehend a single word of it.” (Pinker 1997, 359). Galileo's greatest contribution was, indeed, the “mathematization” of science. On the other hand, Dutch philosopher Benedict Spinoza wrote “Ethics, Demonstrated in Geometrical Order” (in Latin: Ethica, ordine geometrico demonstrata, 1677), perhaps the most ambitious attempt to apply the rigorous method of Euclid to philosophy.
The end of the eighteenth century, the age of the Enlightenment, is a dark and pessimistic period for the future of mathematics, though it has been claimed that the entire project of the Enlightenment was to achieve the rigor and the methods of mathematics and apply these everywhere by means of “analytic thinking.” Later, German philosopher Martin Heidegger, who sharply criticized science, believed the character of truth is purely mathematical.
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- Global Modernity from Coloniality to PandemicA Cross-Disciplinary Perspective, pp. 61 - 80Publisher: Amsterdam University PressPrint publication year: 2022