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Podcast Profile: Opinionated History of Mathematics

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38 episodes
2018 to 2023
Median: 35 minutes
Collection: Physics, Math, and Astronomy

Description (podcaster-provided):

Cracking tales of historical mathematics and its interplay with science, philosophy, and culture. Revisionist history galore. Contrarian takes on received wisdom. Implications for teaching. Informed by current scholarship. By Dr Viktor Blåsjö.

Themes and summary (AI-generated based on podcaster-provided show and episode descriptions):

➤ Historical mathematics • Interplay with science and philosophy • Geometry's evolution • Critiques of traditional views • Rationalism vs. empiricism • Influence of Greek mathematics • Galileo controversies • Innate concepts in geometry

This podcast, titled "Opinionated History of Mathematics," offers an engaging exploration of historical mathematics and its intricate connections with science, philosophy, and culture. Throughout its episodes, the podcast delves into revisionist history, providing contrarian perspectives on widely accepted notions within the field. Each episode is informed by contemporary scholarship and examines the implications of these historical perspectives for modern teaching.

Episodes cover a diverse array of topics related to both ancient and early modern mathematics. A significant portion of the content is dedicated to prominent figures in the history of mathematics and science, such as Copernicus, Einstein, Euclid, and Galileo. Discussions often focus on lesser-known influences on these figures, such as the potential impact of Islamic astronomers on Copernicus or the argumentative reception of Galileo among his contemporaries.

The podcast also frequently addresses the philosophical underpinnings of mathematical theories. It explores how different schools of thought, such as rationalism and empiricism, have influenced the development and interpretation of mathematical concepts over time. Kant’s philosophy of geometry, for instance, is discussed alongside the broader rationalist tradition and its reconciliation with Newtonian science.

A recurring theme in the episodes is the exploration of geometry, its foundational principles, and its cultural impact. Several episodes analyze Euclid's contributions, including his definitions, postulates, and the role of constructions in his Elements. The narrative extends to the societal and cultural reception of geometry, touching on its influence on Gothic architecture, Renaissance painting, and its role in early civilizations’ administration.

Additionally, the podcast dives into the methods and tools of mathematicians, such as the use of diagrams in proofs, the oral tradition of Greek geometry, and the impact of instruments like the telescope on astronomical discoveries. Through these discussions, the podcast sheds light on the evolving nature of mathematical knowledge and its applications throughout history.

Episode Image Did Copernicus steal ideas from Islamic astronomers?
87 minutes
Episode Image Operational Einstein: constructivist principles of special relativity
76 minutes
Episode Image Review of Netz’s New History of Greek Mathematics
52 minutes
Episode Image The “universal grammar” of space: what geometry is innate?
32 minutes
Episode Image “Repugnant to the nature of a straight line”: Non-Euclidean geometry
30 minutes
Episode Image Rationalism 2.0: Kant’s philosophy of geometry
30 minutes
Episode Image Rationalism versus empiricism
43 minutes
Episode Image Cultural reception of geometry in early modern Europe
33 minutes
Episode Image Maker’s knowledge: early modern philosophical interpretations of geometry
49 minutes
Episode Image “Let it have been drawn”: the role of diagrams in geometry
51 minutes
Episode Image Why construct?
78 minutes
Episode Image Created equal: Euclid’s Postulates 1-4
41 minutes
Episode Image That which has no part: Euclid’s definitions
43 minutes
Episode Image What makes a good axiom?
35 minutes
Episode Image Consequentia mirabilis: the dream of reduction to logic
35 minutes
Episode Image Read Euclid backwards: history and purpose of Pythagorean Theorem
41 minutes
Episode Image Singing Euclid: the oral character of Greek geometry
40 minutes
Episode Image First proofs: Thales and the beginnings of geometry
42 minutes
Episode Image Societal role of geometry in early civilisations
36 minutes
Episode Image Why the Greeks?
40 minutes
Episode Image The mathematicians’ view of Galileo
36 minutes
Episode Image Historiography of Galileo’s relation to antiquity and middle ages
35 minutes
Episode Image More things Galileo didn’t do first
53 minutes
Episode Image Galileo was the first to … what exactly?
44 minutes
Episode Image Galileo and the Church
40 minutes
Episode Image Galileo’s theory of comets is hot air
36 minutes
Episode Image Phases of Venus
31 minutes
Episode Image Blemished sun
32 minutes
Episode Image The telescope
31 minutes
Episode Image Heliocentrism before the telescope
31 minutes
Episode Image Heliocentrism in antiquity
31 minutes
Episode Image Galileo’s theory of tides
22 minutes
Episode Image Why Galileo is like Nostradamus
28 minutes
Episode Image Galileo’s errors on projectile motion and inertia
26 minutes
Episode Image The case against Galileo on the law of fall
21 minutes
Episode Image Galilean science in antiquity?
23 minutes
Episode Image Mathematics versus philosophy, then and now
19 minutes
Episode Image Galileo bad, Archimedes good
16 minutes