All Episodes
Intellectual Mathematics — 36 episodes
Death of Archimedes
Torricelli’s trumpet is not counterintuitive
Did Copernicus steal ideas from Islamic astronomers?
Operational Einstein: constructivist principles of special relativity
Review of Netz’s New History of Greek Mathematics
The “universal grammar” of space: what geometry is innate?
“Repugnant to the nature of a straight line”: Non-Euclidean geometry
Rationalism 2.0: Kant’s philosophy of geometry
Rationalism versus empiricism
Cultural reception of geometry in early modern Europe
Maker’s knowledge: early modern philosophical interpretations of geometry
“Let it have been drawn”: the role of diagrams in geometry
Why construct?
Created equal: Euclid’s Postulates 1-4
That which has no part: Euclid’s definitions
What makes a good axiom?
Consequentia mirabilis: the dream of reduction to logic
Read Euclid backwards: history and purpose of Pythagorean Theorem
Singing Euclid: the oral character of Greek geometry
First proofs: Thales and the beginnings of geometry
Societal role of geometry in early civilisations
Why the Greeks?
The mathematicians’ view of Galileo
Historiography of Galileo’s relation to antiquity and middle ages
More things Galileo didn’t do first
Galileo was the first to … what exactly?
Galileo and the Church
Galileo’s theory of comets is hot air
Phases of Venus
Blemished sun
The telescope
Heliocentrism before the telescope
Heliocentrism in antiquity