Did Copernicus steal ideas from Islamic astronomers?
Copernicus’s planetary models contain elements also found in the works of late medieval Islamic...
01:27:03
Operational Einstein: constructivist principles of special relativity
Einstein’s theory of special relativity defines time and space operationally, that is to say, in...
01:16:37
Review of Netz’s New History of Greek Mathematics
Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both...
52:03
The “universal grammar” of space: what geometry is innate?
Geometry might be innate in the same way as language. There are many languages, each of which is...
32:22
“Repugnant to the nature of a straight line”: Non-Euclidean geometry
The discovery of non-Euclidean geometry in the 19th century radically undermined traditional...
30:39
Rationalism 2.0: Kant’s philosophy of geometry
Kant developed a philosophy of geometry that explained how geometry can be both knowable in pure...
29:59
Rationalism says mathematical knowledge comes from within, from pure thought; empiricism that it...
43:50
Cultural reception of geometry in early modern Europe
Euclid inspired Gothic architecture and taught Renaissance painters how to create depth and...
33:47
Maker’s knowledge: early modern philosophical interpretations of geometry
Philosophical movements in the 17th century tried to mimic the geometrical method of the...
49:29
“Let it have been drawn”: the role of diagrams in geometry
The use of diagrams in geometry raise questions about the place of the physical, the sensory, the...
51:11
Euclid spends a lot of time in the Elements constructing figures with his ubiquitous ruler and...
01:18:01
Created equal: Euclid’s Postulates 1-4
The etymology of the term “postulate” suggests that Euclid’s axioms were once questioned. Indeed,...
40:59
That which has no part: Euclid’s definitions
Euclid’s definitions of point, line, and straightness allow a range of mathematical and...
43:32
How should axioms be justified? By appeal to intuition, or sensory perception? Or are axioms...
35:20
Consequentia mirabilis: the dream of reduction to logic
Euclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the...
35:50
Read Euclid backwards: history and purpose of Pythagorean Theorem
The Pythagorean Theorem might have been used in antiquity to build the pyramids, dig tunnels...
41:36
Singing Euclid: the oral character of Greek geometry
Greek geometry is written in a style adapted to oral teaching. Mathematicians memorised theorems...
40:10
First proofs: Thales and the beginnings of geometry
Proof-oriented geometry began with Thales. The theorems attributed to him encapsulate two modes...
42:27
Societal role of geometry in early civilisations
In ancient Mesopotamia and Egypt, mathematics meant law and order. Specialised mathematical...
36:00
The Greek islands were geographically predisposed to democracy. The ritualised, antagonistic...
40:41
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