Death of Archimedes
Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene. Transcript Archimedes di...
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Opinionated History of Mathematics
History of mathematics research with iconoclastic madcap twists
Episodes
20 of 40 episodesTorricelli’s trumpet is not counterintuitive
There is nothing counterintuitive about an infinite shape with finite volume, contrary to the common propaganda version of the calculus trop...
Did Copernicus steal ideas from Islamic astronomers?
Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha Scho...
Operational Einstein: constructivist principles of special relativity
Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure t...
Review of Netz’s New History of Greek Mathematics
Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both mathematical and historical. Netz is dismissive of...
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 an equally coherent and viable paradigm of...
“Repugnant to the nature of a straight line”: Non-Euclidean geometry
The discovery of non-Euclidean geometry in the 19th century radically undermined traditional conceptions of the relation between mathematics...
Rationalism 2.0: Kant’s philosophy of geometry
Kant developed a philosophy of geometry that explained how geometry can be both knowable in pure thought and applicable to physical reality....
Rationalism versus empiricism
Rationalism says mathematical knowledge comes from within, from pure thought; empiricism that it comes from without, from experience and obs...
Cultural reception of geometry in early modern Europe
Euclid inspired Gothic architecture and taught Renaissance painters how to create depth and perspective. More generally, the success of math...
Maker’s knowledge: early modern philosophical interpretations of geometry
Philosophical movements in the 17th century tried to mimic the geometrical method of the ancients. Some saw Euclid—with his ruler and compas...
“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 human in mathematical reasoning. Multiple...
Why construct?
Euclid spends a lot of time in the Elements constructing figures with his ubiquitous ruler and compass. Why did he think this was important?...
Created equal: Euclid’s Postulates 1-4
The etymology of the term “postulate” suggests that Euclid’s axioms were once questioned. Indeed, the drawing of lines and circles can be re...
That which has no part: Euclid’s definitions
Euclid’s definitions of point, line, and straightness allow a range of mathematical and philosophical interpretation. Historically, however,...
What makes a good axiom?
How should axioms be justified? By appeal to intuition, or sensory perception? Or are axioms legitimated merely indirectly, by their logical...
Consequentia mirabilis: the dream of reduction to logic
Euclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the Pythagorean Theorem to the parallelogram area theorem...
Read Euclid backwards: history and purpose of Pythagorean Theorem
The Pythagorean Theorem might have been used in antiquity to build the pyramids, dig tunnels through mountains, and predict eclipse duration...
Singing Euclid: the oral character of Greek geometry
Greek geometry is written in a style adapted to oral teaching. Mathematicians memorised theorems the way bards memorised poems. Several oddi...
First proofs: Thales and the beginnings of geometry
Proof-oriented geometry began with Thales. The theorems attributed to him encapsulate two modes of doing mathematics, suggesting that the id...