Opinionated History of Mathematics

Ranking history

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Latest episodes

• Death of Archimedes

  July 15, 2025 · 26 min

  Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene. Transcript Archimedes died mouthing back at an enemy soldier: “Don’t disturb my circles.” Or that’s how the story goes. Is…

• Torricelli’s trumpet is not counterintuitive

  December 30, 2024 · 57 min

  There is nothing counterintuitive about an infinite shape with finite volume, contrary to the common propaganda version of the calculus trope known as Torricelli’s trumpet. Nor was this result seen as counterintuitive at the time of its…

• Did Copernicus steal ideas from Islamic astronomers?

  November 29, 2023 · 1 hr 27 min

  Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha School, including the Tusi couple and Ibn al-Shatir’s models for the Moon and Mercury. On this basis…

• Operational Einstein: constructivist principles of special relativity

  July 23, 2023 · 1 hr 17 min

  Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure them. This is analogous to the constructivist spirit of classical geometry. Transcript Oh no, we are…

• Review of Netz’s New History of Greek Mathematics

  October 11, 2022 · 52 min

  Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both mathematical and historical. Netz is dismissive of traditional scholarship in the field, but in some ways represents a step backwards with respect to…

• The “universal grammar” of space: what geometry is innate?

  May 20, 2022 · 32 min

  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 thought, and the same can be said for Euclidean and non-Euclidean geometries. As our native…

• “Repugnant to the nature of a straight line”: Non-Euclidean geometry

  February 20, 2022 · 31 min

  The discovery of non-Euclidean geometry in the 19th century radically undermined traditional conceptions of the relation between mathematics and the world. Instead of assuming that physical space was the subject matter of geometry…

• Rationalism 2.0: Kant’s philosophy of geometry

  November 17, 2021 · 30 min

  Kant developed a philosophy of geometry that explained how geometry can be both knowable in pure thought and applicable to physical reality. Namely, because geometry is built into not only our minds but also the way in which we perceive…