Opinionated History of Mathematics

Intellectual Mathematics
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History of mathematics research with iconoclastic madcap twists

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    Death of Archimedes

    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 this fact or fiction? We have third-hand accounts at best so there is plenty of room for doubt. But … Continue reading Death of Archimedes

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    Torricelli’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 trope known as Torricelli’s trumpet. Nor was this result seen as counterintuitive at the time of its discovery in the 17th century, contrary to many commonplace historical narratives. Transcript Torricelli’s trumpet is not counterintuitive. Your … Continue reading Torricelli’s trumpet is not counterintuitive

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    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 School, including the Tusi couple and Ibn al-Shatir’s models for the Moon and Mercury. On this basis many historians have concluded that Copernicus must have gotten his hands on these Maragha ideas somehow or other, even … Continue reading Did Copernicus steal ideas from Islamic astronomers?

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    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 them. This is analogous to the constructivist spirit of classical geometry. Transcript Oh no, we are chained to a wall! Aaah! This is going to mess up our geometry big time. Remember what … Continue reading Operational Einstein: constructivist principles of special relativity

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    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 traditional scholarship in the field, but in some ways represents a step backwards with respect to that tradition. I argue against Netz’s dismissal of many anecdotal historical testimonies as fabrications, and his “ludic proof” … Continue reading Review of Netz’s New History of Greek Mathematics

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    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 thought, and the same can be said for Euclidean and non-Euclidean geometries. As our native language is shaped by experience, so might our “native geometry” be. Yet substantive innate conceptions … Continue reading The “universal grammar” of space: what geometry is innate?

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    “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 and the world. Instead of assuming that physical space was the subject matter of geometry, mathematicians elaborated numerous alternative geometries abstractly and formally, distancing themselves from reality and intuition. Transcript The mathematician has only one nightmare: to … Continue reading “Repugnant to the nature of a straight line”: Non-Euclidean geometry

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    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. Namely, because geometry is built into not only our minds but also the way in which we perceive the world. In this way, Kant solved the applicability problem of classical rationalism, albeit at … Continue reading Rationalism 2.0: Kant’s philosophy of geometry

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History of mathematics research with iconoclastic madcap twists

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    Intellectual Mathematics
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    Opinionated History of Mathematics

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