Opinionated History of Mathematics

Intellectual Mathematics
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Opinionated History of Mathematics

Cracking tales of historical mathematics and its interplay with science, philosophy, and culture. Revisionist history galore. Contrarian takes on received wisdom. Implications for teaching. Informed by current scholarship. By Dr Viktor Blåsjö.

  1. 30/12/2024

    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

    57 min

  2. 29/11/2023

    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?

    1j 27m

  3. 23/07/2023

    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.

    1j 17m

  4. 11/10/2022

    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

    52 min

  5. 20/05/2022

    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 may be a precondition for any linguistic or spatial thought to be possible at all, as Chomsky said for language and Kant for geometry. Just as language learning requires singling out, from all the sounds in the environment, only the linguistic ones, so Poincaré articulated criteria for what parts of all sensory data should be regarded as pertaining to geometry.

    32 min

  6. 20/02/2022

    “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.

    31 min

  7. 17/11/2021

    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 the cost of making our perception of the world around us inextricably subjective. Kant’s theory also showed how rationalism, and philosophy generally, could be reconciled with Newtonian science, with which it had been seen as embarrassingly out of touch. In particular, Kant’s perspective shows how Newton’s notion of absolute space, which had seemed philosophically repugnant, can be accommodated from an epistemological point of view.

    30 min

  8. 18/09/2021

    Rationalism versus empiricism

    Rationalism says mathematical knowledge comes from within, from pure thought; empiricism that it comes from without, from experience and observation. Rationalism led Kepler to look for divine design in the universe, and Descartes to reduce all mechanical phenomena to contact mechanics and all curves in geometry to instrumental generation. Empiricism led Newton to ignore the cause of gravity and dismiss the foundational importance of constructions in geometry.

    44 min
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Cracking tales of historical mathematics and its interplay with science, philosophy, and culture. Revisionist history galore. Contrarian takes on received wisdom. Implications for teaching. Informed by current scholarship. By Dr Viktor Blåsjö.

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