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.

https://intellectualmathematics.com/blog/

Eine durchschnittliche Folge dieses Podcasts dauert 35m. Bisher sind 38 Folge(n) erschienen. Dieser Podcast erscheint alle 1 Monate.

Gesamtlänge aller Episoden: 1 day 45 minutes

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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.


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 November 29, 2023  1h27m
 
 

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.


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 July 23, 2023  1h16m
 
 

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 traditio...


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 October 11, 2022  52m
 
 

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.


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 May 20, 2022  32m
 
 

“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,


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 February 21, 2022  30m
 
 

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.


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 November 18, 2021  30m
 
 

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,


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 September 18, 2021  43m
 
 

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 mathematics went to its head, according to some, and created dogmatic individuals dismissive of other branches of le...


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 July 10, 2021  33m
 
 

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 compass in hand—as a “doer,” and thus characterised geometry as a “maker’s knowledge.


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 May 10, 2021  49m
 
 

“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 sources of evidence speak to how these dilemmas were tackled in antiquity: the linguistics of diagram constructi...


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 March 10, 2021  51m