Opinionated History of Mathematics

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106 reviews
This podcast has
38 episodes
Date created
Average duration
51 min.
Release period
99 days


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.

Podcast episodes

Check latest episodes from Opinionated History of Mathematics podcast

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?
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.
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
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.
“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.
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.
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.
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 learning. Some thought the uncompromising rigour of Euclid went hand in hand with totalitarianism in political and spiritual domains, while others thought creative mathematics was inherently free and liberal.
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.” Others got into a feud about what to do when Euclid was at odds with Aristotle. Descartes thought Euclid’s axioms should be justified via theology.
“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 construction, the state of drawings in the oldest extant manuscripts, commentaries of philosophers, and implicit assumptions in mathematical proofs.
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? Why did he think this was better than a geometry that has only theorems and no constructions? In fact, constructions protect geometry from foundational problems to which it would otherwise be susceptible, such as inconsistencies, hidden assumptions, verbal logic fallacies, and diagrammatic fallacies.
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 regarded as depending on motion, which is supposedly proved impossible by Zeno’s paradoxes. Although whether these postulates correspond to ruler and compass or not is debatable, especially since Euclid seems to restrict himself to a “collapsible” compass in Proposition 2. Furthermore, why did Euclid feel the need to postulate that “all right angles are equal”? Perhaps in order to rule out non-flat surfaces such as cones.

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4.5 out of 5
106 reviews
Sandokanus 2023/06/02
Illuminating History of Mathematics
It’s great to hear an analysis of various historical treaties of math and science history with such clarity! Thank you! I hope there’s more to come. L...
petera256 2023/05/11
This is refreshing and illuminating
The season about Galileo is invaluable. I hope these facts make it into the mainstream writers of history, because it seems there is much, much more t...
aylee yahoo 2022/12/30
Brilliant, witty, and, highest compliment for a mathematician explaining occasionally complex matters, comprehensible to people who have virtually no ...
G&8#8 2022/11/04
Gasping humor, commentary informs
Joining the dots, this commenter sees the bigger picture and then hones in like a perigean falcon upon the biting conclusion. Right or wrong his obser...
LaotianRabbit 2022/09/04
This podcast teaches so much. Add to that the host is extremely intelligent with a biting sense of humor. I really enjoy this. Thank You for creati...
KatieGirl 2022/07/07
I love math🤗🤗🤗🤗
🐶🐾❤️ 2022/05/29
I love math!
Very interesting and a lot of great stories about mathematicians I’ve never heard of before.
Mayhemenway 2022/03/18
Everything you didn’t know you needed plus math
This podcast is so easy to listen to! There is no stress and no nonsense. The topics are interesting and oftentimes funny. The way he explains some of...
SGA2M1 2022/02/08
Perfect listening
At once highly entertaining and soothing, this podcast is like meditation except that you get to learn something, and have food for thought to chew o...
ShrGuy 2021/08/14
Plato was a loudmouth?
The pod about the role of diagrams in geometry was quite wonderful, although I get into a bit of trouble toward the end. Woke up family with my laugh...
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