English
Non-explicit
intellectualmathematics.com
4.40 stars
39:05
Opinionated History of Mathematics
by Intellectual MathematicsHistory of mathematics research with iconoclastic madcap twists
Episodes
Did Copernicus steal ideas from Islamic astronomers?
1h 27m · Published
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
1h 16m · Published
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
Review of Netz’s New History of Greek Mathematics
52m · Published
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?
32m · Published
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?
“Repugnant to the nature of a straight line”: Non-Euclidean geometry
30m · Published
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
Rationalism 2.0: Kant’s philosophy of geometry
30m · Published
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
Rationalism versus empiricism
43m · Published
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 … Continue reading Rationalism versus empiricism
Cultural reception of geometry in early modern Europe
33m · Published
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, … Continue reading Cultural reception of geometry in early modern Europe
Maker’s knowledge: early modern philosophical interpretations of geometry
49m · Published
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 … Continue reading Maker’s knowledge: early modern philosophical interpretations of geometry
“Let it have been drawn”: the role of diagrams in geometry
51m · Published
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 … Continue reading “Let it have been drawn”: the role of diagrams in geometry
Opinionated History of Mathematics has 38 episodes in total of non- explicit content. Total playtime is 24:45:19. The language of the podcast is English. This podcast has been added on November 28th 2022. It might contain more episodes than the ones shown here. It was last updated on May 19th, 2024 03:12.
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