Opinionated History of Mathematics – Détails, épisodes et analyse

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Opinionated History of Mathematics

Opinionated History of Mathematics

Intellectual Mathematics

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Histoire
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Fréquence : 1 épisode/59j. Total Éps: 40

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History of mathematics research with iconoclastic madcap twists
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    14/08/2025
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  • 🇩🇪 Allemagne - mathematics

    14/08/2025
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  • 🇺🇸 États-Unis - mathematics

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  • 🇫🇷 France - mathematics

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    13/08/2025
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  • 🇬🇧 Grande Bretagne - mathematics

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  • 🇩🇪 Allemagne - mathematics

    13/08/2025
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  • 🇺🇸 États-Unis - mathematics

    13/08/2025
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  • 🇫🇷 France - mathematics

    13/08/2025
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Did Copernicus steal ideas from Islamic astronomers?

mercredi 29 novembre 2023 • Durée 01:27:04

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

dimanche 23 juillet 2023 • Durée 01:16:38

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

Why construct?

mercredi 20 janvier 2021 • Durée 01:18:01

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 … Continue reading Why construct?

Created equal: Euclid’s Postulates 1-4

jeudi 10 décembre 2020 • Durée 41:00

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 … Continue reading Created equal: Euclid’s Postulates 1-4

That which has no part: Euclid’s definitions

mardi 3 novembre 2020 • Durée 43:33

Euclid’s definitions of point, line, and straightness allow a range of mathematical and philosophical interpretation. Historically, however, these definitions may not have been in the original text of the Elements at all. Regardless, the subtlety of defining fundamental concepts such as straightness is best seen by considering the geometry not only of a flat plane … Continue reading That which has no part: Euclid’s definitions

What makes a good axiom?

dimanche 4 octobre 2020 • Durée 35:21

How should axioms be justified? By appeal to intuition, or sensory perception? Or are axioms legitimated merely indirectly, by their logical consequences? Plato and Aristotle disagreed, and later Newton disagreed even more. Their philosophies can be seen as rival interpretations of Euclid’s Elements. Transcript What kinds of axioms do we want in our geometry? How … Continue reading What makes a good axiom?

Consequentia mirabilis: the dream of reduction to logic

mardi 8 septembre 2020 • Durée 35:50

Euclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the Pythagorean Theorem to the parallelogram area theorem, and that in turn to triangle congruence. How far can this reductive process be taken, and what should be its ultimate goals? Some have advocated that the axiomatic-deductive program in mathematics is best seen in … Continue reading Consequentia mirabilis: the dream of reduction to logic

Read Euclid backwards: history and purpose of Pythagorean Theorem

jeudi 30 juillet 2020 • Durée 41:37

The Pythagorean Theorem might have been used in antiquity to build the pyramids, dig tunnels through mountains, and predict eclipse durations, it has been said. But maybe the main interest in the theorem was always more theoretical. Euclid’s proof of the Pythagorean Theorem is perhaps best thought of not as establishing the truth of the … Continue reading Read Euclid backwards: history and purpose of Pythagorean Theorem

Singing Euclid: the oral character of Greek geometry

dimanche 21 juin 2020 • Durée 40:10

Greek geometry is written in a style adapted to oral teaching. Mathematicians memorised theorems the way bards memorised poems. Several oddities about how Euclid’s Elements is written can be explained this way. Transcript Greek geometry is oral geometry. Mathematicians memorised theorems the way bards memorised poems. Euclid’s Elements was almost like a song book or … Continue reading Singing Euclid: the oral character of Greek geometry

First proofs: Thales and the beginnings of geometry

vendredi 15 mai 2020 • Durée 42:27

Proof-oriented geometry began with Thales. The theorems attributed to him encapsulate two modes of doing mathematics, suggesting that the idea of proof could have come from either of two sources: attention to patterns and relations that emerge from explorative construction and play, or the realisation that “obvious” things can be demonstrated using formal definitions and … Continue reading First proofs: Thales and the beginnings of geometry

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