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 36 Folge(n) erschienen. Dieser Podcast erscheint alle 1 Monate.

Gesamtlänge aller Episoden: 22 hours 1 minute

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That which has no part: Euclid’s definitions


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,


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 2020-11-03  43m
 
 

What makes a good axiom?


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.


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 2020-10-05  35m
 
 

Consequentia mirabilis: the dream of reduction to logic


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,


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 2020-09-08  35m
 
 

Read Euclid backwards: history and purpose of Pythagorean Theorem


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.


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 2020-07-31  41m
 
 

Singing Euclid: the oral character of Greek geometry


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.


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 2020-06-21  40m
 
 

First proofs: Thales and the beginnings of geometry


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 exp...


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 2020-05-16  42m
 
 

Societal role of geometry in early civilisations


In ancient Mesopotamia and Egypt, mathematics meant law and order. Specialised mathematical technocrats were deployed to settle conflicts regarding taxes, trade contracts, and inheritance. Mathematics enabled states to develop civil branches of governm...


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 2020-03-29  36m
 
 

Why the Greeks?


The Greek islands were geographically predisposed to democracy. The ritualised, antagonistic debates of parliaments and law courts were then generalised to all philosophical domains, creating a unique intellectual climate that put a premium on adversar...


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 2020-02-16  40m
 
 

The mathematicians’ view of Galileo


What did 17th-century mathematicians such as Newton and Huygens think of Galileo? Not very highly, it turns out. I summarise my case against Galileo using their perspectives and a mathematical lens more generally.


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 2020-01-11  36m
 
 

Historiography of Galileo’s relation to antiquity and middle ages


Our picture of Greek antiquity is distorted. Only a fraction of the masterpieces of antiquity have survived. Decisions on what to preserve were made by in ages of vastly inferior intellectual levels. Aristotelian philosophy is more accessible for medio...


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 2019-12-03  35m