Opinionated History of Mathematics

Intellectual Mathematics

History of mathematics research with iconoclastic madcap twists

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40 episodes
Updated Jul 15, 2025

Episodes40

Newest first

Mar 29, 2020 · 36 min
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...
Feb 16, 2020 · 40 min
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...
Jan 11, 2020 · 36 min
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.
Dec 3, 2019 · 35 min
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...
Oct 28, 2019 · 53 min
More things Galileo didn’t do first
What was Galileo’s great innovation in science? To give practical experience more authority than philosophical systems? To insist on mechanical as opposed to teleological or supernatural explanations of natural phenomena?
Sep 21, 2019 · 44 min
Galileo was the first to … what exactly?
Was Galileo “the father of modern science” because he was the first to unite mathematics and physics? Or the first to base science on data and experiments? No. Galileo was not the first to do any of these things,
Aug 15, 2019 · 40 min
Galileo and the Church
Galileo’s sentencing by the Inquisition was avoidable. The Church had no interest in prosecuting mathematical astronomers, but since Galileo had so little to contribute in that domain he foolishly got himself involved with Biblical interpretation.
Jul 7, 2019 · 36 min
Galileo’s theory of comets is hot air
Galileo thought comets were an atmospheric phenomenon, not physical bodies in outer space. How could he be so wrong when all his colleagues got it right? Perhaps because his theory was a convenient excuse for not doing any mathematical astronomy of com...
Jun 2, 2019 · 31 min
Phases of Venus
Telescopic observations of Venus provided evidence for the Copernican view of the solar system. But was Galileo the first to see this, as he claims? Or did he steal the idea from a colleague and lie about having made the observations months before?
May 4, 2019 · 32 min
Blemished sun
Galileo thought sunspots were one of the three best arguments for heliocentrism. He was wrong. Transcript The early days of telescopic astronomy were exhilarating. Listen to this anecdote by Kepler. He is writing in 1610,
Apr 6, 2019 · 31 min
The telescope
The telescope offered a shortcut to stardom for Galileo. We offer some fun cynical twists on the standard story. Transcript The year is 1609. What a time to be alive. In London you can go to the theatre and catch the fresh new play Macbeth.
Mar 9, 2019 · 31 min
Heliocentrism before the telescope
Galileo is credited with defeating Ptolemaic earth-centered astronomy, but most mathematical astronomers had already abandoned this theory long before Galileo. Transcript Does the earth move around the sun, or is it the other way around?
Feb 11, 2019 · 31 min
Heliocentrism in antiquity
Two thousand years before Galileo, Greek astronomers argued that the heavenly bodies revolve around the sun. Their reasoning involved sophisticated mathematics and sound physical considerations. Transcript Is the earth the center of the universe?
Jan 18, 2019 · 22 min
Galileo’s theory of tides
Galileo dismissed the notion that the moon influences the tides as “childish” and “occult.” Instead he argued that tides are a kind of sloshing due to the motion of the earth. This very poor theory is inconsistent with several of his own scientific pri...
Dec 27, 2018 · 28 min
Why Galileo is like Nostradamus
Galileo committed scores of errors in his physics. These are bad in themselves and also undermine Galileo’s claim to credit for the things he did get right. Transcript Nostradamus published a famous book of prophesies in 1555.
Dec 10, 2018 · 26 min
Galileo’s errors on projectile motion and inertia
Galileo gets credit he does not deserve for the parabolic nature of projectile motion, the law of inertia, and the “Galilean” principle of relativity. In reality, his treatments of all of these matters were riddled with errors and fundamental misunders...
Nov 29, 2018 · 21 min
The case against Galileo on the law of fall
Galileo is praised for his work on falling bodies, but his arguments were dishonest and his trifling discoveries were not new. Transcript In 1971, Apollo 15 astronauts conducted a famous experiment on the moon.
Nov 21, 2018 · 23 min
Galilean science in antiquity?
Ancient Greek scientists studied the dynamics of falling bodies. Were “Galileo’s” discoveries anticipated in these treatises that have since been lost? This question leads to a bigger one regarding relativism versus universalism in the history of thoug...
Nov 21, 2018 · 19 min
Mathematics versus philosophy, then and now
Divergent interpretations of Galileo’s alleged greatness cut across disciplinary divides: mathematics versus philosophy, science versus humanities. Understanding Galileo means dealing with these fundamental tensions. Transcript Those who can’t do,
Nov 21, 2018 · 16 min
Galileo bad, Archimedes good
Galileo's bumbling attempts at determining the area of the cycloid suggests a radical new interpretation of his scientific opus. Archimedes's work on floating bodies is an example of excellent Greek science that has not been sufficiently appreciated.

Opinionated History of Mathematics

Societal role of geometry in early civilisations

Why the Greeks?

The mathematicians’ view of Galileo

Historiography of Galileo’s relation to antiquity and middle ages

More things Galileo didn’t do first

Galileo was the first to … what exactly?

Galileo and the Church

Galileo’s theory of comets is hot air

Phases of Venus

Blemished sun

The telescope

Heliocentrism before the telescope

Heliocentrism in antiquity

Galileo’s theory of tides

Why Galileo is like Nostradamus

Galileo’s errors on projectile motion and inertia

The case against Galileo on the law of fall

Galilean science in antiquity?

Mathematics versus philosophy, then and now

Galileo bad, Archimedes good