Opinionated History of Mathematics
Episodes
Death of Archimedes
15 Jul 2025
Contributed by Lukas
Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene. Transcript Archimedes died mouth...
Torricelli’s trumpet is not counterintuitive
30 Dec 2024
Contributed by Lukas
There is nothing counterintuitive about an infinite shape with finite volume, contrary to the common propaganda version of the calculus trope known as...
Did Copernicus steal ideas from Islamic astronomers?
29 Nov 2023
Contributed by Lukas
Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha School, incl...
Operational Einstein: constructivist principles of special relativity
23 Jul 2023
Contributed by Lukas
Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure them. Thi...
Review of Netz’s New History of Greek Mathematics
11 Oct 2022
Contributed by Lukas
Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both mathematical and historical. Netz is dismissive of traditio...
The “universal grammar” of space: what geometry is innate?
20 May 2022
Contributed by Lukas
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, a...
“Repugnant to the nature of a straight line”: Non-Euclidean geometry
20 Feb 2022
Contributed by Lukas
The discovery of non-Euclidean geometry in the 19th century radically undermined traditional conceptions of the relation between mathematics and the w...
Rationalism 2.0: Kant’s philosophy of geometry
17 Nov 2021
Contributed by Lukas
Kant developed a philosophy of geometry that explained how geometry can be both knowable in pure thought and applicable to physical reality. Namely, b...
Rationalism versus empiricism
18 Sep 2021
Contributed by Lukas
Rationalism says mathematical knowledge comes from within, from pure thought; empiricism that it comes from without, from experience and observation. ...
Cultural reception of geometry in early modern Europe
10 Jul 2021
Contributed by Lukas
Euclid inspired Gothic architecture and taught Renaissance painters how to create depth and perspective. More generally, the success of mathematics we...
Maker’s knowledge: early modern philosophical interpretations of geometry
10 May 2021
Contributed by Lukas
Philosophical movements in the 17th century tried to mimic the geometrical method of the ancients. Some saw Euclid—with his ruler and compass in han...
“Let it have been drawn”: the role of diagrams in geometry
10 Mar 2021
Contributed by Lukas
The use of diagrams in geometry raise questions about the place of the physical, the sensory, the human in mathematical reasoning. Multiple sources of...
Why construct?
20 Jan 2021
Contributed by Lukas
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 h...
Created equal: Euclid’s Postulates 1-4
10 Dec 2020
Contributed by Lukas
The etymology of the term “postulate” suggests that Euclid’s axioms were once questioned. Indeed, the drawing of lines and circles can be regard...
That which has no part: Euclid’s definitions
03 Nov 2020
Contributed by Lukas
Euclid’s definitions of point, line, and straightness allow a range of mathematical and philosophical interpretation. Historically, however, these d...
What makes a good axiom?
04 Oct 2020
Contributed by Lukas
How should axioms be justified? By appeal to intuition, or sensory perception? Or are axioms legitimated merely indirectly, by their logical consequen...
Consequentia mirabilis: the dream of reduction to logic
08 Sep 2020
Contributed by Lukas
Euclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the Pythagorean Theorem to the parallelogram area theorem, and th...
Read Euclid backwards: history and purpose of Pythagorean Theorem
30 Jul 2020
Contributed by Lukas
The Pythagorean Theorem might have been used in antiquity to build the pyramids, dig tunnels through mountains, and predict eclipse durations, it has ...
Singing Euclid: the oral character of Greek geometry
21 Jun 2020
Contributed by Lukas
Greek geometry is written in a style adapted to oral teaching. Mathematicians memorised theorems the way bards memorised poems. Several oddities about...
First proofs: Thales and the beginnings of geometry
15 May 2020
Contributed by Lukas
Proof-oriented geometry began with Thales. The theorems attributed to him encapsulate two modes of doing mathematics, suggesting that the idea of proo...
Societal role of geometry in early civilisations
29 Mar 2020
Contributed by Lukas
In ancient Mesopotamia and Egypt, mathematics meant law and order. Specialised mathematical technocrats were deployed to settle conflicts regarding ta...
Why the Greeks?
16 Feb 2020
Contributed by Lukas
The Greek islands were geographically predisposed to democracy. The ritualised, antagonistic debates of parliaments and law courts were then generalis...
The mathematicians’ view of Galileo
11 Jan 2020
Contributed by Lukas
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 u...
Historiography of Galileo’s relation to antiquity and middle ages
03 Dec 2019
Contributed by Lukas
Our picture of Greek antiquity is distorted. Only a fraction of the masterpieces of antiquity have survived. Decisions on what to preserve were made b...
More things Galileo didn’t do first
28 Oct 2019
Contributed by Lukas
What was Galileo’s great innovation in science? To give practical experience more authority than philosophical systems? To insist on mechanical as o...
Galileo was the first to … what exactly?
21 Sep 2019
Contributed by Lukas
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 exp...
Galileo and the Church
15 Aug 2019
Contributed by Lukas
Galileo’s sentencing by the Inquisition was avoidable. The Church had no interest in prosecuting mathematical astronomers, but since Galileo had so ...
Galileo’s theory of comets is hot air
07 Jul 2019
Contributed by Lukas
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 rig...
Phases of Venus
02 Jun 2019
Contributed by Lukas
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? O...
Blemished sun
04 May 2019
Contributed by Lukas
Galileo thought sunspots were one of the three best arguments for heliocentrism. He was wrong. Transcript The early days of telescopic astronomy were ...
The telescope
06 Apr 2019
Contributed by Lukas
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 t...
Heliocentrism before the telescope
09 Mar 2019
Contributed by Lukas
Galileo is credited with defeating Ptolemaic earth-centered astronomy, but most mathematical astronomers had already abandoned this theory long before...
Heliocentrism in antiquity
11 Feb 2019
Contributed by Lukas
Two thousand years before Galileo, Greek astronomers argued that the heavenly bodies revolve around the sun. Their reasoning involved sophisticated ma...
Galileo’s theory of tides
18 Jan 2019
Contributed by Lukas
Galileo dismissed the notion that the moon influences the tides as “childish” and “occult.” Instead he argued that tides are a kind of sloshin...
Why Galileo is like Nostradamus
27 Dec 2018
Contributed by Lukas
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 ge...
Galileo’s errors on projectile motion and inertia
10 Dec 2018
Contributed by Lukas
Galileo gets credit he does not deserve for the parabolic nature of projectile motion, the law of inertia, and the “Galilean” principle of relativ...
The case against Galileo on the law of fall
29 Nov 2018
Contributed by Lukas
Galileo is praised for his work on falling bodies, but his arguments were dishonest and his trifling discoveries were not new. Transcript In 1971, Apo...
Galilean science in antiquity?
21 Nov 2018
Contributed by Lukas
Ancient Greek scientists studied the dynamics of falling bodies. Were “Galileo’s” discoveries anticipated in these treatises that have since bee...
Mathematics versus philosophy, then and now
21 Nov 2018
Contributed by Lukas
Divergent interpretations of Galileo’s alleged greatness cut across disciplinary divides: mathematics versus philosophy, science versus humanities. ...
Galileo bad, Archimedes good
21 Nov 2018
Contributed by Lukas
Galileo's bumbling attempts at determining the area of the cycloid suggests a radical new interpretation of his scientific opus. Archimedes's work on ...