## Opinionated History of Mathematics

### Latest Episodes

##### Rationalism versus empiricism

*September 18, 2021*

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 i

##### Cultural reception of geometry in early modern Europe

*July 10, 2021*

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 dog

##### Maker’s knowledge: early modern philosophical interpretations of geometry

*May 10, 2021*

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.

##### “Let it have been drawn”: the role of diagrams in geometry

*March 10, 2021*

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 constructi...

##### Why construct?

*January 20, 2021*

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,

##### Created equal: Euclid’s Postulates 1-4

*December 10, 2020*

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.

##### That which has no part: Euclid’s definitions

*November 03, 2020*

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,

##### What makes a good axiom?

*October 04, 2020*

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.

##### Consequentia mirabilis: the dream of reduction to logic

*September 08, 2020*

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,

##### Read Euclid backwards: history and purpose of Pythagorean Theorem

*July 30, 2020*

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.