Opinionated History of Mathematics

Archimedes’s emblematic death makes sense psychologically and embodies a rich historical p... more

There is nothing counterintuitive about an infinite shape with finite volume, contrary to ... more

Copernicus’s planetary models contain elements also found in the works of late medieval Is... more

Einstein’s theory of special relativity defines time and space operationally, that is to s... more

Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both m... more

Geometry might be innate in the same way as language. There are many languages, each of wh... more

The discovery of non-Euclidean geometry in the 19th century radically undermined tradition... more

Kant developed a philosophy of geometry that explained how geometry can be both knowable i... more

Rationalism says mathematical knowledge comes from within, from pure thought; empiricism t... more

Euclid inspired Gothic architecture and taught Renaissance painters how to create depth an... more

Philosophical movements in the 17th century tried to mimic the geometrical method of the a... more

The use of diagrams in geometry raise questions about the place of the physical, the senso... more

Euclid spends a lot of time in the Elements constructing figures with his ubiquitous ruler... more

The etymology of the term “postulate” suggests that Euclid’s axioms were once questioned. ... more

Euclid’s definitions of point, line, and straightness allow a range of mathematical and ph... more

How should axioms be justified? By appeal to intuition, or sensory perception? Or are axio... more

Euclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the Pyt... more

The Pythagorean Theorem might have been used in antiquity to build the pyramids, dig tunne... more

Greek geometry is written in a style adapted to oral teaching. Mathematicians memorised th... more

Proof-oriented geometry began with Thales. The theorems attributed to him encapsulate two ... more