Death of Archimedes
Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene. Transcript Archimedes died mouthin...
Torricelli’s trumpet is not counterintuitive
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?
Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha School, includ...
Operational Einstein: constructivist principles of special relativity
Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure them. This ...
Review of Netz’s New History of Greek Mathematics
Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both mathematical and historical. Netz is dismissive of traditiona...
The “universal grammar” of space: what geometry is innate?
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
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
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
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
Euclid inspired Gothic architecture and taught Renaissance painters how to create depth and perspective. More generally, the success of mathematics we...