Intellectual Mathematics

Reviel Netz, in his new book Why the Ancient Greeks Matter, Cambridge University Press, 2025, goes out of his way to frame half the book as a refutation of alleged “errors” in Kuhn and Koyré: “Koyré and Kuhn are wrong” (70) “Koyré and Kuhn were wrong” (76)

Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene.

The following bibliography was prepared by Jan Hogendijk.

There is nothing counterintuitive about an infinite shape with finite volume, contrary to the common propaganda version of the calculus trope known as Torricelli’s trumpet.

Michael N.

Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha School, including the Tusi couple and Ibn al-Shatir’s models for the Moon and Mercury.

Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure them.

Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both mathematical and historical.

A strangely petty review by Victor Pambuccian of my article on Greek operationalism has appeared in zbMATH.

In 2014 and 2018 I challenged the common view that Copernicus stole ideas from Maragha astronomers.

Geometry might be innate in the same way as language.

The discovery of non-Euclidean geometry in the 19th century radically undermined traditional conceptions of the relation between mathematics and the world.

Kant developed a philosophy of geometry that explained how geometry can be both knowable in pure thought and applicable to physical reality.

Rationalism says mathematical knowledge comes from within, from pure thought; empiricism that it comes from without, from experience and observation.

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

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

The use of diagrams in geometry raise questions about the place of the physical, the sensory, the human in mathematical reasoning.

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

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

Euclid’s definitions of point, line, and straightness allow a range of mathematical and philosophical interpretation.

How should axioms be justified?

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.

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.

Greek geometry is written in a style adapted to oral teaching.

Proof-oriented geometry began with Thales.

How did Leibniz view the foundations of infinitesimals?

In ancient Mesopotamia and Egypt, mathematics meant law and order.

The Greek islands were geographically predisposed to democracy.

Galileo is the most overrated figure in the history of science.

What did 17th-century mathematicians such as Newton and Huygens think of Galileo?

Our picture of Greek antiquity is distorted.

What was Galileo’s great innovation in science?

Was Galileo “the father of modern science” because he was the first to unite mathematics and physics?

Galileo’s sentencing by the Inquisition was avoidable.

Galileo thought comets were an atmospheric phenomenon, not physical bodies in outer space.

Telescopic observations of Venus provided evidence for the Copernican view of the solar system.

Galileo thought sunspots were one of the three best arguments for heliocentrism.

The telescope offered a shortcut to stardom for Galileo.

Galileo is credited with defeating Ptolemaic earth-centered astronomy, but most mathematical astronomers had already abandoned this theory long before Galileo.

Two thousand years before Galileo, Greek astronomers argued that the heavenly bodies revolve around the sun.