Opinionated History of Mathematics

Death of Archimedes

Torricelli’s trumpet is not counterintuitive

Did Copernicus steal ideas from Islamic astronomers?

Operational Einstein: constructivist principles of special relativity

Review of Netz’s New History of Greek Mathematics

The “universal grammar” of space: what geometry is innate?

“Repugnant to the nature of a straight line”: Non-Euclidean geometry

Rationalism 2.0: Kant’s philosophy of geometry

Rationalism versus empiricism

Cultural reception of geometry in early modern Europe

Maker’s knowledge: early modern philosophical interpretations of geometry

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

Why construct?

Created equal: Euclid’s Postulates 1-4

That which has no part: Euclid’s definitions

What makes a good axiom?

Consequentia mirabilis: the dream of reduction to logic

Read Euclid backwards: history and purpose of Pythagorean Theorem

Singing Euclid: the oral character of Greek geometry

First proofs: Thales and the beginnings of geometry

Societal role of geometry in early civilisations

Why the Greeks?

The mathematicians’ view of Galileo

Historiography of Galileo’s relation to antiquity and middle ages

More things Galileo didn’t do first

Galileo was the first to … what exactly?

Galileo and the Church

Galileo’s theory of comets is hot air

Phases of Venus

Blemished sun

The telescope

Heliocentrism before the telescope

Heliocentrism in antiquity

Galileo’s theory of tides

Why Galileo is like Nostradamus

Galileo’s errors on projectile motion and inertia

The case against Galileo on the law of fall

Galilean science in antiquity?

Mathematics versus philosophy, then and now

Galileo bad, Archimedes good