Opinionated History of Mathematics

In ancient Mesopotamia and Egypt, mathematics meant law and order. Specialised mathematical technocrats were deployed to settle conflicts regarding taxes, trade contracts, and inheritance. Mathematics enabled states to develop civil branches of government instead of relying on force and violence. Mathematics enabled complex economies in which people could count on technically competent administration and an … Continue reading Societal role of geometry in early civilisations

The Greek islands were geographically predisposed to democracy. The ritualised, antagonistic debates of parliaments and law courts were then generalised to all philosophical domains, creating a unique intellectual climate that put a premium on adversarialism and pure reason. This style of thought proved ideal for mathematics. Transcript Why the Greeks, of all people? Why did … Continue reading Why the Greeks?

What did 17th-century mathematicians such as Newton and Huygens think of Galileo? Not very highly, it turns out. I summarise my case against Galileo using their perspectives and a mathematical lens more generally. Transcript I’m going to conclude my case against Galileo with this final episode on this subject. Here’s a little anecdote I found … Continue reading The mathematicians’ view of Galileo

Our picture of Greek antiquity is distorted. Only a fraction of the masterpieces of antiquity have survived. Decisions on what to preserve were made by in ages of vastly inferior intellectual levels. Aristotelian philosophy is more accessible for mediocre minds than advanced mathematics and science. Hence this simpler part of Greek intellectual achievement was eagerly … Continue reading Historiography of Galileo’s relation to antiquity and middle ages

What was Galileo’s great innovation in science? To give practical experience more authority than philosophical systems? To insist on mechanical as opposed to teleological or supernatural explanations of natural phenomena? To take mathematical physics as our best window into the fundamental nature of reality as opposed to just a computational tool for a small set … Continue reading More things Galileo didn’t do first

Was Galileo “the father of modern science” because he was the first to unite mathematics and physics? Or the first to base science on data and experiments? No. Galileo was not the first to do any of these things, despite often being erroneously credited with these innovations. Transcript Galileo is “the father of modern science,” … Continue reading Galileo was the first to … what exactly?

Galileo’s sentencing by the Inquisition was avoidable. The Church had no interest in prosecuting mathematical astronomers, but since Galileo had so little to contribute in that domain he foolishly got himself involved with Biblical interpretation. His scriptural interpretations not only got him into hot water: they are also scientifically unsound and blatantly inconsistent with his … Continue reading Galileo and the Church

Galileo thought comets were an atmospheric phenomenon, not physical bodies in outer space. How could he be so wrong when all his colleagues got it right? Perhaps because his theory was a convenient excuse for not doing any mathematical astronomy of comets. We also discuss his unsavoury ways of dealing with data in the case … Continue reading Galileo’s theory of comets is hot air

Telescopic observations of Venus provided evidence for the Copernican view of the solar system. But was Galileo the first to see this, as he claims? Or did he steal the idea from a colleague and lie about having made the observations months before? Transcript Galileo and the phases of Venus: it’s a plot that mirrors … Continue reading Phases of Venus

Galileo thought sunspots were one of the three best arguments for heliocentrism. He was wrong. Transcript The early days of telescopic astronomy were exhilarating. Listen to this anecdote by Kepler. He is writing in 1610, right after the appearance of Galileo’s first telescope reports. Here’s what Kepler says: “My friend the Baron Wakher von Wachenfels … Continue reading Blemished sun