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

History of mathematics research with iconoclastic madcap twists

Opinionated History of Mathematics

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’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 … <a href="https://intellectualmathematics.com/blog/galileo-and-the-church/" rel="nofollow" target="_blank">Continue reading Galileo and the Church</a>

Galileo and the Church

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

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 … <a href="https://intellectualmathematics.com/blog/societal-role-of-geometry-in-early-civilisations/" rel="nofollow" target="_blank">Continue reading Societal role of geometry in early civilisations</a>

Societal role of geometry in early civilisations

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

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 … <a href="https://intellectualmathematics.com/blog/more-things-galileo-didnt-do-first/" rel="nofollow" target="_blank">Continue reading More things Galileo didn’t do first</a>

More things Galileo didn’t do first

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

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 … <a href="https://intellectualmathematics.com/blog/the-mathematicians-view-of-galileo/" rel="nofollow" target="_blank">Continue reading The mathematicians’ view of Galileo</a>

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

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 … <a href="https://intellectualmathematics.com/blog/historiography-of-galileos-relation-to-antiquity-and-middle-ages/" rel="nofollow" target="_blank">Continue reading Historiography of Galileo’s relation to antiquity and middle ages</a>

Historiography of Galileo’s relation to antiquity and middle ages

Galileo is praised for his work on falling bodies, but his arguments were dishonest and his trifling discoveries were not new. Transcript In 1971, Apollo 15 astronauts conducted a famous experiment on the moon. Here’s a bit of the original recording: “In my left hand I have a feather. In my right hand a hammer. … Continue reading The case against Galileo on the law of fall

Galileo is praised for his work on falling bodies, but his arguments were dishonest and his trifling discoveries were not new. Transcript In 1971, Apollo 15 astronauts conducted a famous experiment on the moon. Here’s a bit of the original recording: “In my left hand I have a feather. In my right hand a hammer. … <a href="https://intellectualmathematics.com/blog/the-case-against-galileo-on-the-law-of-fall/" rel="nofollow" target="_blank">Continue reading The case against Galileo on the law of fall</a>

The case against Galileo on the law of fall

Galileo gets credit he does not deserve for the parabolic nature of projectile motion, the law of inertia, and the “Galilean” principle of relativity. In reality, his treatments of all of these matters were riddled with errors and fundamental misunderstandings. Transcript Pick up a rock and throw it in front of you. It makes a … Continue reading Galileo’s errors on projectile motion and inertia

Galileo gets credit he does not deserve for the parabolic nature of projectile motion, the law of inertia, and the “Galilean” principle of relativity. In reality, his treatments of all of these matters were riddled with errors and fundamental misunderstandings. Transcript Pick up a rock and throw it in front of you. It makes a … <a href="https://intellectualmathematics.com/blog/galileos-errors-on-projectile-motion-and-inertia/" rel="nofollow" target="_blank">Continue reading Galileo’s errors on projectile motion and inertia</a>

Galileo’s errors on projectile motion and inertia

Ancient Greek scientists studied the dynamics of falling bodies. Were “Galileo’s” discoveries anticipated in these treatises that have since been lost? This question leads to a bigger one regarding relativism versus universalism in the history of thought. Transcript Quiz! Who said the following: “The study of mechanics is eagerly pursued by all those interested in … Continue reading Galilean science in antiquity?

Ancient Greek scientists studied the dynamics of falling bodies. Were “Galileo’s” discoveries anticipated in these treatises that have since been lost? This question leads to a bigger one regarding relativism versus universalism in the history of thought. Transcript Quiz! Who said the following: “The study of mechanics is eagerly pursued by all those interested in … <a href="https://intellectualmathematics.com/blog/galilean-science-in-antiquity/" rel="nofollow" target="_blank">Continue reading Galilean science in antiquity?</a>

Galilean science in antiquity?

Galileo committed scores of errors in his physics. These are bad in themselves and also undermine Galileo’s claim to credit for the things he did get right. Transcript Nostradamus published a famous book of prophesies in 1555. Some people like to praise him for having predicted the future. Allegedly he foresaw all kinds of things … Continue reading Why Galileo is like Nostradamus

Galileo committed scores of errors in his physics. These are bad in themselves and also undermine Galileo’s claim to credit for the things he did get right. Transcript Nostradamus published a famous book of prophesies in 1555. Some people like to praise him for having predicted the future. Allegedly he foresaw all kinds of things … <a href="https://intellectualmathematics.com/blog/why-galileo-is-like-nostradamus/" rel="nofollow" target="_blank">Continue reading Why Galileo is like Nostradamus</a>

Why Galileo is like Nostradamus

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

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 … <a href="https://intellectualmathematics.com/blog/galileos-theory-of-comets-is-hot-air/" rel="nofollow" target="_blank">Continue reading Galileo’s theory of comets is hot air</a>

Galileo’s theory of comets is hot air

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