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History of mathematics research with iconoclastic madcap twists
Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene. Transcript Archimedes di...
There is nothing counterintuitive about an infinite shape with finite volume, contrary to the common propaganda version of the calculus trop...
Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha Scho...
Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure t...
Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both mathematical and historical. Netz is dismissive of...
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...
The discovery of non-Euclidean geometry in the 19th century radically undermined traditional conceptions of the relation between mathematics...
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 obs...
Euclid inspired Gothic architecture and taught Renaissance painters how to create depth and perspective. More generally, the success of math...
Philosophical movements in the 17th century tried to mimic the geometrical method of the ancients. Some saw Euclid—with his ruler and compas...
The use of diagrams in geometry raise questions about the place of the physical, the sensory, the human in mathematical reasoning. Multiple...
Euclid spends a lot of time in the Elements constructing figures with his ubiquitous ruler and compass. Why did he think this was important?...
The etymology of the term “postulate” suggests that Euclid’s axioms were once questioned. Indeed, the drawing of lines and circles can be re...
Euclid’s definitions of point, line, and straightness allow a range of mathematical and philosophical interpretation. Historically, however,...
How should axioms be justified? By appeal to intuition, or sensory perception? Or are axioms legitimated merely indirectly, by their logical...
Euclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the Pythagorean Theorem to the parallelogram area theorem...
The Pythagorean Theorem might have been used in antiquity to build the pyramids, dig tunnels through mountains, and predict eclipse duration...
Greek geometry is written in a style adapted to oral teaching. Mathematicians memorised theorems the way bards memorised poems. Several oddi...
Proof-oriented geometry began with Thales. The theorems attributed to him encapsulate two modes of doing mathematics, suggesting that the id...
In ancient Mesopotamia and Egypt, mathematics meant law and order. Specialised mathematical technocrats were deployed to settle conflicts re...
The Greek islands were geographically predisposed to democracy. The ritualised, antagonistic debates of parliaments and law courts were then...
What did 17th-century mathematicians such as Newton and Huygens think of Galileo? Not very highly, it turns out. I summarise my case against...
Our picture of Greek antiquity is distorted. Only a fraction of the masterpieces of antiquity have survived. Decisions on what to preserve w...
What was Galileo’s great innovation in science? To give practical experience more authority than philosophical systems? To insist on mechani...
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 a...
Galileo’s sentencing by the Inquisition was avoidable. The Church had no interest in prosecuting mathematical astronomers, but since Galileo...
Galileo thought comets were an atmospheric phenomenon, not physical bodies in outer space. How could he be so wrong when all his colleagues...
Telescopic observations of Venus provided evidence for the Copernican view of the solar system. But was Galileo the first to see this, as he...
Galileo thought sunspots were one of the three best arguments for heliocentrism. He was wrong. Transcript The early days of telescopic astro...
The telescope offered a shortcut to stardom for Galileo. We offer some fun cynical twists on the standard story. Transcript The year is 1609...
Galileo is credited with defeating Ptolemaic earth-centered astronomy, but most mathematical astronomers had already abandoned this theory l...
Two thousand years before Galileo, Greek astronomers argued that the heavenly bodies revolve around the sun. Their reasoning involved sophis...
Galileo dismissed the notion that the moon influences the tides as “childish” and “occult.” Instead he argued that tides are a kind of slosh...
Galileo committed scores of errors in his physics. These are bad in themselves and also undermine Galileo’s claim to credit for the things h...
Galileo gets credit he does not deserve for the parabolic nature of projectile motion, the law of inertia, and the “Galilean” principle of r...
Galileo is praised for his work on falling bodies, but his arguments were dishonest and his trifling discoveries were not new. Transcript In...
Ancient Greek scientists studied the dynamics of falling bodies. Were “Galileo’s” discoveries anticipated in these treatises that have since...
Divergent interpretations of Galileo’s alleged greatness cut across disciplinary divides: mathematics versus philosophy, science versus huma...
Galileo's bumbling attempts at determining the area of the cycloid suggests a radical new interpretation of his scientific opus. Archimedes'...