Imagine writing a book so influential it becomes the undisputed authority on the nature of the universe for the next 14 centuries. Now, imagine its core premise is completely wrong. That's the legacy of Claudius Ptolemy. In this episode, we're exploring the ancient world's ultimate spreadsheet guy. Ptolemy didn't just guess that the Earth was the centre of the cosmos; he built a stunningly complex and predictive mathematical model to prove it; a system of circles-on-circles that could accurately chart the strange, looping paths of the planets. We'll follow his influence from the library of Alexandria to the courts of Islamic scholars and the universities of Renaissance Europe. We'll look at his world maps that inspired Columbus (for better or worse) and his theorems that enabled modern trigonometry. This is the story about the power of a useful idea and why, in the history of maths, being right isn't always the most important thing.

Join Benjamin Cornish as he uncovers the story of Theon of Smyrna (c. 70 CE), the ancient world's ultimate study-guide writer! He wasn't a revolutionary, but Theon's "Mathematical Matters Useful for Reading Plato" was a game-changer for anyone trying to decipher the mathematical underpinnings of Plato's philosophy. In this episode, we explore: Theon's life and philosophical context as a Middle Platonist. His monumental work: a comprehensive guide to Pythagorean and Platonic arithmetic, music theory, and a glimpse into ancient astronomy. The fascinating world of ancient "number personalities," where numbers were categorized as noble, deficient, or abundant The monochord : how Theon used a simple instrument to demonstrate the mathematical structure of music and the cosmos. Why Theon's seemingly unoriginal work was crucial for preserving Greco-Roman mathematical thought through the Islamic Golden Age and beyond. Discover the often-overlooked importance of the "Great Explainers" – the compilers and clarifiers who ensure that genius remains accessible. Theon didn't just push knowledge forward; he carried it, providing the essential "cheat sheet" for understanding the universe through numbers and the role of maths.     Keywords: Theon of Smyrna, Plato, ancient maths, history of maths, Pythagoras, Nicomachus, Middle Platonism, Greek philosophy, mathematical history, arithmetic, music theory, astronomy, monochord, harmony of the spheres, perfect numbers, figurate numbers, ratios, ancient Greece, Roman Empire, historical figures, mathematical concepts, podcast, education, Benjamin Cornish, The Mathematicians Podcast. Hashtags: #TheonOfSmyrna #HistoryOfMaths #AncientMaths #Plato #Pythagoras #MathematicalHistory #Podcast #MathsEducation #Philosophy #GreekMaths #Arithmetic #MusicTheory #Astronomy #AncientGreece #TheMathematiciansPodcast #STEM   The music was: "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/

In this episode of The Mathematicians Podcast, Benjamin Cornish explores the life and works of Nicomachus of Gerasa—a philosopher, mystic, and mathematician whose obsession with numbers shaped centuries of thought. From perfect and amicable numbers to cosmic harmonies and the mystical side of arithmetic, Nicomachus blended maths with philosophy, music, and spirituality in ways that still resonate today. We’ll look at how his Introduction to Arithmetic became the medieval go-to textbook, how his Pythagorean passions fed into Neopythagorean and Neoplatonist traditions, and why he thought numbers weren’t just useful but divine.  Whether you’re into number theory, history of maths, philosophy, or just like your integers with a side of cosmic karaoke, this episode has something for you. Keywords: Nicomachus of Gerasa, history of mathematics, perfect numbers, amicable numbers, Neopythagoreanism, Neoplatonism, Pythagoras, number theory, arithmetic, medieval philosophy, music theory, quadrivium, maths podcast, philosophy of numbers. Hashtags:#MathematiciansPodcast #HistoryOfMaths #Nicomachus #Pythagoras #NumberTheory #PerfectNumbers #AmicableNumbers #PhilosophyOfMaths #Quadrivium #Neopythagorean #Neoplatonism #MathsAndMusic

In this episode of The Mathematicians Podcast, Benjamin Cornish explores the life and work of Menelaus of Alexandria; the mathematician who transformed how we think about geometry on curved surfaces. From his treatise Sphaerica to the elegant power of Menelaus’s Theorem, discover how this quiet figure of ancient Alexandria helped shape spherical geometry, astronomy, and the trigonometry still used in navigation, GPS, and astronomy today.   The music was: "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/ Keywords :Menelaus of Alexandria, spherical geometry, Menelaus’s Theorem, history of mathematics, spherical trigonometry, ancient astronomy, Greek mathematicians, geometry podcast, mathematics history, Euclid, Hipparchus, Ptolemy, trigonometry in navigation, GPS and geometry. Hashtags:#MathematiciansPodcast #Menelaus #SphericalGeometry #Trigonometry #HistoryOfMathematics #Geometry #AncientMathematics #MathematicalHistory #Euclid #Hipparchus #Ptolemy

In this one-to-one edition of The Mathematicians Podcast, part of our Injectives subseries, host Benjamin Cornish sits down with philosopher, peace theorist, and long-time educator Dr Thomas Daffern to explore the deep and often surprising intersections between mathematics and religion. Together, they trace the parallel histories of mystical belief and mathematical thought, from the temples of ancient Egypt and the philosophies of Greece to the shifting theological landscapes leading up to the Islamic Golden Age. Why were certain numbers considered sacred? Was ancient religion a catalyst for mathematical inquiry; or was it the other way around? And how has religious belief shaped our understanding of the infinite, harmony, and even the very definition of mathematics? This conversation ranges from Thales to Galileo, from pre-Islamic Arabia to modern mathematical axioms, all with a generous sprinkling of curiosity, nuance, and dry wit. Expect reflections on sacred ratios, philosophical migrations, and a surprising number of  school memories. If you've ever wondered whether math and faith are fundamentally at odds—or fundamentally entwined—this episode is for you.   Books that have been mentioned: Alphabet vs the goddess https://www.alphabetvsgoddess.com/index.html Herod the Great https://www.jewishbookcouncil.org/book/herod-the-great-jewish-king-in-a-roman-world Talking Commentary on the Qur'an http://www.educationaid.net/homepage.html?../pages/lectures.html Drunk with Blood https://www.eden.co.uk/christian-books/bible-study/academic-bible-study/drunk-with-blood-gods-killings-in-the-bible/ Being and Knowledge https://www.lulu.com/shop/dr-thomas-clough-daffern/being-and-knowledge-volume-one/paperback/product-1jqk6wvk.html?srsltid=AfmBOop3Vrge4wmi0YwHjhYMC9W2FZYELvLRu21pLBdz1HpOitQAnRU0&page=1&pageSize=4 Encyclopedia of Druid Studies https://www.lulu.com/shop/dr-thomas-clough-daffern/encyclopaedia-of-druid-studies-volume-one/paperback/product-1y5gmeyv.html?srsltid=AfmBOoop6XoUBqvxafFMBOyxW6yqU646gl4yE_BcxU_F7QKTyyZW6sbd&page=1&pageSize=4 Periodic table of world religions https://interfaithpeacetreaty.wordpress.com/periodic-table-of-the-worlds-religious-philosophical-traditions/   Dr Daffern's main web page: http://www.educationaid.net/homepage.html   Keywords: Mathematics and Religion, History of Maths, Ancient Mathematics, Philosophy of Mathematics, Sacred Numbers, Mathematical Harmony, Religious Influence on Science, Islamic Golden Age, Ancient Philosophy, Dr Thomas Daffern, The Mathematicians Podcast, Interdisciplinary Thinking, Mathematics and Metaphysics, Education and Belief Systems, Maths and Faith Hashtags: #MathematicsPodcast #HistoryOfMaths #MathsAndReligion #AncientMaths #PhilosophyOfMaths #SacredNumbers #IslamicGoldenAge #MathsThroughHistory #TheMathematiciansPodcast #DrThomasDaffern #InjectivesSeries #MathsAndPhilosophy #MathsEducation #InterdisciplinaryThinking #SpiritualMaths   The music was:   "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/

In this one-to-one edition of The Mathematicians Podcast, part of our Injectives subseries, host Benjamin Cornish sits down with philosopher, peace theorist, and long-time educator Dr Thomas Daffern to explore the deep and often surprising intersections between mathematics and religion. Together, they trace the parallel histories of mystical belief and mathematical thought, from the temples of ancient Egypt and the philosophies of Greece to the shifting theological landscapes leading up to the Islamic Golden Age. Why were certain numbers considered sacred? Was ancient religion a catalyst for mathematical inquiry; or was it the other way around? And how has religious belief shaped our understanding of the infinite, harmony, and even the very definition of mathematics? This conversation ranges from Thales to Galileo, from pre-Islamic Arabia to modern mathematical axioms, all with a generous sprinkling of curiosity, nuance, and dry wit. Expect reflections on sacred ratios, philosophical migrations, and a surprising number of  school memories. If you've ever wondered whether math and faith are fundamentally at odds—or fundamentally entwined—this episode is for you.   Books that have been mentioned: Alphabet vs the goddess https://www.alphabetvsgoddess.com/index.html Herod the Great https://www.jewishbookcouncil.org/book/herod-the-great-jewish-king-in-a-roman-world Talking Commentary on the Qur'an http://www.educationaid.net/homepage.html?../pages/lectures.html Drunk with Blood https://www.eden.co.uk/christian-books/bible-study/academic-bible-study/drunk-with-blood-gods-killings-in-the-bible/ Being and Knowledge https://www.lulu.com/shop/dr-thomas-clough-daffern/being-and-knowledge-volume-one/paperback/product-1jqk6wvk.html?srsltid=AfmBOop3Vrge4wmi0YwHjhYMC9W2FZYELvLRu21pLBdz1HpOitQAnRU0&page=1&pageSize=4 Encyclopedia of Druid Studies https://www.lulu.com/shop/dr-thomas-clough-daffern/encyclopaedia-of-druid-studies-volume-one/paperback/product-1y5gmeyv.html?srsltid=AfmBOoop6XoUBqvxafFMBOyxW6yqU646gl4yE_BcxU_F7QKTyyZW6sbd&page=1&pageSize=4 Periodic table of world religions https://interfaithpeacetreaty.wordpress.com/periodic-table-of-the-worlds-religious-philosophical-traditions/   Dr Daffern's main web page: http://www.educationaid.net/homepage.html   Keywords: Mathematics and Religion, History of Maths, Ancient Mathematics, Philosophy of Mathematics, Sacred Numbers, Mathematical Harmony, Religious Influence on Science, Islamic Golden Age, Ancient Philosophy, Dr Thomas Daffern, The Mathematicians Podcast, Interdisciplinary Thinking, Mathematics and Metaphysics, Education and Belief Systems, Maths and Faith Hashtags: #MathematicsPodcast #HistoryOfMaths #MathsAndReligion #AncientMaths #PhilosophyOfMaths #SacredNumbers #IslamicGoldenAge #MathsThroughHistory #TheMathematiciansPodcast #DrThomasDaffern #InjectivesSeries #MathsAndPhilosophy #MathsEducation #InterdisciplinaryThinking #SpiritualMaths   The music was:  "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/    

This week, Benjamin Cornish invites you to step into the steam-powered sandals of Hero of Alexandria—the ancient world’s most enthusiastic gadgeteer. Was he a mathematician? An engineer? A magician in a toga? Yes. Yes. And absolutely yes. From vending machines that accepted drachmas to the first recorded steam engine (that did absolutely nothing useful), Hero turned math into motion and geometry into gears. Join us as we unpack Hero’s life in the shadow of Archimedes, his flair for theatrical automation, and his deeply satisfying triangle-area formula that has saved generations of students from drawing impossible altitudes. Along the way, we reflect on mirrors, vending machines, and whether Hero secretly invented the Rube Goldberg machine 1,900 years before Goldberg was born.   Keywords: Hero of Alexandria, ancient mathematics, triangle area formula, aeolipile, Greek engineering, historical inventions, automata, classical geometry, ancient optics, early machines, Metrica, Heron’s formula, steam engine history Hashtags:#MathsPodcast #HistoryOfMaths #HeroOfAlexandria #AncientInventions #SteamPowerBeforeItWasCool #MathematicalHistory #EngineeringOrigins #HeronsFormula #Pneumatics #AlexandriaEra 

In this episode of The Mathematicians Podcast, Benjamin Cornish dives into the life and legacy of Hipparchus, the Greek thinker who gave us trigonometry, mapped the stars, and even invented tools to measure the heavens.  From creating the first star catalog and predicting eclipses to introducing spherical projections and the chord table, Hipparchus wasn’t just stargazing, he was shaping the future of science. We’ll explore his inventions, his obsession with accuracy, and why Greenland is not as big as your world map told you.  Perfect for maths enthusiasts, history lovers, and anyone curious about the origins of the tools we still use today. Keywords: Hipparchus, trigonometry, spherical projection, history of maths, Greek astronomy, star catalog, precession of the equinoxes, ancient inventions, mathematics podcast, navigation, geography, astrolabe, astronomy history. Hashtags:#MathematiciansPodcast #Hipparchus #HistoryOfMaths #Trigonometry #AncientAstronomy #MathsPodcast #AstronomyLovers #STEMHistory

This week on The Mathematicians Podcast, Benjamin Cornish presents a double bill of underappreciated thinkers from the back shelves of Greek geometry: Dionysodorus of Amisus and Hypsicles of Alexandria in an episode that's part mathematical history, part cubic conundrum, part "wait, he also did astronomy?" We begin with Dionysodorus, who solved the doubling of the cube problem the way most of us try to solve awkward social encounters: by introducing a few curves. Using a hyperbola and a parabola, he cracked a cubic equation long before Cardano showed up with his pen and existential dread. Along the way, we explore his contributions to sphere-cutting, tomb-building, and possibly very literal underground thinking. Then it's on to Hypsicles, the man who gave us Book XIV of Euclid’s Elements, redefined the zodiacal calendar, and possibly invented the idea of π/6 symmetry just to impress his astrologer friends. We look at what he added to geometry, why ancient timekeeping is a cosmic mess, and how his legacy has been hiding in plain sight; like a leap day with good PR. Come for the cubes. Stay for the calendar. And don’t forget to intersect your conics responsibly.   #TheMathematiciansPodcast#GreekMathematics#HistoryOfMaths#Dionysodorus#Hypsicles#DoublingTheCube#CubicEquation#AncientGeometry#ConicSections#EuclidsElements#MathsPodcast#MathematicalHistory#AstronomicalMaths#ZodiacMath#GeometricConstruction#AlgebraBeforeAlgebra#ClassicMathematicians#MathsEducation#CurvedThinking

This week on The Mathematicians Podcast, Benjamin Cornish reflects on a tragic bagel incident, files an HR complaint, and somehow ends up discussing the mathematics of toroidal cross-sections. Join us as we explore the life and work of Perseus the quietly brilliant 2nd-century BCE mathematician who gave us spiric sections. We slice through geometry, history, and a bit too much cream cheese, uncovering how one man's fascination with intersecting bagels helped shape the maths behind modern physics, computer graphics, and breakfast regret.   #SpiricSections #MathsHistory #Torus #AncientMath #MathsPodcast #PerseusTheMathematician #TorusTalk #BagelMaths  #MathsIsEverywhere #HistoryOfMaths #NonConicCurves #MathsWithFlair #HellenisticGeometry #MathsPuns

In this episode of The Mathematicians Podcast, Benjamin Cornish turns his attention to Apollonius of Perga—the ancient Greek mathematician whose work on conic sections shaped the way we understand curves, orbits, and even space travel. We explore Apollonius' life, his lesser-known contributions beyond geometry, and the deep mathematical ideas that earned him the nickname "The Great Geometer." From the invention of the terms ellipse, parabola, and hyperbola, to the legendary Apollonius Problem—a deceptively simple tangency puzzle with lasting implications—we trace his influence through history and into the modern age. Perfect for students, teachers, and lovers of mathematical storytelling, this episode offers technical depth, historical intrigue, and a few terrible puns on the side. Keywords: Apollonius of Perga, conic sections, ancient Greek mathematics, ellipse, parabola, hyperbola, Apollonius problem, tangency geometry, history of mathematics, mathematical storytelling Hashtags:#ApolloniusOfPerga#ConicSections#HistoryOfMathematics#GreekMathematics#Ellipse #Parabola #Hyperbola#GeometryPodcast#MathematicsEducation#AncientMathematics#TheMathematiciansPodcast#MathematicalStorytelling

What do ancient logic, Stoic philosophy, and paradoxes have in common? Chrysippus of Soli. In this episode, Ben Cornish explores how Chrysippus revolutionised logic and gave Stoicism its rational backbone. Discover his pioneering work in propositional logic, his take on fate and free will, and why his ideas still matter today. #MathematicalLogic #PropositionalLogic #StoicMathematics #Chrysippus #FormalLogic #HistoryOfMaths #AncientMathematics #LogicalReasoning #PhilosophyOfMaths #MathematicsPodcast #TheMathematiciansPodcast

In this episode of The Mathematicians Podcast, host Benjamin Cornish paddles upstream—literally and figuratively—to explore the remarkable life and ideas of Eratosthenes of Cyrene, the polymath who measured the Earth with astonishing precision and devised one of the most famous algorithms in history: the Sieve of Eratosthenes. In the show today How Eratosthenes measured Earth’s circumference over 2,000 years ago The ingenious method behind the Sieve of Eratosthenes and why it still matters in modern computing His groundbreaking work in geography, including latitude, longitude, and early ideas of a spherical Earth His role as chief librarian at the Library of Alexandria—aka the Google of the ancient world From ancient geometry to prime numbers and historical timekeeping, this episode is a celebration of interdisciplinary thinking, curiosity, and mathematical creativity. Whether you're a teacher, student, or just a curious mind, you'll come away with a renewed appreciation for how math shapes our understanding of the world. Plus: Learn how to get involved with Un-Natural Numbers, a new YouTube maths chat show supporting emerging voices in math communication. https://docs.google.com/forms/d/e/1FAIpQLSfve_tIM3e9jh5b_kzIPICmRViIXIcBJ38DyQ5YwfBLzNMHKg/viewform?usp=sharing&ouid=108012955586926932884      Oh no, a list of Keywords (for SEO):Eratosthenes, Sieve of Eratosthenes, measure Earth circumference, Library of Alexandria, prime numbers, ancient Greek mathematicians, history of mathematics, geography and maths, interdisciplinary STEM, maths communication, educational podcast, number theory, velocity problems, maths teaching podcast Have a free list of Hashtags:#MathematicsPodcast #Eratosthenes #PrimeNumbers #MathsEducation #HistoryOfMaths #STEM #MathsInRealLife #MathsTeacher #LibraryOfAlexandria #GeographyAndMaths #EducationalPodcast #NumberTheory #UnNaturalNumbers

Grab your ventriloquist dummies and your gimbles, as we catapult ourselves into a story about the worlds first mathematical engineer. If you thought Leonardo Da Vinci was pretty metal, well you're about to meet the 'wood and papyrus' version. It's Philo of Byzantium.   In an exciting new segment of the 'Episode Show Notes', may I present an unappealing list of hashtags for the Search Engine Optimisation: #MathHistory #MathsHistory#AncientMath #AncientMaths#PhiloOfByzantium#GreekMathematics#HistoryOfMath #HistoryOfMaths#AncientScience#EngineeringHistory#ByzantineScience#MathematicalHeritage#SciencePodcast#MathPodcast #MathsPodcast#AncientEngineers#PhiloTheEngineer#MechanicsHistory#HellenisticScience#InventionHistory#MathAndMachines #MathsAndMachines#GreekInventors#MathematicsThroughTime#FromPhiloToPhysics   The music was: "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/

In this week's episode we look at the life an works of the Great Archimedes. A man who was so much more than what we all think, and we all think quite highly of him. But let's look behind the claw, the screw and the lever and find out who was the mathematician behind the engineer.   You can also find my debut YouTube video about the Quadrature of the Parabola here: @Un-Applied-Maths https://www.youtube.com/channel/UCG-SNPXWN-Q3YxLp_R   https://www.youtube.com/channel/UCG-SNPXWN-Q3YxLp_RiDaAQ   The Music was:  "Danse Macabre - Finale" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 http://creativecommons.org/licenses/by/3.0/  

This week we look at a man who looked at the moon whilst it looked at the sun and thought: "Gosh, that looks far away".   But how far away is the sun, really. Or the better question would be: "How far away are we?"   Let's find out as we measure the life and works of Aristarchus of Samos. The second greatest Samos-ian that we have covered so far.   The music was:  "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/

This episode has been a real favourite of mine to record - I sit down with the co-creator of www.euclidea.xyz to ask all of my puzzling questions on how the game was developed, the inspiration behind the puzzles and the role of Euclidean geometry in today's world.    Further reading for some of the referenced papers:  https://arxiv.org/abs/1709.02562 https://www.cut-the-knot.org/triangle/TriangleFromBisectors.shtml   The music was: "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/    

This week: The big cheese. It's Euclid time. Come with me on a journey through his optics, astronomy and or course the elements - a week of exceptionally good maths.   The Music was: "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/

This week we look up to one of the most influential stargazers of all time. Autolycus, the very first non-Euclidean geometer, even before Euclid hit the scene.    The music is:  "Danse Macabre - Finale" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 http://creativecommons.org/licenses/by/3.0/

This week we have a big one! One of the greats, if not the greatest, philosophers of all time: Aristotle. We will explore how this philosopher-scientist also wears a heavy crown of mathematics, despite never publishing a work of maths. Tune in for discussions on logic, set theory, combinatorics and the ever interesting syllogism.   The music: "Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/