The Mathematicians Podcast

Episode 31 - Hipparchus - Going Supernova

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

Episode 32 - Hero of Alexandria - A Hero to us all

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 

Episode 33 - Injectives with Dr Daffern - Religion and Maths - Part 1

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/
 
 

Episode 34 - Injectives with Dr Daffern - Religion and Maths - Part 2

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/

Episode 35 - Menelaus of Alexandria - The straightest Curve

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

Episode 36 - Nicomachus of Gerasa - That which divides us

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

Episode 37 - Theon of Smyrna - A Number for a Name

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/

Episode 38 - Ptolemy - Beneath the Sheets

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.

Episode 39 - Diophantus of Alexandria - A whole lot of fun

This week, we're taking another trip to ancient Alexandria to meet Diophantus, often hailed as the "Father of Algebra." 
Join us as we untangle the fuzzy biography of a mathematician whose life story is a riddle, and whose monumental work, the Arithmetica, started us working  towards systematic equation-solving. From the proto-symbols of syncopated algebra to the birth of Diophantine equations (where only whole numbers dare to tread!), we explore how this ancient Greek genius sought to generalize mathematical problems, shifting math from "apples" to "variables."
 
Keywords: Diophantus, Algebra, Arithmetica, Diophantine Equations, Ancient Greece, Alexandria, History of Mathematics, Number Theory, Equation Solving, Rational Numbers, Integers, Fermat's Last Theorem, Hilbert's 10th Problem, Undecidability, Al-Khwarizmi, Brahmagupta, Cryptography, Computer Science, Podcast.
Hashtags: #MathematiciansPodcast #Diophantus #AlgebraHistory #AncientMaths #NumberTheory #DiophantineEquations #MathsPodcast #STEM #HistoryOfScience #Fermat #HilbertProblems #ProblemSolving #MathsFacts #Alexandria #EquationSolver #MathematicalJourney #ListenAndLearn
 
The music was-"Danse Macabre - Finale"Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0http://creativecommons.org/licenses/by/3.0/
 

Episode 40 - Pappus of Alexandria - Burn the Bridges

This week, Pappus of Alexandria, a pivotal figure in 4th-century mathematics. Often considered one of the last great Greco-Roman geometers, Pappus compiled the monumental Synagogue, a comprehensive collection that sought to revive classical Greek geometry.
In this episode: A candid look at Pappus's personality and his notorious public critique of the female mathematician Pandrosion and her student. Pappus’s distinction between "plane," "solid," and the more expansive "linear" problems. Concepts like the Pappus Chain (or Steiner Chain) and his non-Euclidean approach to classic problems like doubling the cube.
Join us as we explore Pappus's legacy, his undeniable impact on the history of mathematics, and Benjamin’s honest (and sometimes scathing!) personal opinions on this complex figure. Plus, a crucial discussion about the often-overlooked women in mathematics and a personal announcement about the future of the podcast!
Keywords: Pappus, Alexandria, Greek Geometry, Synagogue, History of Mathematics, Pandrosion, Female Mathematicians, Euclidean Geometry, Analytic Geometry, Steiner Chain, Pappus Chain, Doubling the Cube, Menaechmus, Archimedes, Apollonius, Ptolemy, Theon of Alexandria, Diophantus, Descartes, Fermat, Newton, Euler, Ancient Greece, Roman Empire, Mathematics Podcast, Geometry, Algebra, History of Science, Mathematical Concepts, Platonic Solids.
Hashtags: #Pappus #MathematicsHistory #GrecoRomanGeometry #AncientMaths #Podcast #TheMathematiciansPodcast #GeometryProblems #AnalyticGeometry #WomenInSTEM #MathsEducation #HistoryOfScience #Alexandria  #STEM #ClassicalMathematics