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 3.0 http://creativecommons.org/licenses/by/3.0/

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 3.0 http://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 3.0 http://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 3.0 http://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 3.0 http://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