The Mathematicians Podcast

This week on The Mathematician's Podcast, we take a break from the philosophical and theological debates of the past to chat with an intellectual heavyweight of our own age! In another special "Injectives" episode, Ben is joined by Hope Duncan, a maths communicator and researcher at the University of Leeds whose particular interest is infinity.

Join us as Hope tackles some fundamental (and some silly!) questions from Ben's school students, concepts like dividing by zero and the mass of the universe. The conversation quickly escalates into a fascinating discussion on the history and modern understanding of infinity...

Welcome back to The Mathematicians Podcast! This episode introduces our first "John" – John Philoponus, also known as John the Grammarian or John of Alexandria. This Christian theologian, philosopher, and arguably mathematician from 6th-century Egypt is primarily known for his religious doctrine, but we look into the fascinating overlap between mathematics and religion: the nature of infinity.

Join us as we explore Philoponus's arguments against the Aristotelian view of an eternal cosmos, his insights into the conservation of momentum and the concept of "initial impetus," and his revolutionary thoughts on the vacuum and fluid drag. We'll trace the his...

The Romans are here, in ROME! Discover the dramatic rise and fall of the Roman Empire, its lasting global impact, and the fascinating (and sometimes contentious) question of who inherited its crown. Then, meet Boethius, the last classical scholar, whose time on death row led to The Consolation of Philosophy. This episode unpacks his brilliant philosophy of causation, free will, and how god knows the future without pre-determining our choices. We'll explore Aristotle's Sea Battle paradox, Boethius's own #LogicalInnovations (like De hypotheticis syllogismis), and his monumental effort to translate Greek mathematics and #Philosophy, shaping the entire medieval intellectual landscape. Get ready f...

This week we explore the brilliant, and tragically short, life of Hypatia of Alexandria. Born around 370 CE, she was a pioneering female mathematician and philosopher who led the last great school of mathematics in the ancient world. 

Hypatia’s story is also a dramatic tale of political and religious upheaval. A respected pagan intellectual with influence in Alexandria's civic life, she found herself caught in the violent conflicts of the early Christian church. Join us as we examine the forces that shaped her world and led to her untimely end, reflecting on the fragile legacy of knowledge and...

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, hi...

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, Alexa...

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...

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 cat...

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...

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/

Key...

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...

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...

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 imposs...

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...

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...

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 #Ma...

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, teache...

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 spheri...

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 Duration: 00:21:46

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

...

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 A...

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 A...

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 3.0
http://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: 

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

This week we finally come full circle on the Quadratrix, and meet a man who was able to draw a square with equal area to the circle. Yes, that ancient problem finally gets solved: for a given definition of solved. Tune in to find out exactly how one does 'Square the Circle'.

"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 take a crucial next step into the history of algebra and simultaneous equations with the Bloom of Thymaridas. Listen along for a bloomin' good time!

The music was:

"Danse Macabre - Finale"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
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Today we introduce the conic section, and it's iconic founder Menaechmus. A bit of a one trick pony, but my goodness what a trick that was. 

The Music was:

"Danse Macabre - Finale"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
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There are a Myriad reasons to listen along this week as we explore the formation of ancient Greek number, as well as looking at early combinatorics with Xenocrates.

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 take an exhaustive look at the mathematician that invented calculus... arguably. We can certainly have that argument. So let us enjoy the good life, by taking pleasure in the pursuit of knowledge with Eudoxus.

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/

Today we introduce the titular character from Plato's 7th greatest dialogue and discover the contributions he made to the 'Platonic' solids and more.

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 episode is modelled on the the form of the good, or at least the good podcast. Step out from the shadows of your caves and enjoy a dialogue on Plato. Sadly, there is nothing in this episode that you didn't already know, from before you were born - but perhaps I can help you to recollect it. 

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 today's episode we have a special treat as I sit down with Professor Peter Adamson to ask all of the questions that have been brewing over the past 10 weeks. Be prepared for significantly more expertise from a professional of philosophy and a podcast ledged himself.

You can find Peter's work at: https://historyofphilosophy.net/ , and I highly recommend that you do.

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/

Today we learn about the man who invented the wooden pigeon, along with some slightly more serious contributions. We've learnt already about how the Pythagoreans thought everything was made up of numbers, now it is time to meet the guy that said 'Well why don't we use numbers to describe stuff then?' 

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/

Today I plan to share with you the smallest possible unit of information, and I will do this an infinite number of times. Are we talking about the introduction of calculus? A theory of atoms? Both? Who can say, well hopefully I can in this episode. 

The music was :

"Danse Macabre - Finale"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
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This week we explore beauty, in the form of some more very old maths. Theodorus, one of the leading figures in the Pythagorean movement, will move you to joy, I am sure.

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, let me draw you into a story about an ancient curve-ist, as we meet the first non-circular curve that is formally defined - and the mand who first drew it.

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 do the impossible - square the circle... or at least part of it. Listen in to hear what the cutting edge of research mathematics was in the 4thC BCE.

Follow on Instagram @mathematicians.pod

"Danse Macabre - Finale"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
http://creativecommons.org/licenses/by/3.0/

Let me invite you to drink in the joys of learning about a Mathematician you have possibly never heard of. This week we measure the tilt of the earth using the most advanced technology of the day: a stick.

Follow @mathematicians.pod on Instagram for more, less serious, content.

"Danse Macabre - Finale"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
http://creativecommons.org/licenses/by/3.0/

I would invite you to press play on this podcast, but alas motion is illusory, so you finger will not move. Hopefully I will move you to like and subscribe with this whimsical history of Zeno of Elea. 

Follow @mathematicians.pod on Instagram for more, less serious, content.

The Music was:

"Danse Macabre - Finale"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
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In this exciting episode we discover who Pythagoras really was. Did he really do Pythagoras' theorem? Did he have a golden leg? Was he a human embodiment of god?  ... Maybe!

Join me on Instagram @mathematicians.pod

The Music was:

"Danse Macabre - Finale"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
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The first mathematician to have a theorem named after them; Thales - Come with me to the 6th Century BCE to learn more about what it meant to be a mathematician in ancient times.

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/

Our first look at a mathematician dating back to 1700 BCE - Ahmes. What was maths like back in Ancient Egypt?

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/