Where we explore the historical figures that count. An in-depth look at the history of mathematics, in chronological order, looking at the people, the theories, the ideas - with as fewer gaps as possible. Each episode we focus in on a single character or contribution to the history of maths and explore why it is significant, and how it evolved.
Was Varāhamihira the world's first statistician? Could a sixth-century mathematician really predict the monsoon using observational data? And how did Bhāskara I produce one of the greatest approximations to the sine function over a thousand years before modern calculators? In this episode of The Mathematicians Podcast, Benjamin Cornish explores two remarkable figures from the golden age of Indian mathematics. First, we meet Varāhamihira, author of the Bṛhat Saṃhitā and the Pañcasiddhāntikā. Discover how he preserved the Five Astronomical Schools of India, collected generations of weather observations to forecast the monsoon, classified clouds, investigated geography, gemstones and groundwater, and pioneered a surprisingly modern approach to gathering and analysing data. Then we turn to Bhāskara I, one of Aryabhata's greatest successors. His commentary preserved Aryabhata's revolutionary ideas for future generations, while his elegant rational approximation for sin(x) remains one of the most impressive achievements in early mathematics. ━━━━━━━━━━━━━━ Support the Podcast If you enjoy the show and would like to help support future episodes, you can buy me a coffee here: https://ko-fi.com/benjamincornish ━━━━━━━━━━━━━━ Follow The Mathematicians Podcast Bluesky: https://bsky.app/profile/mathematicians-pod.bsky.social ━━━━━━━━━━━━━━ Music 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 Varāhamihira, Bhāskara I, Bhaskara I, Aryabhata, Brahmagupta, Ancient Indian mathematics, History of mathematics, Indian astronomy, Pañcasiddhāntikā, Panchasiddhantika, Bṛhat Saṃhitā, Brihat Samhita, sine approximation, sin x approximation, trigonometry, statistics, weather forecasting, monsoon prediction, Gupta Empire, Ujjain, Ujjayini, mathematical history, mathematicians podcast, Benjamin Cornish, history podcast, science history, astronomy history, ancient science, Indian mathematicians. Hashtags #Mathematics #HistoryOfMathematics #IndianMathematics #Varahamihira #BhaskaraI #Aryabhata #Brahmagupta #AncientIndia #Astronomy #Trigonometry #Statistics #HistoryPodcast #SciencePodcast #STEM #MathsPodcast #TheMathematiciansPodcast
The Gupta Empire reaches its scientific zenith as we meet one of the greatest mathematicians of Late Antiquity. Aryabhata (476–550 CE) helped transform astronomy and mathematics in India through a remarkable combination of elegant algorithms and practical computation. In this episode we explore his Aryabhatiya, from recursive square and cube root algorithms to the famous Kuttaka ("Pulveriser") method for solving indeterminate equations. Along the way we investigate his astonishingly accurate value of π, some of the earliest trigonometric tables, numerical methods that hint at calculus over a thousand years before Newton, and his important role in the long, collective story of the invention of zero. We also take a tour through the Gupta Empire, discuss why astronomy drove so much mathematical innovation, and ask whether Aryabhata deserves his reputation as one of history's greatest mathematicians. As always, there are terrible puns, historical tangents, and probably more discussion of Huns than anyone expected. 📚 Further Reading • Walter Eugene Clark (1930), The Aryabhatiya of Aryabhata (English Translation) https://www.wilbourhall.org/pdfs/aryabhatiyaenglish.pdf ☕ Support the Podcast If you'd like to help support the show, commission a future episode, or simply buy me a coffee, you can do so here: https://ko-fi.com/benjamincornish 🌐 Follow The Mathematicians Podcast Bluesky: https://bsky.app/profile/mathematicians-pod.bsky.social 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/ Hashtags #Mathematics #MathsHistory #HistoryOfMathematics #Aryabhata #AncientIndia #IndianMathematics #Astronomy #HistoryPodcast #MathsPodcast #Pi #Zero #Trigonometry #Algorithms #ScienceHistory #STEM Keywords Aryabhata, Aryabhata biography, Aryabhata mathematics, Aryabhatiya, ancient mathematics, history of mathematics, Indian mathematics, Gupta Empire, Nalanda University, astronomy history, mathematical astronomy, origins of zero, history of zero, invention of zero, pi approximation, history of pi, square root algorithm, cube root algorithm, Kuttaka algorithm, pulveriser algorithm, indeterminate equations, Diophantine equations, trigonometry, sine tables, recursive algorithms, numerical methods, ancient science, mathematics podcast, history podcast, Benjamin Cornish, The Mathematicians Podcast, STEM education, famous mathematicians, mathematical history, ancient India, classical India, Gupta mathematics, history of astronomy.
The Silk Road carried spices, gemstones, ideas... and, occasionally, trigonometry. In this episode of The Mathematicians Podcast, we follow the mysterious figure known as Yavanesvara, the "Lord of the Greeks," whose translation of Greek astronomical and astrological knowledge into Sanskrit helped spark a mathematical transformation in ancient India. Along the way, we explore merchant trade across the Indian Ocean, the origins of sine tables, spherical astronomy, navigation, observational error, and the surprisingly rich mathematics hidden inside astrology. We also take a brief detour through gem shops, Roman trade deficits, and the everyday mathematics of merchants using techniques such as double false position and casting out nines. History remembers Yavanesvara only dimly, but the mathematical journey he represents would help bridge the gap between the early Indian traditions and the age of Aryabhata. Because sometimes the most important travellers don't carry goods; they carry ideas. ☕ Support the show: Ko-Fi: https://ko-fi.com/benjamincornish 🌐 Follow Benjamin Cornish: BlueSky @mathematicians-pod 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/ #Mathematics #HistoryOfMathematics #Yavanesvara #AncientIndia #IndianMathematics #SilkRoad #Astronomy #Trigonometry #Aryabhata #HistoryPodcast #MathsPodcast #BenjaminCornish #AncientScience #SineFunction #MathematicalHistory #IndianAstronomy
Episode 42: Pingala – The Poet of Binary Why is a 2nd-century BCE Indian grammarian being featured on a mathematics podcast? Because centuries before the "Founding Fathers" of Western mathematics were born, Pingala was already encoding the universe. In this special rhythmic episode, I step out of the traditional lecture hall and into the world of spoken word. After a transformative experience at the 'Beat up the Poets' conference, I will explore the Chandaḥśāstra; Pingala’s ancient treatise on prosody. We look into how the study of Sanskrit poetic meters led to the earliest known descriptions of: Binary Number Systems: How stressed and unstressed syllables created a mathematical logic long before Turing. The Concept of Zero (Shunya): The "original gap" in the poetic flow. The Fibonacci Sequence: Why the "Man from Pisa" was actually a few centuries late to the party. Pascal’s Triangle: Uncovering the "Meru Prastāra" hidden in ancient Vedic verses. From "off-by-one" errors to the combinatorics of rhythmic beats, this episode is a lyrical journey into the seismic foundations of ancient Indian mathematics. Note from me:This is my final pre-recorded episode before I head off on paternity leave! Thank you all for your incredible support. I’ll be taking a short writing break to welcome the new addition to the family, but the podcast will return soon. Support the Show & Connect: Bluesky: Follow the conversation @mathematicians-pod Support the Paternity Leave Fund: If you enjoyed this episode, consider buying me a coffee (or a box of nappies!) on Ko-fi: https://ko-fi.com/benjamincornish Keywords: Pingala, History of Maths, Chandaḥśāstra, Sanskrit Prosody, Binary Code, Fibonacci Sequence, Pascal’s Triangle, Combinatorics, Vedic Mathematics, Ancient India, Zero, Shunya, Benjamin Cornish. Hashtags: #maths #historyofmaths #pingala #mathematicians #podcast #binary #poetry #fibonacci #ancientindia #stem #mathematics 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 special book club episode of 'The Mathematicians Podcast', I sit down with author, maths communicator, and museum learning consultant, Thomas K. Briggs. Join us for a glass of wine and a deep dive into Tom's book, 'The Mathematicians Library', a title so intriguing it was a must-have for the show. This 'Injectives' sub-series episode is a one-to-one conversation; today exploring the vast history of mathematical literature. Discover the oldest book in Tom's personal collection and unravel the criteria for what truly constitutes a "book of mathematics". Tom paints a vivid picture of ancient mathematical works, describing the evolution of writing media before the age of flat sheets and ink. The discussion navigates through the emergence of authorship in the Mediterranean, Indian, and Chinese traditions, and Tom shares his favourite example of a significant mathematical work without a known author. He also recounts the fascinating journey of a particular mathematical text through the ages, a story of translation and transcription that has preserved ancient knowledge. In a new segment of "Desert Island Codex," Tom reveals which ancient mathematical document he would choose to study in solitude and which ancient lecture he would love to have heard. Moving beyond the book, the episode looks into Tom's work as a museum consultant. He sheds light on the origins of encryption and the methods ancient leaders used to send secret messages. The discussion also explores the vast, untranslated collection of Babylonian tablets and what they might still reveal about Mesopotamian mathematical understanding. Finally, Tom offers his own insightful, pithy definition of what mathematics truly is. He also reveals which mathematician he is most excited to see featured on a future episode of the podcast. Tune in for a captivating conversation that journeys through the annals of mathematical history, from ancient texts to modern museum exhibits. You can find Ben on Bluesky @mathematicians-pod. You can support him at ko-fi.com/benjamincornish. You can find Tom: on his website https://tkbriggs.co.uk/ ; on Bluesky @TeaKayB.mathsy.space ; Join the History and Mathematics in Education Network https://historyand.mathsy.space/ ; 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: history of maths, ancient mathematics, mathematical literature, Thomas K. Briggs, The Mathematicians' Library, Euclid, ancient texts, encryption, Bletchley Park, Babylonian tablets, museums, history of science, mathematics podcast. Hashtags: #TheMathematiciansPodcast #HistoryOfMaths #AncientMaths #MathematicalBooks #STEM #Podcast #Interview #Maths #History #Science #Books #Museums #Encryption #TheMathematiciansLibrary
In this episode of The Mathematicians Podcast, I am jumping ahead 800 years and travelling 5,000 km back to India to pick up the threads of a fascinating mathematical tradition. I’ll be introducing you to Umaswati, a pivotal figure from around the 2nd Century CE who helped systematise the teachings of Jainism, a religion where "Right Knowledge" and the study of the cosmos made maths a fundamental pursuit. Together, we explore the four broad periods of Indian religious development: Vedic, Śhramana, Puranic, and Bhakti, and see how the Jain tradition carved out a unique space for mathematical inquiry. We’ll discuss: The approximation of \pi : Why the Jains used \sqrt{10} and how they handled circular segments. The power of place value: How ancient Indian poets and scholars were comfortably using numbers as large as 10^64 while the Greeks were still stuck at the Myriad The Five Types of Infinity: Long before Georg Cantor revolutionised set theory in the 19th century, Umaswati and the Jain scholars were already classifying different scales of the infinite and the transfinite. Join me as I navigate the intersection of faith, philosophy, and the infinite. You can find Ben on Bluesky @mathematicians-pod. You can support him at ko-fi.com/benjamincornish. Hashtags:#Maths #HistoryOfMaths #Mathematics #Jainism #Umaswati #India #History #Infinity #LargeNumbers #AncientIndia #STEMPodcast #TheMathematiciansPodcast Keywords:Umaswati, Jaina Mathematics, Indian Mathematics, History of Maths, Brahmanism, Vedic Tradition, Śramaṇa, Mahabharata, Place Value System, Transfinite Numbers, Enumerable and Innumerable, Pi Approximation, Mathematical Philosophy, Ancient Indian Scholars. 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/
When is an approximation "good enough"? This week on The Mathematicians Podcast, host Benjamin Cornish opens the doors to his gem and fossil shop to discuss why a polished piece of glass, or a clever mathematical shortcut, can sometimes be just as effective as the real thing. We are shifting our focus toward the sprawling, shifting history of Mesopotamia. Today, we tackle a double bill of Babylonian titans: Nabu-rimanni and Kidinu. Though separated by two centuries and a revolving door of empires (from the Persians to the Greeks), these two temple astronomers foresaw the blossoming of predictive science. In this episode, we explore: The "Feet of Clay" History: A whirlwind tour of Babylon, from the Tower of Babel and Hammurabi’s Code to the rise of the Persians and the lightning conquest of Alexander the Great. System A vs. System B: How Nabu-rimanni’s constant velocity model evolved into Kidinu’s sophisticated "zigzag" acceleration system. The Two-Second Error: How ancient mathematicians using little more than water clocks calculated the synodic month with a precision that rivals modern satellite data. The Babylonian Legacy: Why the Greeks (including Hipparchus) owe their greatest discoveries to the meticulous clay tablets of the East. Keywords:Babylonian Mathematics, History of Astronomy, Nabu-rimanni, Kidinu, System A and System B, Synodic Month, Ancient Babylon, Cuneiform Tablets, Persian Empire, Seleucid Empire, Mathematical History, Benjamin Cornish, Naburimannu, Kidinnu. Hashtags:#Mathematics #HistoryOfMaths #Astronomy #AncientBabylon #NabuRimanni #Kidinu #STEMHistory #SciencePodcast #AncientHistory #Babylon #MathsIsBeautiful #TheMathematiciansPodcast #PersianHistory #ScientificDiscovery Support the Show:If you enjoy the history of the people that count, consider supporting Benjamin via his tips page at https://ko-fi.com/benjamincornish Connect with us:Follow Benjamin on BlueSky at @mathematicians-pod 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/
Episode 52 of The Mathematicians Podcast, takes us deep into the world of ancient Indian mathematics with a focus on Apastamba and his contributions to the Sulvasutras. Following in the footsteps of Baudhayana, Apastamba codified and clarified Vedic ritual geometry, transforming abstract rules into practical, modular construction techniques. We explore his mathematical approach, the subtle differences between his Sulvasutras and those of Baudhayana, and his work on the Dharma Sutra, which laid out ethical and social laws with remarkable precision. Keywords & Hashtags: Ancient mathematics, Indian mathematics, Apastamba, Sulvasutras, Vedic mathematics, Baudhayana, Yajurveda, Dharma Sutra, Indian mathematicians, history of mathematics, geometry, Pythagoras, ethics, moral philosophy, Vedic ritual, math history podcast, mathematicians podcast, Benjamin Cornish, mathematicians, educational podcast, maths podcast, Indian history, cultural history, modular constructions, ritual geometry, maths enthusiasts, STEM history, historical maths #AncientMathematics #IndianMathematics #Apastamba #Sulvasutras #VedicMathematics #Baudhayana #Yajurveda #DharmaSutra #MathsPodcast #HistoryOfMathematics #Geometry #Ethics #MathematicsHistory #BenjaminCornish #MathematiciansPodcast #STEMHistory #MathsEnthusiasts #EducationalPodcast Support me here: https://ko-fi.com/benjamincornish 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 a journey back to 800 BCE to explore the life and work of Baudhayana, one of the earliest known mathematicians from the Indian tradition. This episode also offers context on the Vedic tradition, the role of mathematics in ritual practices, and the broader connections between ethical, social, and technical knowledge. We discuss how mathematics was a practical, problem-solving craft in ancient India, designed to be memorized, teachable, and repeatable, an engineering mindset long before modern formalizations. Listeners will gain a rich understanding of the spiritual, cultural, and mathematical landscape in which Baudhayana worked, and why his contributions remain significant today. Finally, the episode touches on questions of historical credit, colonial narratives in mathematics, and how we name mathematical discoveries, challenging us to reconsider what we think we “know” about the history of ideas. You can support my work here: https://ko-fi.com/benjamincornish, any tips are most gratefully received. Keywords: Baudhayana, Sulbasutras, Vedic mathematics, ancient India, Pythagoras’ theorem, history of mathematics, approximations of pi, √2, sacred geometry, mathematical history, applied mathematics, Indian mathematicians, Vedic tradition Hashtags: #Baudhayana #VedicMathematics #Sulbasutras #AncientIndia #PythagorasTheorem #MathsHistory #SacredGeometry #AppliedMaths #HistoryOfMaths #MathematiciansPodcast 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/
How do you get a wolf, a goat, and a cabbage across a river without turning the boat into a buffet? Welcome to the Season 1 Finale of The Mathematicians Podcast! Today, we go to the court of Charlemagne to meet Alcuin of York: clergyman, poet, teacher, and potentially history’s first queer mathematician. Alcuin arguably invented the genre of "Recreational Mathematics." In this episode, we open his book Propositiones ad Acuendos Juvenes (Problems to Sharpen the Young), a collection of logic puzzles that includes the world’s first recorded river-crossing problems, inheritance riddles, and a few "impossible" questions designed solely to troll his students. We also discuss Alcuin’s contribution to literacy (specifically the invention of the question mark), his thoughts on baptism, and why he might have been the original miniscule fan. Housekeeping:Please note that the show will be moving to a monthly release schedule as I prepare for the arrival of a new family member. If you would like to support the show through this next phase, please visit the new Ko-Fi page below! Support the Show: Ko-Fi.com/BenjaminCornish Contact: @mathematicians-pod on Bluesky Keywords:Alcuin of York, Charlemagne, Carolingian Renaissance, Recreational Mathematics, History of Mathematics, Logic Puzzles, River Crossing Problem, Medieval History, Education History, Series Finale. Hashtags:#MathsHistory #AlcuinOfYork #LogicPuzzles #Charlemagne #MedievalHistory #RecreationalMaths #Podcast #STEMHistory #CarolingianRenaissance #SeasonFinale
Was Bede a mathematician? Well, he certainly made history count. Join Benjamin Cornish for a trip to Northumbria (which is definitely in England) to meet the "OG monk" who mastered the calendar. In this episode, we dip into "On the Reckoning of Time" to discover how one man calculated the date of Easter, argued with the tides, and dated the Garden of Eden to a Tuesday (or close enough). We also explore why we use the AD/BC system and why you should never trust a Solstice. Keywords: Bede, History of Mathematics, Northumbria, Calendars, Paschal Moon, Tides, Chronology, AD/BC. Hashtags: #MathsHistory #TheVenerableBede #MedievalHistory #Podcast #Calendar #Northumbria #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 on The Mathematicians Podcast, join Benjamin Cornish as he shines a spotlight on Eutocius of Ascalon, the unsung hero who kept the flames of ancient mathematics burning! Born in 480 CE, Eutocius headed the prestigious Alexandrian school and dedicated his life to preserving and elucidating the monumental works of mathematical titans like Archimedes. We'll explore his crucial commentaries on "On the Sphere and Cylinder" and "Measurement of a Circle," unravelling fascinating insights into early approximations of pi and the elusive origins of square root calculations. Discover why some figures count more than their theorems. Keywords: Eutocius of Ascalon, History of Mathematics, Archimedes, Alexandrian School, Greek Mathematics, Mathematical Commentaries, Pi Approximation, Square Root, Ancient Geometry, Preservation of Knowledge, On the Sphere and Cylinder, Measurement of a Circle, Apollonius' Conics, Doubling the Cube, Mathematical Heritage. #EutociusOfAscalon #HistoryOfMathematics #Archimedes #AncientGreece #AlexandrianSchool #MathematicalCommentaries #Pi #SquareRoots #MathematicalHeritage #Podcast
This week, we bridge the gap between Alexandria and Constantinople with Isidorus of Miletus, a mathematician and architect who preferred teaching to writing. We look into how he and his partner, Anthemius of Tralles, were commissioned to build the legendary Hagia Sophia in a mere five years, after a sports riot burned down half the city. Discover the architectural genius behind its "floating" dome, a marvel of pendentives that has stood for centuries. Then, we follow the extraordinary journey of a lost text by Archimedes, which Isidorus himself studied. From a library in Constantinople to a 10th-century copy in Jerusalem, this priceless work was scraped clean by a monk for a prayer book, painted over by an art forger, and finally sold at auction for millions. Uncover the cutting-edge science that resurrected the hidden text, revealing Archimedes' work in combinatorics—the Stomachion puzzle. It’s a tale of genius, destruction, and incredible rediscovery, proving that sometimes the most interesting things are hiding in the most boring places. Hashtags:#HistoryOfMathematics #IsidorusOfMiletus #HagiaSophia #ByzantineArchitecture #Archimedes #Palimpsest #AncientHistory #MathsPodcast #STEM #Constantinople #HistoryPodcast #Architecture Keywords:Isidorus of Miletus, Hagia Sophia, Anthemius of Tralles, Byzantine, Constantinople, Archimedes Palimpsest, The Method, Stomachion, Procopius, Justinian, Nika Riots, Pendentive Dome, History of Science, Combinatorics, Eutocius of Ascalon.
Join us on The Mathematicians Podcast as host Benjamin Cornish uncovers the whimsical and often mischievous side of Anthemius of Tralles, the Byzantine Greek architect and mathematician! From earthquake pranks on his neighbour Zeno to pioneering work in optics and conic sections, Anthemius proves that genius can be seriously fun. Discover the forgotten history of burning mirrors, the true shape of light, and the secrets behind the magnificent Hagia Sophia. Keywords: Anthemius of Tralles, Byzantine mathematics, history of optics, conic sections, Hagia Sophia, ancient architects, mischievous mathematicians, podcast, mathematics history, geometry Hashtags: #MathematiciansPodcast #AnthemiusOfTralles #HistoryOfMaths #Optics #ConicSections #HagiaSophia #AncientGreece #MathsHumor #STEMeducation
Welcome back to The Mathematicians Podcast! In this episode, host Benjamin Cornish takes us back to the 6th century CE to explore the life and legacy of Simplicius of Cilicia. A pivotal figure caught between two intellectual giants, Simplicius studied under both Aristotelian and Platonic traditions, becoming one of the last significant scholars of Plato's Academy before its closure by Justinian. Join us as we uncover Simplicius's crucial role as a pagan apologist, philosopher, astronomer, and mathematician. Learn how he became a conduit for preserving ancient knowledge, meticulously commenting on the works of Aristotle and Plato, and attempting to bridge their philosophical divide on topics like rationalism vs. empiricism, and idealism vs. realism. The episode also revisits the epic debate between Simplicius and John Philoponus on the nature of infinity, the eternal universe, and the concept of motion and impetus. Keywords: Simplicius, John Philoponus, Plato's Academy, Aristotle, Neoplatonism, Pagan philosophy, Byzantine Empire, Persian Empire, infinity, actual infinity, potential infinity, momentum, cause and effect, unmoved mover, ancient mathematics, philosophy of mathematics, history of science, ancient Greece, late antiquity. Hashtags: #TheMathematiciansPodcast #Simplicius #AncientPhilosophy #HistoryOfMathematics #Plato #Aristotle #Neoplatonism #JohnPhiloponus #Infinity #Paganism #ByzantineHistory #ClassicalStudies #Philosophy #ScienceHistory #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, covering: The historical struggle with infinitesimals and their surprising decline in modern calculus. The dichotomy of potential vs. actual infinity, from ancient philosophers to modern #SetTheory. How we can "increase" infinity without changing its #Cardinality, illustrated with clever #Bijections between natural numbers and integers. The work of #Cantor in proving that not all infinities are created equal, introducing the concept of different "sizes" of infinity, like the uncountably infinite Real Numbers. A look at the #ZFC axioms, exploring the foundations of modern set theory, from the obvious (axiom of extensionality) to the profoundly abstract (axiom of choice). The implications of #Gödel's incompleteness theorems, revealing the inherent limits of axiomatic systems and the existence of independent statements within ZFC. Hope's personal research into #LargeCardinals – even bigger infinities that offer new ways to tackle unsolved mathematical problems. This episode is a captivating journey through the evolution of one of maths' most mysterious concepts, revealing that even at the bedrock of mathematics, there's still so much to explore and discover. Hope shares what motivates her to sit with the uncomfortable "why" of mathematics, making set theory sound like the ultimate puzzle. You can find out more from Hope on Bluesky @hopeiona.bsky.social, or Youtube @hopeduncanmaths 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: #Mathematics #MathsPodcast #Infinity #SetTheory #Calculus #Infinitesimals #Cantor #ZFC #Axioms #Gödel #IncompletenessTheorems #LargeCardinals #PhilosophyOfMaths #HopeDuncan #TheMathematiciansPodcast
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 historical arguments around infinity from Zeno to Aristotle, Euclid, and Archimedes, showing how Philoponus's ideas shaped both theological orthodoxy and the future of scientific thought. You'll also discover John Philoponus's crucial role in documenting and popularizing the astrolabe, a pivotal scientific instrument of his era. Prepare for an episode that proves how deeply intertwined mathematics, physics, and theological debates were in the ancient world. Keywords: John Philoponus, John the Grammarian, John of Alexandria, infinity, Aristotelian physics, Christian theology, ancient mathematics, history of science, astrolabe, momentum, vacuum, impetus, ancient Egypt, 6th century CE, philosophy of mathematics, cosmology, Unmoved Mover, Theism, Pantheism, Deism, The Mathematicians Podcast. Hashtags:#TheMathematiciansPodcast #HistoryOfMaths #JohnPhiloponus #Infinity #AncientScience #ChristianTheology #Aristotle #Astrolabe #Momentum #Vacuum #PhilosophyOfScience #MathematicalHistory #Podcast #SciencePodcast #AncientEgypt #6thCentury #EarlyScience #MathsAndReligion #Cosmology
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 for #AncientHistory, deep #PhilosophyPodcast, and the "sneaky maths" that saved #WesternThought! Keywords: #Boethius #ConsolationOfPhilosophy #RomanEmpire #LateAntiquity #MedievalPhilosophy #TemporalLogic #FreeWill #Causation #Providence #Fate #Quadrivium #HistoryOfMaths #HistoryPodcast
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 the powerful impact of teachers, both ancient and modern. Keywords: Hypatia, Alexandria, history of mathematics, female mathematicians, ancient philosophy, Neoplatonism, Theon of Alexandria, early Christianity, Roman Empire, ancient history, mathematics, philosophy, women in STEM, The Mathematicians Podcast. Hashtags: #Hypatia #HistoryOfMaths #WomenInMaths #AncientAlexandria #Philosophy #Neoplatonism #TheMathematiciansPodcast #HistoryPodcast #WomenInSTEM #AncientHistory
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
Producer's note
Steal the structure. Not the show.
Keep the useful structure, then change the audience, point of view, and voice until the idea is unmistakably yours.
