The Mathematicians Podcast

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

 

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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/