The Mathematicians Podcast

Brahmagupta
What does it take to call yourself a mathematician? Is it enough to enjoy a Sudoku, or should you be able to solve an equation that would keep most of us busy for a year? And how do you go about making nothing into something?

In this episode of The Mathematicians Podcast, we meet Brahmagupta, one of the great figures of the Indian mathematical tradition. Born around 600 CE, Brahmagupta made extraordinary contributions to arithmetic, algebra, geometry and astronomy. He also seems to have had a rather high opinion of his own abilities; which, given the mathematics, might be difficult to argue with.

We explore his treatment of zero as a number in its own right, his rules for negative numbers expressed through the language of debts and fortunes, and his algorithms for multiplication and square roots. We also encounter cyclic quadrilaterals, a rather elegant result involving perpendicular diagonals, and the famous problem that challenges anyone wishing to call themselves a mathematician.

Along the way, we look at how mathematical ideas travelled from India into the Islamic world and beyond, and ask what happens when the history of mathematics is told through the surviving records of colonial scholarship. Because mathematical truth may be universal, but the stories we tell about it are anything but neutral.

And, naturally, there are a few quadrilaterals, some questionable puns, and an opportunity to become a mathematician yourself.

In this episode we discuss:

Brahmagupta's life and work in seventh-century India.

The Brahmasphuṭasiddhānta and Khaṇḍakhādyaka.

Zero as a number, and the arithmetic of debts and fortunes.

The development and acceptance of negative numbers.

Early algorithms for multiplication and square roots.

The relationship between Brahmagupta's method and the work of Heron and Newton.

Cyclic quadrilaterals, Brahmagupta's theorem and the area formula.

The Brahmagupta identity and the solution of indeterminate quadratic equations.

Pell equations and the search for integer solutions.

Quadratic interpolation and the calculation of sine values.

The transmission of Indian mathematics into the Islamic world and Europe.

The role of translation, colonialism and historical perspective in deciding whose mathematics gets remembered.

Oh my gosh, all that and more.

A link: H. T. Colebrooke's 1817 translation of Brahmagupta and Bhāskara II:
https://www.hist-math.fr/textes/Colebrooke1817_BrahmeguptaBhaskaracharya.pdf

 

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Keywords
Brahmagupta, Indian mathematics, history of mathematics, zero, negative numbers, algebra, arithmetic, quadratic equations, Brahmagupta identity, Pell equation, cyclic quadrilaterals, Brahmagupta's theorem, square root algorithms, interpolation, sine tables, Aryabhata, Heron of Alexandria, Islamic Golden Age, mathematical history, ancient mathematics, Colebrooke.

Hashtags
#Mathematics #HistoryOfMathematics #MathsHistory #MathsPodcast #TheMathematiciansPodcast #Brahmagupta #IndianMathematics #HistoryOfScience #Algebra #Zero #NumberTheory

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.

 

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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

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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

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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/