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:
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Brahmagupta's life and work in seventh-century India.
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The Brahmasphuṭasiddhānta and Khaṇḍakhādyaka.
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Zero as a number, and the arithmetic of debts and fortunes.
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The development and acceptance of negative numbers.
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Early algorithms for multiplication and square roots.
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The relationship between Brahmagupta's method and the work of Heron and Newton.
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Cyclic quadrilaterals, Brahmagupta's theorem and the area formula.
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The Brahmagupta identity and the solution of indeterminate quadratic equations.
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Pell equations and the search for integer solutions.
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Quadratic interpolation and the calculation of sine values.
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The transmission of Indian mathematics into the Islamic world and Europe.
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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
