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Did Indian mathematicians have a philosophy of zero?

Vikram Sethi Fellow
· 3 replies
Philosophy of mathematicsIndian#history-of-mathematics#zero
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Brahmagupta's Brāhmasphuṭasiddhānta (628 CE) gives rules for arithmetic with zero as a number: adding zero to a number leaves it unchanged, multiplying by zero gives zero, and so on. He also tried to define division by zero, not quite successfully. Earlier, the prosodist Piṅgala used the word śūnya in his work on metres.

People often link this to the Buddhist concept of śūnyatā (emptiness), and to Indian philosophy's interest in absence (abhāva) as a category. Is that link real, or a romantic story? Did Indian mathematicians have a philosophy of zero, or just very good arithmetic?

3 answers

  1. Meera Kulkarni

    Fellow

    The link is plausible but unproven. What's clearer is that Nyāya-Vaiśeṣika treated absence (abhāva) as a real category, with types like prior absence and absolute absence. A culture comfortable treating absence as something you can know and talk about might find zero as a number less strange.

    Helpful · 1
  2. Tomasz Wójcik

    Fellow

    Whatever the origin, treating zero as a number rather than a placeholder is a conceptual step. Babylonian and Mayan systems had placeholders. Brahmagupta's rules treat zero as something you can operate on, which is what makes it mathematics rather than notation.

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  3. Layla Haddad

    Fellow

    It travelled through Arabic: al-Khwārizmī's work on Indian numerals in the ninth century, then Latin translations, then Fibonacci in 1202. The Arabic ṣifr (empty) became Latin zephirum, Italian zero, and also English "cipher". The word itself carries the idea of emptiness the whole way.

    Helpful · 3

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