Historical figure · Pearson Edexcel International GCSE revision on Incandio

Brahmagupta

Incandio publishes no likeness of Brahmagupta: no photograph exists that is out of copyright or offered under a licence this product may use, and every candidate found was refused rather than stretched. In place of a face the app shows a deliberate cipher — a monogram set on a ruled manuscript page — because a missing photograph must never quietly demote the person. The life below is complete; only the picture is missing.

Who Gave Nothing Its Rules · Astronomer & Mathematician · 598 – c. 668

The astronomer who gave zero and negative quantities their arithmetic — the first person anywhere to write down the rules for calculating with nothing and with less than nothing.

Defend these ideas against Brahmagupta

Incandio is a free revision platform for the Pearson Edexcel International GCSE, and on it a topic counts as mastered only once you have learned it, proved it in questions, taught it back and defended it against the person with the strongest claim on it. Brahmagupta is that person for 2 topics on the course:

Who was Brahmagupta?

Brahmagupta was born in 598, probably at Bhillamala in what is now Rajasthan, and later directed the observatory at Ujjain, the foremost centre of astronomy in India. At the age of thirty he composed the Brahmasphutasiddhanta, the Correctly Established Doctrine of Brahma, in Sanskrit verse. It is principally a work of astronomy — planetary positions, eclipses, the calendar — but its eighteenth chapter contains the passage that made his name outside India. In it he sets out, as plainly as anyone sets out the rules for ordinary numbers, what happens when nothing and less-than-nothing are added, subtracted, multiplied and divided. He speaks of fortunes and of debts. The sum of two debts is a debt; a fortune and an equal debt make nothing; a debt subtracted from nothing becomes a fortune; the product of two debts is a fortune. Zero itself is treated as a number rather than as an absence: a quantity minus itself is zero, and zero added to anything leaves it unchanged. This was new. Earlier mathematics had a place-holder for an empty column, and Brahmagupta did not invent the numerals or the symbol; what he gave was the arithmetic. He was also a working astronomer of sharp temper, criticising Aryabhata repeatedly and by name, and he produced the formula for the area of a four-sided figure inscribed in a circle, an interpolation method, and important work on indeterminate equations. One of his rules is simply wrong: he states that zero divided by zero is zero. Around 770 an Indian embassy carried his book to Baghdad, where it was translated as the Sindhind — the route by which these methods reached the Islamic world and, eventually, Europe.

Major achievements

Life in brief

Explore the life of Brahmagupta — five chapters

  1. Bhillamala and Ujjain — An astronomer in a tradition of astronomers
  2. The Eighteenth Chapter — Fortunes, debts, and the arithmetic of nothing
  3. The Rule That Was Wrong — Nothing divided by nothing
  4. Against Aryabhata — What disagreement looked like in Sanskrit verse
  5. The Road to Baghdad — How a Sanskrit treatise reached Europe

Read the five-chapter life of Brahmagupta →

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