Bhāskara, also made major contributions to algebra, arithmetic, geometry and trigonometry. Calculus is used to measure rates of changes and is important in almost every branch of science, notably underpinning many key discoveries in modern physics.īut Indian mathematician Bhāskara had already discovered many of Leibniz’s ideas over 500 years earlier. Gottfried Wilhelm Leibniz was one of the first Europeans to use zero and the negatives in a systematic way in his development of calculus in the late 17th century. This reluctance to adopt negative numbers, and indeed zero, held European mathematics back for many years. From then on, every cow he buys goes to his positive total. If the first farmer goes out to buy some animals to repay his debt, he has to buy 7 cows and give them to the second farmer in order to bring his cow tally back to 0. Indian and Chinese mathematicians recognised early on that one answer to this question was debts.įor example, in a primitive farming context, if one farmer owes another farmer 7 cows, then effectively the first farmer has -7 cows. They reasoned that numbers were developed for counting and questioned what you could count with negative numbers. Many took the view that negative numbers were absurd. Brahmagupta also knew that “The product of a debt and a fortune is a debt” – a positive number multiplied by a negative is a negative.įor the large part, European mathematicians were reluctant to accept negative numbers as meaningful. This latter statement is the same as the rule we learn in school, that if you subtract a negative number, it is the same as adding a positive number. He wrote down rules that have been interpreted by translators as: “A fortune subtracted from zero is a debt,” and “a debt subtracted from zero is a fortune”. He referred to positive numbers as fortunes and negative numbers as debts. Rules for negative numbersīrahmagupta also demonstrated rules for working with negative numbers. In his seminal text, the astronomer Brahmagupta introduced rules for solving quadratic equations (so beloved of secondary school mathematics students) and for computing square roots. In the seventh century, the first written evidence of the rules for working with zero were formalised in the Brahmasputha Siddhanta. In comparison, these sorts of tools were not popularised in the West until the early 13th century, though Fibonnacci’s book liber abaci. These accessible mechanical tools for working with mathematical concepts, in combination with a strong and open scholastic and scientific culture, meant that, by around 600AD, all the ingredients were in place for an explosion of mathematical discoveries in India. It is reasonable to believe that this representation using powers of ten played a crucial role in the development of the decimal-place value system in India. For example, 365 might be expressed as three hundreds (3x10²), six tens (6x10¹) and five units (5x10⁰), though each power of ten was represented with a name rather than a set of symbols. In these texts, numbers were commonly expressed as combinations of powers of ten. The number systemĪs far back as 1200 BC, mathematical knowledge was being written down as part of a large body of knowledge known as the Vedas. Perhaps most significantly, the decimal system that we still employ worldwide today was first seen in India. Mathematics on the Indian subcontinent has a rich history going back over 3,000 years and thrived for centuries before similar advances were made in Europe, with its influence meanwhile spreading to China and the Middle East.Īs well as giving us the concept of zero, Indian mathematicians made seminal contributions to the study of trigonometry, algebra, arithmetic and negative numbers among other areas. It should come as no surprise that the first recorded use of the number zero, recently discovered to be made as early as the 3rd or 4th century, happened in India.
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