Melvyn Bragg and guests delve into the mysterious history of negative numbers, tracing their acceptance in math from Chinese solutions to European embrace. They explore the resistance faced, the contrast of mathematical progress across regions, the evolution of math into complex numbers, and the practical significance of negative numbers in science and technology.
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Quick takeaways
Negative numbers were initially considered non-existent and mysterious by some mathematicians, but gradually accepted through cultural exploration and practical applications.
Hamilton's contributions to understanding complex numbers as pairs of real numbers with unique rules of combination revolutionized mathematical perspectives and applications.
Deep dives
Negative Numbers Throughout History
Negative numbers have had a tumultuous history, initially being considered mysterious and non-existent by some, like Mazar and William Friend. Early mathematicians such as the Chinese, Indians, and Arabs began to explore the use of negative numbers in calculations. Western mathematicians, notably during the Renaissance, gradually accepted these perplexing numbers despite initial suspicions. The journey towards understanding negative numbers involved various cultures, mathematicians, and practical applications like commercial calculations.
Contribution of Mathematicians to Complex Numbers
Mathematicians like Hamilton made significant contributions to understanding complex numbers as pairs of real numbers with specific rules of combination. Hamilton's work introduced the concept of quaternions, extending the understanding beyond complex numbers to quadruples. This shift in perspective helped in applying complex numbers more effectively in various mathematical and scientific fields.
Hamilton's Innovations in Algebra
Hamilton's mathematical innovations centered around defining complex numbers as pairs of real numbers with unique multiplication rules. His approach aimed to provide a purely algebraic basis for the existence of complex numbers, diverging from traditional geometric interpretations. Hamilton's work laid the foundation for applying complex numbers in advanced mathematical concepts.
Practical Applications and Impact of Negative Numbers
Negative numbers and complex numbers have become integral in everyday mathematics, engineering, physics, and finance. While users often don't explicitly think about negative numbers in their calculations, they underpin various technological advancements and scientific theories. From financial valuation to electrical engineering and even Einstein's special relativity, negative and complex numbers continue to play vital roles across diverse fields.
Melvyn Bragg and guests discuss negative numbers, a history of mystery and suspicion. In 1759 the British mathematician Francis Maseres wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". Because of their dark and mysterious nature, Maseres concluded that negative numbers did not exist, as did his contemporary, William Friend. However, other mathematicians were braver. They took a leap into the unknown and decided that negative numbers could be used during calculations, as long as they had disappeared upon reaching the solution. The history of negative numbers is one of stops and starts. The trailblazers were the Chinese who by 100 BC were able to solve simultaneous equations involving negative numbers. The Ancient Greeks rejected negative numbers as absurd, by 600 AD, the Indians had written the rules for the multiplication of negative numbers and 400 years later, Arabic mathematicians realised the importance of negative debt. But it wasn't until the Renaissance that European mathematicians finally began to accept and use these perplexing numbers. Why were negative numbers considered with such suspicion? Why were they such an abstract concept? And how did they finally get accepted? With Ian Stewart , Professor of Mathematics at the University of Warwick; Colva Roney-Dougal , Lecturer in Pure Mathematics at the University of St Andrews; Raymond Flood , Lecturer in Computing Studies and Mathematics at Kellogg College, Oxford.
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