Eric Temple Bell (1883-1960) was a Scottish-born mathematician and science fiction writer who also wrote extensively about the history of mathematics. His book Historia de las matemÃ¡ticas, first published in 1937, is a comprehensive and engaging account of the development of mathematical ideas and discoveries from ancient times to the 20th century.
Bell's style is lively and accessible, combining historical facts with anecdotes and insights. He also discusses the philosophical and cultural implications of mathematics, as well as its connections with other sciences and arts. He shows how mathematics is not only a collection of abstract symbols and rules, but also a creative and human endeavor that reflects the spirit of its times.
Historia de las matemÃ¡ticas is a classic work that has been translated into several languages and reprinted many times. It is a valuable resource for anyone who wants to learn more about the history and evolution of mathematics. You can find it online in PDF format for free[^1^] [^2^] [^3^].
In the following paragraphs, we will summarize some of the main themes and highlights of Bell's book, following his chronological and thematic division. We will also mention some of the criticisms and limitations of his approach, as well as some of the updates and corrections that have been made by later historians of mathematics.
The Age of Empiricism: A Firm Foundation (Greece 600 BC - 300 AD)
This section covers the origins and achievements of Greek mathematics, from the early Pythagoreans and their discovery of irrational numbers, to the classical works of Euclid, Archimedes, Apollonius, and Diophantus. Bell emphasizes the role of geometry as the main source of mathematical rigor and proof, as well as the development of algebraic methods and notation. He also discusses the influence of astronomy, mechanics, and optics on mathematical research.
The European Depression: The Detour through India, Arabia, and Spain (400-1300)
This section deals with the decline and stagnation of mathematics in Europe during the Middle Ages, and the transmission and preservation of mathematical knowledge by other civilizations, especially India, Arabia, and Spain. Bell highlights the contributions of Indian mathematicians such as Aryabhata, Brahmagupta, Bhaskara II, and Mahavira to topics such as decimal notation, zero, negative numbers, algebraic equations, trigonometry, and calculus. He also acknowledges the role of Arabic mathematicians such as Al-Khwarizmi, Al-Karaji, Al-Biruni, Al-Haytham, Omar Khayyam, and Nasir al-Din al-Tusi in advancing algebra, arithmetic, geometry, astronomy, and optics. He also mentions some of the European scholars who learned from these sources, such as Fibonacci, Adelard of Bath, and Gerard of Cremona.
Four Centuries of Transition (1202-1603)
This section covers the gradual revival and transformation of mathematics in Europe from the 13th to the 16th centuries. Bell traces the emergence of new mathematical concepts and techniques such as logarithms, analytic geometry, algebraic notation, complex numbers, and symbolic manipulation. He also explores the impact of new discoveries and inventions such as printing, gunpowder, navigation, and perspective on mathematical practice and education. He introduces some of the leading figures of this period such as Vieta, Cardano, Tartaglia, Bombelli, Napier, Stevinus, Kepler, Galileo, and others.