Topics in the History of Mathematics
BBC Open University Productions
- The Emergence of Greek Mathematics
- The Vernacular Tradition
- Marin Mersenne: The Birth of Modern Geometry
- The Founding of the Royal Society
- The Birth of Calculus
- Non-Euclidean Geometry
- Paris and the New Mathematics
- The Liberation of Álgebra
The Emergence of Greek Mathematics
The Vernacular Tradition
Deals largely with the low-level mathematics of the Middle Ages and its application to problems of commerce and everyday life. Renaissance notational styles are compared by looking at the works of Luca Pacioli and Nicholas Chuquet. Each of these works were compendiums of basic mathematical knowledge which themselves derive from the work of Leonardo of Pisa, also known as Fibonacci. Leonardo’s ‘Liber Abaci’ was the first in Europe to promote calculation methods using the Hindu-Arabic numerals. Illustrates a problem-solving method known as double false position, which could be used to solve algebraic-type problems without any knowledge of algebra. These methods owe their inspiration to a work by an Islamic mathematician, Al-Khwarizmi. Shows his method of solving quadratic equations. Concludes by showing how the Hindu-Arabic numeral system developed and was adopted first in the Arabic countries, then later in Europe.
Marin Mersenne: The Birth of Modern Geometry
Marin Mersenne was a 17th-century French monk who was also an able scientist who wrote widely on the study of sound. His contribution to mathematics comes from his ambition to see the formation of scientific societies. Amongst the great discoveries of the time, which Mersenne had a part in publicising, are Roberval’s method for the calculation of the area under a cycloid, Descartes’ method of co-ordinate geometry, Desargues’ projective geometry, and Pascal’s theorem on the hexagon. The concepts of Mersenne led to the foundation of the French Academy of Science shortly after his death. Re-creates the character of Mersenne, interspersed with animation and studio demonstrations constructed to match readings from the works of some of the mathematicians of the time. Uses contemporary etchings, books and music to reconstruct the mood of the period.
The Founding of the Royal Society
Describes the various scientific groups that began to form in 17th-century England: at Gresham College, London, in 1645 and in Oxford in 1657, culminating with the founding of the Royal Society in 1660. Looks at the problems addressed by the society, particularly the calculation of longitude at sea, which lead to the foundation of the Royal Greenwich Observatory. Discusses Newton’s ‘Principia Mathematica’ of 1687.
The Birth of Calculus
With the discovery of calculus, mathematics received its greatest boost since the time of the Greeks. Discusses the early work of Newton and Leibniz that led to their independent formulations of the methods of calculus. Filmed in Cambridge, tracing Newton’s lines of thought through his notebooks, and in Hanover, where Leibniz’s original notes are stored, noting his very different approach to the same problem.
During the 18th and 19th centuries mathematicians were increasingly questioning the foundations of geometry. Shows how investigations led to the development of non-Euclidean geometry, discussing the work of Saccheri, Lambert, Bolyai, Lobachevskii and Beltrami.
Paris and the New Mathematics
During the French Revolution the new republic saw mathematics as a tool to be used in its service. Describes some of the revolutionary mathematics and the developments that were to arise from it. Centres around the the life of one of France’s greatest revolutionary mathematicians, Gaspard Monge, who was to found the École Polytechnique, originally to train military engineers. It was there that post-revolutionary mathematicians trained and did their research. Looks at the library of the present-day École Polytechnique and the early 19th-century books and papers which chronicle this period of French educational reform.
The Liberation of Álgebra
Looks at the work of William Rowan Hamilton in Dublin and George Boole in Cork. Uses Hamilton’s discovery of quaternions to Boole’s ’The Laws of Thought’, as the foundations for work in the fields of astrophysics and computer design.