History of Mathematics

From this page you can access a collection of materials dealing with some important areas from the History of Mathematics. For Maynooth University students, this material is typically covered in parts of History of Mathematics (MT382A). These resources are not a replacement for the material covered in your lectures and assignments, rather you should use them as extra support to aid your understanding of any material you may have difficulties with.

Miscellaneous - General

Podcasts - General

In our time (with Melvyn Bragg) podcasts from BBC4

  • Maths in the Early Islamic World Melvyn Bragg and guests discuss the flourishing of maths in the early Islamic world, as thinkers from across the region developed ideas in places such as Baghdad's House of Wisdom. Among them were the Persians Omar Khayyam, who worked on equations, and Al-Khwarizmi, latinised as Algoritmi and pictured above, who is credited as one of the fathers of algebra, and the Jewish scholar Al-Samawal, who converted to Islam and worked on mathematical induction. As well as the new ideas, there were many advances drawing on Indian, Babylonian and Greek work and, thanks to the recording or reworking by mathematicians in the Islamic world, that broad range of earlier maths was passed on to western Europe for further study. (February 2017).
  • Johannes Kepler Melvyn Bragg and guests discuss the German astronomer Johannes Kepler (1571 - 1630). Although he is overshadowed today by Isaac Newton and Galileo, he is considered by many to be one of the greatest scientists in history. The three laws of planetary motion Kepler developed transformed people's understanding of the Solar System and laid the foundations for the revolutionary ideas Isaac Newton produced later. Kepler is also thought to have written one of the first works of science fiction. However, he faced a number of challenges. He had to defend his mother from charges of witchcraft, he had few financial resources and his career suffered as a result of his Lutheran faith. (December 2016).
  • Charles Babbage was a British polymath, mathematician and a man widely hailed as the father of modern computing. In this special episode, host Emma Duncan is joined by two renowned computer science experts to explore the life and work of the eponymous inventor.
  • Euclid's Elements Melvyn Bragg and guests discuss Euclid's Elements, a mathematical text book attributed to Euclid and in use from its appearance in Alexandria, Egypt around 300 BC until modern times, dealing with geometry and number theory. It has been described as the most influential text book ever written. (April 2016).
  • P vs NP Melvyn Bragg and guests discuss the problem of P versus NP, which has a bearing on online security. There is a $1,000,000 prize on offer from the Clay Mathematical Institute for the first person to come up with a complete solution. At its heart is the question "are there problems for which the answers can be checked by computers, but not found in a reasonable time?" If the answer to that is yes, then P does not equal NP. However, if all answers can be found easily as well as checked, if only we knew how, then P equals NP. The area has intrigued mathematicians and computer scientists since Alan Turing. (November 2015).
  • e Euler's number, also known as e, was first discovered in the 17th century by the Swiss mathematician Jacob Bernoulli when he was studying compound interest. e is now recognised as one of the most important and interesting numbers in mathematics. Roughly equal to 2.718, e is useful in studying many everyday situations, from personal savings to epidemics. It also features in Euler's Identity, sometimes described as the most beautiful equation ever written (September 2014).
  • Bishop Berkeley George Berkeley, an Anglican bishop, was one of the most important philosophers of the 18th century. Bishop Berkeley believed that objects only truly exist in the mind of somebody who perceives them - an idea he called immaterialism. His work on the nature of perception was a spur to many later thinkers, including Hume and Kant. The clarity of Berkeley's writing, and his ability to pose a problem in an easily understood form, has made him one of the most admired early modern thinkers (March 2014).
  • Pascal Pascal was a brilliant 17th-century mathematician and scientist who invented one of the first mechanical calculators and made important discoveries about fluids and vacuums while still a young man. In his thirties he experienced a religious conversion, after which he devoted most of his attention to philosophy and theology. Although he died in his late thirties, Pascal left a formidable legacy as a scientist and pioneer of probability theory, and as one of seventeenth century Europe's greatest writers (September 2013).
  • Bertrand Russell Melvyn Bragg and his guests discuss the influential British philosopher Bertrand Russell. Born in 1872, Russell is widely regarded as one of the founders of Analytic philosophy, today the dominant philosophical tradition in the English-speaking world. His theory of descriptions had profound consequences for the discipline. Russell also played an active role in many social and political campaigns. He supported women's suffrage, was imprisoned for his pacifism during World War I and was a founder of the Campaign for Nuclear Disarmament (December 2012).
  • Fermat's Last Theorem Melvyn Bragg and his guests discuss Fermat's Last Theorem. In 1637 the French mathematician Pierre de Fermat scribbled a note in the margin of one of his books. He claimed to have proved a remarkable property of numbers, but gave no clue as to how he'd gone about it. Fermat's theorem became one of the most iconic problems in mathematics and for centuries mathematicians struggled in vain to work out what his proof had been. It was not until 1995 that the puzzle was finally solved by the British mathematician Andrew Wiles (October 2012).
  • Game Theory Melvyn Bragg and his guests discuss game theory, the mathematical study of decision-making. Some of the games studied in game theory have become well known outside academia - they include the Prisoner's Dilemma, an intriguing scenario popularised in novels and films. Today game theory is seen as an important tool in evolutionary biology, economics, computing and philosophy (May 2012).
  • Ptolemy Melvyn Bragg and his guests discuss the ancient Greek astronomer and mathematician Ptolemy, and consider how and why his geocentric theory of the universe held sway for more than a thousand years. It was not until 1543, and Copernicus's heliocentric theory of the world, that the Ptolemaic model was finally challenged. But how and why did Ptolemy's system survive for so long? (November 2011).
  • Logic The philosophy of logic - first mapped out by Aristotle in the 4th century BC; disregarded by Descartes in the 17th century and revived and reworked by Gottlob Frege in the 19th century; logic is at the heart of computer science and is a mathematical as well as a philosophical disclipline (October 2010).
  • Imaginary Numbers The concept of imaginary numbers. Perplexing digits that underpin the majority of technology we take for granted today, from radios to computers to MRI scans; not to mention quantum mechanics (September 2010).
  • Mathematics' Unintended Consequences Melvyn Bragg and guests explore the unintended consequences of mathematical discoveries (February 2010).
  • Pythagoras Melvyn Bragg and guests discuss the ideas of Pythagoras and the Pythagoreans (December 2009).
  • Calculus The dispute between Sir Isaac Newton and Gottfried Leibniz over who invented calculus (September 2009).
  • Godel’s Incompleteness Theorems Melvyn Bragg and guests discuss the mathematician Kurt Godel and his work (October 2008).
  • Probability Melvyn Bragg and guests discuss the strange mathematics of probability (May 2008).
  • The Fibonacci Sequence Melvyn Bragg discusses the mathematical and cultural mysteries of the Fibonacci Sequence (November 2007).
  • Symmetry Melvyn Bragg discusses the idea of symmetry in art and nature (April 2007).
  • Archimedes Melvyn Bragg discusses the Greek mathematician Archimedes and his famous cry of “eureka!” (January 2007).
  • Indian Mathematics Melvyn Bragg and guests discuss the 5000 year long story of Indian Maths (December 2006).
  • The Poincaré Conjecture Melvyn Bragg and guests discuss a puzzle that may explain the shape of the universe (November 2006).
  • Negative Numbers Melvyn Bragg and guests discuss negative numbers, a history of mystery and suspicion (March 2006).
  • Renaissance Maths Melvyn Bragg explores Renaissance Mathematics, when maths moved from an art to a science (June 2005).
  • Pi Melvyn Bragg examines the history of the longest and most detailed number in nature (September 2004).
  • Zero Melvyn Bragg examines the number between 1 and -1, once denounced as the devil's work (May 2004).
  • Cryptography Melvyn Bragg and guests discuss the origins and history of codes (January 2004).
  • Infinity Melvyn Bragg and guests discuss the nature and existence of mathematical infinity (October 2003).
  • The Calendar Melvyn Bragg explores the ancient origins of our Gregorian calendar (December 2002).
  • Mathematics and Platonism Melvyn Bragg examines whether mathematics is a process of invention or of discovery (January 2001).
  • Mathematics Melvyn Bragg examines the importance of mathematics in relation to other sciences (May 1999).