Euclid’s Elements has been the best-selling mathematics book of all time, being used continuously for over 2000 years. Who was Euclid, and why did his writings have such influence? What does the Elements contain, and why did it create so much controversy over the years?
Who invented algebra?
Arabic mathematicians embraced the mathematics of Ancient Greece and India. What did they do, and how did their achievements influence Europe in the Middle Ages? We trace the story up to the establishment of universities, the development of perspective in art, and Fibonacci’s problem of the rabbits.
Who invented the calculus? - and other 17th century topics
The development of the calculus brought together two seemingly unrelated problems: how do things change, and how large are they? We develop the story from the early days of logarithms in Gresham College, to Newton’s work on gravitation and the calculus, and ask: Did the apple really fall on Newton’s head?
Problems with schoolgirls
Block designs are used in agriculture in connection with the planting of wheat. But earlier they arose in the so-called ‘schoolgirls problem’. What are block designs, what is the schoolgirls problem, and what is their connection with geometry and music?
How hard is a hard problem?
How can we distinguish between 'easy problems' and 'hard problems'? In this lecture I shall explain what is meant by an 'algorithm', and present some celebrated algorithms that can be used to solve a range of practical problems. I then investigate the efficiency of these algorithms and describe what is meant by a 'polynomial algorithm'. Finally, I shall explain the symbols P and NP, and pose ?the most important unsolved problem in current mathematics?: does P = NP?
Much ado about zero
The concept of zero developed in many cultures over thousands of years. Why did such a 'natural' idea take so long? This lecture illustrated the wide-ranging mathematical achievements of China, India and Central America over a thousand-year period - some not to be rediscovered in Europe for a further thousand years - before returning to the elusive origins of zero.
Most people know the story of Newton and the apple, but why was it so important? What sort of person was Newton? What was his major work Principia Mathematica about, what difficulties did it raise, and how were they resolved? Was Newton really the first to discover the calculus, and why did it matter?
Maps, Maidens and Molecules
How many colours are needed to colour a map? What was the 15 schoolgirl’s problem? How many alcohols and paraffins are there? This talk visits the fascinating world of Victorian mathematics and the contributions to it by eccentric lawyers, academics and clergymen.
Prime numbers form the building blocks of arithmetic. But if we make a list of them, many questions arise. Pairs of primes differing by 2 (such as 5 and 7, or 101 and 103) seem to occur 'all the way up', but there can also be huge gaps between successive primes.
So how are the prime numbers distributed? The Riemann hypothesis is a major unsolved problem whose solution would help us to answer this question.
Who invented the equals sign?
With the invention of printing, mathematical writings became widely available for the first time. What influence did this have? We discuss this question in the context of 16th-century navigation and astronomy, the solving of equations, and some breakthroughs in geometry and algebra, and ask: is this a record?
The story of e
The story of i
The story of pi
And many more- go over lectures by Robin Wilson
Others worth having a look- Raj Perasaud, John Barrow, Avinash Persaud