Mathematics

  • Story of Maths

    Four part series about the history of mathematics, presented by Oxford professor Marcus du Sautoy.

    In the first episode, The Language of the Universe, after showing how fundamental mathematics is to our lives, du Sautoy explores the mathematics of ancient Egypt, Mesopotamia and Greece. In Egypt, he uncovers use of a decimal system based on ten fingers of the hand, while in former Mesopotamia he discovers that the way we tell the time today is based on the Babylonian Base 60 number system. In Greece, he looks at the contributions of some of the giants of mathematics including Plato, Euclid, Archimedes and Pythagoras, who is credited with beginning the transformation of mathematics from a tool for counting into the analytical subject we know today.

    The second episode, The Genius of the East, sees du Sautoy leaving the ancient world. When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. Du Sautoy visits China and explores how maths helped build imperial China and was at the heart of such amazing feats of engineering as the Great Wall. In India, he discovers how the symbol for the number zero was invented and Indian mathematicians' understanding of the new concepts of infinity and negative numbers. In the Middle East, he looks at the invention of the new language of algebra and the spread of Eastern knowledge to the West through mathematicians such as Leonardo Fibonacci, creator of the Fibonacci Sequence.

    The Frontiers of Space. By the 17th century, Europe had taken over from the Middle East as the world's powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was now on to discover the mathematics to describe objects in motion. In the third part of the series, Marcus du Sautoy explores the work of René Descartes and Pierre Fermat, whose famous Last Theorem would puzzle mathematicians for more than 350 years. He also examines Isaac Newton's development of the calculus, and goes in search of Leonard Euler, the father of topology or 'bendy geometry' and Carl Friedrich Gauss, who, at the age of 24, was responsible for inventing a new way of handling equations: modular arithmetic.

    The fourth episode, To Infinity and Beyond, concludes the series. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he looks at how mathematics was itself thrown into chaos by the discoveries of Kurt Godel, who showed that the unknowable is an integral part of maths, and Paul Cohen, who established that there were several different sorts of mathematics in which conflicting answers to the same question were possible. He concludes his journey by considering the great unsolved problems of mathematics today, including the Riemann Hypothesis, a conjecture about the distribution of prime numbers. A million dollar prize and a place in the history books await anyone who can prove Riemann's theorem.

    4 Part series total running time 295 Min.

  • A Brilliant Madness: John Nash

    A Brilliant Madness is the story of a mathematical genius whose career was cut short by a descent into madness. At the age of 30, John Nash, a stunningly original and famously eccentric MIT mathematician, suddenly began claiming that aliens were communicating with him and that he was a special messenger.

    Diagnosed with paranoid schizophrenia, Nash spent the next three decades in and out of mental hospitals, all but forgotten. During that time, a proof he had written at the age of 20 became a foundation of modern economic theory. In 1994, as Nash began to show signs of emerging from his delusions, he was awarded a Nobel Prize in Economics. The program features interviews with John Nash, his wife Alicia, his friends and colleagues, and experts in game theory and mental illness.

    Go beyond the Oscar-winning drama "A Beautiful Mind" and learn more about the life of troubled mathematician and Nobel Prize-winner John Nash and his struggle with mental illness in this PBS "American Experience" documentary. Exclusive interviews with Nash and wife Alicia are included.

    Running time 55 Min.

  • Arithmetic, Population and Energy (Lecture)

    Professor Al Bartlett begins his one-hour talk with the statement, The greatest shortcoming of the human race is our inability to understand the exponential function.

    He then gives a basic introduction to the arithmetic of steady growth, including an explanation of the concept of doubling time. He explains the impact of unending steady growth on the population of Boulder, of Colorado, and of the world.

    He then examines the consequences steady growth in a finite environment and observes this growth as applied to fossil fuel consumption, the lifetimes of which are much shorter than the optimistic figures most often quoted.

    Running time 1 hour, 14 minutes.

  • Dangerous Knowledge

    In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.

    The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity.

    Ludwig Boltzmann's struggle to prove the existence of atoms and probability eventually drove him to suicide. Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death.

    Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

    The film also talks to the latest in the line of thinkers who have continued to pursue the question of whether there are things that mathematics and the human mind cannot know. They include Greg Chaitin, mathematician at the IBM TJ Watson Research Center, New York, and Roger Penrose.

    Dangerous Knowledge tackles some of the profound questions about the true nature of reality that mathematical thinkers are still trying to answer today.

    2 parts 44 min each.

  • Dimensions: A Walk Through Mathematics

    A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed!

    Dimension Two - Hipparchus shows us how to describe the position of any point on Earth with two numbers... and explains the stereographic projection: how to draw a map of the world.

    Dimension Three - M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like.

    The Fourth Dimension - Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension... and shows a parade of four-dimensional polytopes, strange objects with 24, 120 and even 600 faces!

    Complex Numbers - Mathematician Adrien Douady explains complex numbers. The square root of negative numbers made easy! Transforming the plane, deforming images, creating fractal images...

    Fibration - Mathematician Heinz Hopf explains his "fibration". Using complex numbers he constructs pretty patterns of circles in space. Circles, tori... everything rotating in four-dimensional space.

    Proof - Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem concerning the stereographic projection. Support the authors and buy the DVD here.

    Running time 125 Min.

  • Fermat's Last Theorem

    Simon Singh and John Lynch’s film tells the enthralling and emotional story of Andrew Wiles. A quiet English mathematician, he was drawn into maths by Fermat’s puzzle, but at Cambridge in the ’70s, FLT was considered a joke, so he set it aside. Then, in 1986, an extraordinary idea linked this irritating problem with one of the most profound ideas of modern mathematics: the Taniyama-Shimura Conjecture, named after a young Japanese mathematician who tragically committed suicide.

    The link meant that if Taniyama was true then so must be FLT. When he heard, Wiles went after his childhood dream again. “I knew that the course of my life was changing.” For seven years, he worked in his attic study at Princeton, telling no one but his family. “My wife has only known me while I was working on Fermat”, says Andrew.

    In June 1993 he reached his goal. At a three-day lecture at Cambridge, he outlined a proof of Taniyama – and with it Fermat’s Last Theorem. Wiles’ retiring life-style was shattered. Mathematics hit the front pages of the world’s press. Then disaster struck. His colleague, Dr Nick Katz, made a tiny request for clarification. It turned into a gaping hole in the proof. As Andrew struggled to repair the damage, pressure mounted for him to release the manuscript – to give up his dream. So Andrew Wiles retired back to his attic. He shut out everything, but Fermat.

    A year later, at the point of defeat, he had a revelation. “It was the most important moment in my working life. Nothing I ever do again will be the same.” The very flaw was the key to a strategy he had abandoned years before. In an instant Fermat was proved; a life’s ambition achieved; the greatest puzzle of maths was no more.

    Running time 49 min.

  • Fractals: Hunting the Hidden Dimension

    Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature. You may not know it, but fractals, like the air you breathe, are all around you.

    Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart.

    In this film, we takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry.

    Running time 52 min.

  • Fractals: The Colors of Infinity

    The Mandelbrot set - someone has called it the thumb-print of God - is one of the most beautiful and remarkable discoveries in the entire history of mathematics.

    With Arthur C. Clarke as narrator and interviews with a number of notable mathematicians, including Benoît Mandelbrot, this program graphically illustrates how simple formulas can lead to complicated results: it explains the set, what it means, its internal consistency, and the revolutions in thought resulting from its discovery. Asked if the real universe goes on forever, Stephen Hawking defines its limit of smallness; the Mandelbrot set, on the other hand, may go on forever.

    The invention of the silicon chip in the 1970's created a revolution in computers and communication and hence transformed our way of life. We are now seeing another revolution which is going to change our view of the universe and give us a better understanding of its' working.

    This film will explore the fractal universe and on our voyage of discovery, we will be helped by: Professor Ian Stewart of the Mathematics Institute, University of Warwick, an author of over 100 published scientific works; Dr. Michael Barnsley, former professor of mathematics at Georgia Institute of Technology who received a 2.5 million dollar government grant in 1991 to develop a fractal image compression systems.

    Running time 64 min.

  • Genius of Pythagoras

    This Documentary describes Pythagoras. It was produced by Cromwell Productions in 1996.

    Pythagoras (fl. 530 BCE) must have been one of the world’s greatest men, but he wrote nothing, and it is hard to say how much of the doctrine we know as Pythagorean is due to the founder of the society and how much is later development.

    The word Genius perfectly describes Pythagoras; at times his ideas and theories were so radical, they were considered dangerous or subversive by the rulers of their day.

    Set against the backdrop of Ancient Greece, this film tells the story of a true genius. Immortalized in the popular imagination by a single mathematical theorem, Pythagoras' place in history was assured.

    Running time 45 min.

  • High Anxieties: The Mathematics of Chaos

    The documentary looks at the modern advances in mathematics and how they affect our understanding of physics, economics, environmental issues and human psychology.

    The film looks at how developments in 20th Century mathematics have affected our view of the world, and particularly how the financial economy and earth’s environment are now seen as inherently unpredictable.

    The film looks at the influence the work of Henri Poincare and Alexander Lyapunov had on later developments in mathematics. It includes interviews with David Ruelle, about chaos theory and turbulence, the economist Paul Ormerod about the unpredictability of economic systems, and James Lovelock the founder of Gaia theory about climate change and tipping points in the environment.

    As we approach tipping points in both the economy and the climate, the film examines the mathematics we have been reluctant to face up to and asks if, even now, we would rather bury our heads in the sand rather than face harsh truths.

    Running time 60 min.

  • Infinity and Beyond

    Documentary examining current ideas about very large numbers and infinity in regards to mathematics and the observable universe.

    By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever.

    But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.

    Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last.

    And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you.

    Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

    Running time 59 min.

  • The Story of One

    Our world is built on numbers and the first of these was the number 1. Starting with scratches on a bone and heading through the Greek philosophers to the development of the Roman Numerals and the Arabic number system that fed through to the numbers we use today.

    Using Terry Jones semi-comic presentation style, the film is built on two key aspects. The main part of the film is based on Jones' narration, the actual words he says. Without being aloof or inaccessible, the film tells the story in a fascinating and enlightening way – never going into too much detail but doing enough to actually make you feel like you have learn something and have a very broad knowledge base on which to go off and find out more.

    Running time 59 min.