While some might not automatically put math and documentary together, we’re able to recommend the following list.
1. Dimensions: A Walk Through Mathematics
A film for a wide audience. Nine chapters, two hours of math, 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.
2. 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.
The other aspect is the delivery style – colorful, irreverent and fun. Mostly this works and the graphics and comedy add entertainment value to the film without taking away from the interesting content; however at times the constant computerized numbers do get a little annoying and I did want it to be too cheerful and populist but I suppose it was damned if it does and damned if it doesn't.
Jones is a good presenter because he holds these two directions together – seeming genuinely enticed by the subject while also enjoying himself. He is perfect for the broad approaching while he also drops in some great little bits of trivia (the word bankrupt coming from the Italian courts punishing a cheating banker by breaking his table; or the Italian zero being so mistrusted as a symbol that its original name giving us the word "cipher" today).
Overall, it may annoy the more aloof viewer of intellectual, stuffy documentaries about math and science but this film succeeds in presenting the potentially dull subject in such a lively and entertaining manner that it deserves the audience it won. Perhaps a little too populist at times, it is still very interesting and enjoyable and is the sort of programme that almost makes you think that the BBC is fulfilling its public service charter.
3. The 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 math 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 math, 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. N is a Number: A Portrait of Paul Erdös
In an age when genius is a mere commodity, it is useful to look at a person who led a rich life without the traditional trappings of success.
A man with no home and no job, Paul Erdös was the most prolific mathematician who ever lived. Born in Hungary in 1913, Erdös wrote and co-authored over 1,500 papers and pioneered several fields in theoretical mathematics. At the age of 83 he still spent most of his time on the road, going from math meeting to math meeting, continually working on problems. He died on September 20, 1996 while attending such a meeting in Warsaw, Poland.
The film opens at Cambridge University's 1991 honorary doctorate ceremony, where Erdös received an award he says he would gladly trade for a "nice new proof." For Erdös, the meaning of life is "to prove and conjecture."
The structure of N is a Number is based on Erdös's 50 years of perpetual wandering, "like a bumblebee," carrying news and mathematical information from university to university. Erdös established himself as a serious mathematician at the age of 20 when he devised a more elegant proof for Chebyshev's theorem, i.e., that there is always a prime number between any number and its double.
N is a Number is a one-hour 16mm documentary filmed over a four-year period in four countries between 1988 and 1991. The film was produced, directed and edited by George Paul Csicsery. Cinematography is by John Knoop and original music was composed by Mark Adler.
5. 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.
6. 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 math 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 math was no more.
7. 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.
8. The Genius of Srinivasa Ramanujan
It is impossible to be a number theorist and not to be a huge admirer and fan of Srinivasa Ramanujan. And even if you’re a mathematician espousing another allegiance (even if you’re a logician!) it is still extremely unlikely — No! It’s impossible! — that you’re not at least cognizant of the myth as well as the magic of this wonderful mathematician whose short life ended so tragically in 1920, when he was only 32.
"The Genius of Srinivasa Ramanujan" features well-known number theorists from around the world associated with Ramanujan's oeuvre, most notably A. Raghuram and Ken Ono. Shot at various locations in Chennai, Namakkal, Kumbakonam, Erode, and Cambridge, this documentary highlights the trajectory of Ramanujan's seminal work and its relevance today. His scientific legacy continues to grow well beyond anything that previous generations of mathematicians could have ever imagined.
9. Colors of Math
To most people math appears abstract, mysterious, complicated, inaccessible. But math is nothing but a different language to express the world. Math can be sensual. Math can be tasted, it smells, it creates sound and color. One can touch it – and be touched by it....
It has been translated into 12 languages, it had a successful Russian theatrical release and was shown in many universities and science conferences.
Documentary filmmaker Ekaterina Eremenko is famous for unique, innovative documentaries. Her new film Colors of Math (The Russian title, Чувственная математика – Sensual Mathematics – is better) is an intellectually stimulating and beautifully shot film invites us to look at mathematics from a new angle – as the arena of the senses.
10. The Boy With The Incredible Brain
This is the breathtaking story of Daniel Tammet. A twenty-something with extraordinary mental abilities, Daniel is one of the world’s few savants. He can do calculations to 100 decimal places in his head, and learn a language in a week.
He also meets the world’s most famous savant, the man who inspired Dustin Hoffman’s character in the Oscar winning film ‘Rain Man’
This documentary follows Daniel as he travels to America to meet the scientists who are convinced he may hold the key to unlocking similar abilities in everyone.
11. The Great Math Mystery
A provocative exploration of math's astonishing power across the centuries.
We discover math's signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the successful landing of rovers on Mars. But where does math get its power? Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond, all leading to the ultimate riddle: Is math an invention or a discovery? Humankind's clever trick, or the language of the universe? Whether we think we're good with numbers or not, we all use math in our daily lives. The Great Math Mystery sheds fascinating light on how math works in our brains and ponders the ultimate mystery of why it works so well when decoding the universe.