Mathematics

brilliant mathematicians whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing 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.

Dr Hannah Fry explores a paradox at the heart of modern maths, discovered by Bertrand Russell, which undermines the very foundations of logic that all of maths is built on. These flaws suggest that maths isn't a true part of the universe but might just be a human language - fallible and imprecise. However, Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.
Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature. But if we accept that maths is part of the structure of the universe, there are two main problems: firstly, the two main theories that predict and describe the universe - quantum physics and general relativity - are actually incompatible; and secondly, most of the maths behind them suggests the likelihood of something even stranger - multiple universes.
We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.

brilliant mathematicians, whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide. 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.

The ultimate adventure in scientific inquiry, this fascinating program follows the exploits of a small group of pioneering mathematicians who discovered a whole area of study that is revolutionizing all branches of understanding in the world: fractal geometry. Fractals are most recognized as a series of circular shapes with a border surrounded by jagged "tail-like" objects. The program, aimed at the average viewer does a fine job of explaining the background of fractals, first by beginning with the story of Pixar co-founder, Loren Carpenter's work at Boeing, developing 3D terrain from scratch using fractals. From there the program starts at the beginning with an introduction to Benoit Mandelbrot and his revolutionary work. The explanations are full of solid factual information but never talk above the level of a viewer who has some understanding of basic mathematical principles. Once the concept is presented the program spends the rest of the time showing how prevalent the fractal is in life. For a program about a mathematical concept, "Fractals" is very engaging, showing how the process was applied to special effects as far back as the Genesis planet from "Star Trek II" all the way to the spectacular finale on Mustafar in "Star Wars: Episode III." I found myself astonished at how fractals were the source of the lava in constant motion and action during the Obi-Wan/Anakin fight. What is more amazing is when the program delves into practical applications such as cell phone antennas, and eventually the human body. For the average person who enjoys watching science related programs, even on a sporadic basis, "Fractals" will prove to be a very worthwhile experience. The program is well produced, integrating talking head interviews (including some with Mandelbrot himself) with standard "in the field" footage. The structure of the program is very logical and never finds itself jumping around without direction. In simplest terms, this is a program as elegant as the designs it focuses on.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.

Dr. Hannah Fry takes us on a whistle-stop tour around the mathematics of success, to help us understand how to get more of what we want in our own lives. From the best way to bag a budget dinner or keep the kids quiet, to averting nuclear Armageddon and negotiating global climate change agreements.