I want to see a TV show about great mathematicians of the past on a channel like BBC Four. Programmes about mathematics tend to be rather condescending, at least to anyone who has a bit of mathematical knowledge. Perhaps a way around this is to delve into the social and historical circumstances of the great mathematicians and how that along with their personality produced the mathematical results for which they are famous.
I apologise if this sounds like dumbed down nonsense to you. Personally, I can think of six mathematicians whose lives and results are interesting and important enough to create a series of great programmes. I'm thinking of those shows where scenes from someone's life are re-enacted. Obviously you would need a bit of poetic license to augment what is already known, but as long as things weren't too over the top it would be ok.
I've put my six choices in chronological order. I am not sure you would need to do that for a series because if you were to make six more choices, they probably would fall in and these choices. For example there are many more interesting choices for a mathematician from antiquity.
Pythagoras of Samos (c. 570BCE to c. 495BCE) would be included as his theorem that dominates high school mathematics is an obvious starting point for how mathematics became integral to western philosophy and science. You also have the intrigue surrounding the Pythagorean school that influenced organisations like the masons and the Rosicrucians. The Pythagoreans were also the first to rigorously apply the concept of proof to their arguments. Obviously mathematics got started a lot long before the work of Pythagoras and the exact origin of many mathematical concepts are still uncertain, but both the theorem and the cult associated with the man provide a fair amount of drama to be mined.
Muhammad ibn Mūsā al-Khwārizmī (c. 780CE to c. 850CE), known colloquially as Algoritmi (from whom we get the word algorithm), was generally held to be the father of Algebra by many Renaissance thinkers. Of course, as with Pythagoras of Samos, much of the results attributed to him come from the collation of older, more disparate, sources. However, he is interesting enough to be the focal point of an episode: one that shows how much of western thought is indebted to the work of not only medieval Islamic thinkers but also the Hindu and Buddhist thinkers and scientists that had influenced them.
Isaac Newton (1642CE to 1727CE) is pretty much the daddy of all mathematicians. A true polymath who had a great influence on his age and who, by all accounts, was a bit of a git, should make for an interesting programme. Especially if you combine his work with his contemporary Leibniz (1646CE to 1716CE) who concurrently and independently conceived of calculus.
Évariste Galois (1811CE to 1832CE). Newton may well have the cultural sway because of his overall contribution but surely no mathematician exceeds Galois for dramatic life story. He died aged 20 in a pistol duel, he hung around with revolutionaries and was imprisoned for it, and in frustration he threw a board rubber at the august and revered Cauchy (series two maybe?) during an exam. He was a total badass. Oh and he conceived of a totally new way of thinking about algebra that totally proves something about quintics. It also made me cry while having to revise what the hell it was all about as an undergraduate. (Personally I think Galois needs his own film or, better yet, a musical.)
In contrast to Galois, Georg Cantor (1845CE to 1918CE) lived long enough to be driven to the edge of sanity by the results he was able to prove about real numbers and set theory. For a long period of his life he suffered from what we now know as bipolar disorder but the results he was able to prove are wacky enough to make the heads of even the best of us spin. He proved that there are many types of infinities: this doesn't have much to do with the price of fish but it has profound philosophical implications, hence the debilitating effect it had on his psyche. Of course he wasn't helped by a rivalry with Leopold Kronecker, a man who kept dismissing Cantor's work and dissing him in public big time. While Cantor was not a happy man in his life time, he would be pleased to know that he laid the foundation for much of modern mathematics and things that his detractors dismissed are now crucial elements in basic analysis courses.
For my last choice, I have chosen Sofia Kovalevskaya (1850CE to 1891CE) because otherwise there would be no women. Mathematics does a poor job to this day of attracting women, which is a shame because there have been many important female mathematicians. For example Ada Lovelace, who is widely credited with assisting Charles Babbage in the creation of a prototypical mechanical computer called the difference engine; Emmy Noether, who made important advances in modern algebra and theoretical physics; and Hypatia, who wrote commentaries on Euclid and was cruelly murdered by Christians who skinned her alive with oyster shells. Sofia Kovalevskaya produced some important results on differential equations. In order to do so, she had to attend university but this was not possible in Russia at the time. She enrolled in Germany but needed permission from her father or her husband. Unmarried she nonetheless concocted a fictitious marriage in order to be able to study. Her "husband" would go on to collaborate with Charles Darwin. Tragically, she died of influenza in 1891, aged just 41.
So those are my (first) six. You can see from my references to other mathematicians that there would be plenty of people to consider beyond that. I didn't even mention Euler who was hugely prolific, had one eye, and had two "great" patrons in Frederick the Great of Prussia and Catherine the Great of Russia. And Ramanujan! And Erdös! Stay tuned for season two!
Who would you like to see dramatised in a series about great mathematicians? Please let me know in the comments!