It is with Bernhard Riemann's work that we finally have the mathematical glasses to explore such worlds of the mind. And now my journey through the abstract world of 20th century mathematics has revealed that maths is the true language that the universe is written in. They key to understanding the world around us. Mathematicians aren't motivated by money and material gain, or even by practical applications of their work. For us it's the glory of solving one of the great unsolved problems that have outwitted previous generations of mathematicians. David Hilbert was right; it’s the unsolved problems of mathematics which make it a living subject. Which obsess each new generation of mathematicians. Despite all the things we've discovered over the last 7 millennia, there are still many things we don't understand. And its Hilbert’s call of "We must know, we will know" which drives mathematics.
Conclusion in BBC's The Story of Maths, episode 4
Five hundred years ago, when faced with an eclipse, many of us would have believed it was the work of an angry god. But as we've unearthed the language of the Code, we've discovered that the apparent mysteries of our world can be understood without invoking the supernatural. And this for me is what's so remarkable. That despite the incredible complexity of the world we live in, it can all, ultimately, be explained by numbers. Just like the orbit of the planets, life too follows a pattern. And it can all be reduced to cause and effect.In the end, even the flip of a coin is determined by how fast it's spinning and how long it takes to hit the ground. The ultimate symbol of chance isn't random at all. It only appears that way. When we don't understand the Code, the only way we can make sense of our world is to make up stories. But the truth is far more extraordinary. Everything has mathematics at its heart. When everything is stripped away all that remains is the Code.
Conclusion in BBC's The Code, episode 3.
I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.