Category:
**Math**

Hannah travels down the fastest zip wire in the world to learn more about Newton's ideas on gravity. His discoveries revealed the movement of the planets was regular and predictable. James Clerk Maxwell unified the ideas of electricity and magnetism, and explained what light was. As if that wasn't enough, he also predicted the existence of radio waves. His tools of the trade were nothing more than pure mathematics. All strong evidence for maths being discovered. But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.

Numbers as God

Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented. Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer.

2018 • Math

Expanded Horizons

Hannah travels down the fastest zip wire in the world to learn more about Newton's ideas on gravity. His discoveries revealed the movement of the planets was regular and predictable. James Clerk Maxwell unified the ideas of electricity and magnetism, and explained what light was. As if that wasn't enough, he also predicted the existence of radio waves. His tools of the trade were nothing more than pure mathematics. All strong evidence for maths being discovered. But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.

2018 • Math

Weirder and Weirder

Hannah 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.

2018 • Math

Decoded

Secret codes run the world. The code of life, DNA, is the operating system for all organisms, which spawned intelligent life like us who eventually created codes of our own--language that allows us to talk and the alphabet that lets us write.

**11/17** •
Big History •
2013 •
Math

Is math discovered or invented?

Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself? Jeff Dekofsky traces some famous arguments in this ancient and hotly debated question.

The mathematical secrets of Pascal’s triangle

Pascal’s triangle, which at first may just look like a neatly arranged stack of numbers, is actually a mathematical treasure trove. But what about it has so intrigued mathematicians the world over?

Tails You Win: The Science of Chance

Professor David Spiegelhalter tries to pin down what chance is and how it works in the real world. A blend of wit and wisdom, animation, graphics and gleeful nerdery is applied to the joys of chance and the mysteries of probability, the vital branch of mathematics that gives us a handle on what might happen in the future. How can you maximise your chances of living till you're 100? Why do many of us experience so many spooky coincidences? Should I take an umbrella? These are just some of the everyday questions the film tackles as it moves between Cambridge, Las Vegas, San Francisco and Reading. Spiegelhalter discovers One Million Random Digits, a book full of hidden patterns and shapes, introduces us to the unit called the micromort (a one-in-a-million chance of dying), and uses the latest infographics to demonstrate how life expectancy has increased in his lifetime and how it is affected by our lifestyle choices - drinking, obesity, smoking and exercise.

2012 • Math

What is Zeno's Dichotomy Paradox?

Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible - but where's the flaw in his logic? Colm Kelleher illustrates how to resolve Zeno's Dichotomy Paradox.