One hundred green-eyed logicians have been imprisoned on an island by a mad dictator. Their only hope for freedom lies in the answer to one famously difficult logic puzzle. Can you solve it? Alex Gendler walks us through this green-eyed riddle.
Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.
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.
3/3 • Magic Numbers: Hannah Fry's Mysterious World of Maths • 2018 • Math
Predictions underlie nearly every aspect of our lives, from sports, politics, and medical decisions to the morning commute. With the explosion of digital technology, the internet, and “big data,” the science of forecasting is flourishing. But why do some predictions succeed spectacularly while others fail abysmally? And how can we find meaningful patterns amidst chaos and uncertainty? From the glitz of casinos and TV game shows to the life-and-death stakes of storm forecasts and the flaws of opinion polls that can swing an election, “Prediction by the Numbers” explores stories of statistics in action. Yet advances in machine learning and big data models that increasingly rule our lives are also posing big, disturbing questions. How much should we trust predictions made by algorithms when we don’t understand how they arrive at them? And how far ahead can we really forecast?
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.