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Gödel’s Theorem
Journey into Maths Country - S1 - E5
In this episode, we look at the relationship between maths and truth. Maths is meant to be certain, either right or wrong. Turns out, it’s not that simple. For Gödel's theorem has proved that there are “undecidable” theories, which one can neither prove nor disprove.
Journey into Maths Country: Season 1 - 15 Episode s
1x1 - Benford’s Law
September 23, 2021
Frank Benford observed that the number one seems to pop up a lot in both in the supermarket and on tax bills. In understanding this law, it helps to simply look at the world from a different perspective.
1x2 - Newton and the Infinitesimal Calculation
September 23, 2021
Speed is such a common term that it's easy to forget how much of a role maths plays in understanding it. Until three or four centuries ago, there was no speed at all. It was only since the Renaissance that the concept of movement crept into the world of mathematics, thanks to calculus and Isaac Newton.
1x3 - To Infinity, and Beyond
September 23, 2021
A circle is also a triangle and a triangle is a square. Sound impossible? Not in the realm of topology, which even applies to 3-dimensional spaces and anything from donuts, UFOs and potatoes. The discipline's inventor, Henri Poincaré, created one of the most difficult problems in mathematics.
1x4 - On the Road to Infinity
September 23, 2021
In this episode of our travels in the land of maths, we are heading towards Infinity. And even beyond, because infinity comes in many sizes. That may seem strange, but Georg Kantor and his set theory will help us come to terms with this maths concept of dizzying scale.
1x5 - Gödel’s Theorem
September 23, 2021
In this episode, we look at the relationship between maths and truth. Maths is meant to be certain, either right or wrong. Turns out, it’s not that simple. For Gödel's theorem has proved that there are “undecidable” theories, which one can neither prove nor disprove.
1x6 - The Prisoner’s Dilemma
September 23, 2021
Two prisoners must choose between cooperation and betrayal without consulting each other. This famous prisoner's dilemma that will take us to the heart of game theory. We think mathematically about a very philosophical question: is it in our interest to collaborate with others?
1x7 - The Game of Life
September 23, 2021
In October 1970 Scientific American magazine introduced a game under the heading “Mathematical Games” that quickly became a cult classic. The idea behind John Conway’s “Game of Life” is cellular automaton. The game’s creator hoped to help with the understanding, simulating or even recreation of life itself.
1x8 - Irrationality
September 23, 2021
25 centuries ago, the well-ordered world of natural integers and fractions had to expand to accommodate monsters like π and √2. It's a dizzying mathematical expedition where we will realise that real life numbers are only the tip of the iceberg.
1x9 - A Complex Picnic
September 23, 2021
We have known for a long time that some equations can't be solved as the answers are numbers that don't exist. Fortunately, a slew of mathematicians have uncovered a new field of numbers that now play a vital role in modern mathematics.
1x10 - Episode 10
September 23, 2021
1x11 - Episode 11
September 30, 2021
1x12 - Episode 12
October 7, 2021
1x13 - Episode 13
October 14, 2021
1x14 - Episode 14
October 21, 2021
1x15 - Episode 15
October 28, 2021