Voyages au pays des maths

Mathewelten

The Land of Mathematics

La conjetura de Poincaré

W krainie matematyki

Viaggio nel paese della matematica

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.

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Journey into Maths Country

To Infinity, and Beyond

A circle is also a triangle and a triangle is a square. Sound impossible? Not in the realm of topology

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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. 

Gödel's Theorem

Maths is meant to be certain, either right or wrong. Turns out, it's not that simple...

25 centuries ago, the well-ordered world of natural integers and fractions had to expand to accommodate monsters like pi and √2. It's a dizzying mathematical expedition where we will realise that real life numbers are only the tip of the iceberg.

Irrationality

25 centuries ago, the well-ordered world of natural integers and fractions had to expand to accommodate monsters like pi and √2

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.

A Complex Picnic

We have known for a long time that some equations can't be solved as the answers are numbers that don't exist

The distribution of prime numbers is still a mystery. Riemann developed a hypothesis considered valid but still not proven. Buckle up, it's a long journey ahead...

Prime Numbers and the Rieman Hypothesis

The distribution of prime numbers is still a mystery

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?

The Prisoner's Dilemma

We think mathematically about a very philosophical question: is it in our interest to collaborate with others?

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.

Newton and the Infinitesimal Calculation

Speed is such a common term that it's easy to forget how much of a role maths plays in understanding it

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.

On the Road to Infinity

In this episode of our travels in the land of maths, we are heading towards Infinity

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

The Game of Life

In October 1970 Scientific American magazine introduced a game under the heading "Mathematical Games" that quickly became a cult classic

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.

Benford's Law

Frank Benford observed that the number one seems to pop up a lot in both in the supermarket and on tax bills

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We will be able to upgrade our brains with a microchip, blurring the boundaries between man and machine in a way that we've never seen before. But what will happen to us when our computers become smarter than we are? Helen Fares is on a mission to test the limits of the human brain.

Homo Digitalis

Helen Fares is on a mission to test the limits of the human brain

The Upgraded Brain

Does living in a digitised world divert sexual pleasure away from other people and towards the screen? A recent study confirms the trend in both Japan and Europe. Since the advent of the smartphone, the amount of sex couples have has decreased. At the same time, sex robots are now a reality. Helen Fares meets one of these lovers of the future.

Does living in a digitised world divert sexual pleasures away from other people and towards the screen?

The Digital Orgasm

The pole vault is a discipline is based on the transformation of kinetic energy into elastic energy and then into gravitational energy. Athletes must play with energy, optimise it, transform it, and conserve it.

Pole Vaulting: Overcoming Gravity

Athletes must play with energy, optimise it, transform it, and conserve it

The Strongest of Them All

Are rural eco-neighborhoods a weapon against the rural exodus? We take a look at three next generation, eco-friendly villages in France to find out.

Rural Eco-homes

Are rural eco-neighborhoods a weapon against the rural exodus?

Ecotopia

Will human relationships become obsolete in the future, to be replaced by artificial intelligence and virtual reality? Today, researchers can simulate the presence of a loved one. In this episode, Helen Fares finds herself faced with the hologram of her best friend Josy, and explores the nature of friendship in the digital age.

Will human relationships become obsolete in the future, to be replaced by artificial intelligence and virtual reality?

The Perfect Friend

Eco-neighbourhoods are experiments in how to live together but do they represent the future for our cities?

Cities of the Future

Are eco-neighbourhoods the future for our cities?

Rubbish sorting systems differ according to the eco-neighborhoods. It's not always simple to manage it in a green way, and each eco-village has developed their own methods.

Green Waste Management

It's not always simple to manage waste in a green way

Ectopia

Have you ever seen a windsurfer who slices through the waves with the help of the breeze, as if flying over water? That's all thanks to the centreboard, and a physical concept: lift. The same force that makes planes fly and propels javelins over long distances.

Windsurfing and Lift

The Mechanics of Strength

Eternal life: an impossible dream or our reality in just a few decades? And would you even be willing to modify your DNA to live longer? Is the body is only a computer and DNA the source code? Quite possibly...

Is the body is only a computer and DNA the source code?

Eternal Youth

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Behind his polite exterior lies a formidable leader with a ruthless character, ready to do anything to make China the world's leading power by the People’s Republic’s centenary in 2049. This well-documented portrait of the Chinese president gives an unprecedented insight into his politics and shows how Xi Jinping's personal journey has shaped his choices as he steers China towards world domination.

A portrait of the Chinese president giving an unprecedented insight into his politics and showing how Xi Jinping's personal journey has shaped his choices as he steers China towards world domination.

The New World of Xi Jinping

After two months of fighting, the Russian troops had their advance towards the West blocked by fierce Ukrainian resistance. Forced to leave the suburbs of Kyiv, the occupying army left behind mass graves and horrific accounts of rape and abuse in their wake. Russia is now turning its efforts to the Dobas and the coastline along the Sea of ​​Azov. In Kyiv, the return of spring is also the return of many residents who had fled.

 In Kyiv, the return of spring is also the return of many residents who had fled

Ukraine: Kyiv in Spring

The Maginot Line is a giant: Thousands of underground bunkers and concrete defences lining the French border, from Belgium to the Mediterranean. In its time it was celebrated as a technical masterpiece and thought to be impregnable, today it also stands for the trauma of the French defeat in 1940. The documentary looks at a military construction that is as fascinating as it is controversial.

France's Defensive Barrier

Thought to be impregnable, the French defensive barrier did not halt the German invasion in 1940.

The Maginot Line

Far away from the South Korean capital of Seoul is the Buddhist Gameunsa Temple. Three nuns live, pray and cook together here as they preserve the knowledge of centuries-old temple cuisine. The abbess of this small monastery is the charismatic Wookwan Sunim, revered in Asia as one of the best cooks in the world.

South Korea: Magic Temple Food

Far away from the South Korean metropolis of Seoul is the Buddhist Gameunsa Temple where three nuns live, pray and cook together 

Geo Reportage

Lockdowns, crop failures due to climate change and the war in Ukraine are all to blame for soaring prices around the world.

Geopolitics of Inflation

Mapping the World Essentials

The literary source for Richard Strauss’s opera immortalizing the degeneracy of Herodes Antipas, King of Judea, and his step-daughter Salome, was supplied by Oscar Wilde. It tells of Herodes, who is keeping the prophet Jochanaan captive inside a cistern. Salome tries to seduce him and on being rebuffed, forces her stepfather to serve her the prophet’s head on a silver platter.

Directed by Christof Loy in Helsinki

Rejected by the prophet Jochanaan, Salome forces her abusive stepfather to exact revenge.

Richard Strauss: Salome

The planet's jet streams are being affected by rising temperatures in the Arctic. These streams are part of a wind system that circulates at high altitude around the Earth, and they have an influence on extreme weather events. Changes in them are bad news for life on Earth.

How Climate Change Makes Storms Worse

Changing jet streams are bad news for life on Earth

Winds of Change

ARTE Concert Festival welcomes a legend, Damon Albarn. He performs his new album live: The Nearer the Fountain, More Pure the Stream Flows.

ARTE Concert Festival 2021

ARTE Concert Festival welcomes a legend, Damon Albarn

Damon Albarn

Three Japanese men have fallen under the charms of high school student Rinko, a character from the video game Love Plus. The game finally leads them to the seaside resort of Atami, where the virtual world and real life collides.

Three Japanese men have fallen under the charms of high school student Rinko, a character from the video game Love Plus

Petit ami parfait

An investigation into a little-known story from the Second World War. Having planned and executed their mass murders, the Nazis meticulously eliminated traces of their crimes against humanity between 1942 and 1944: The so-called Operation 1005.

How the Nazis Covered up their Crimes

The Nazis meticulously eliminated traces of their crimes against humanity between 1942 and 1944: The so-called Operation 1005.

Operation 1005

Ordinary Ukrainian citizens are preparing to resist the Russian invader by joining the army and helping the resistance in any way they can.

Ukraine: Resisting the Agressor

ARTE Reportage

The Russian invasion of Ukraine has brought the people of Kyiv together like nothing else. Calling on the spirit of the Maidan Revolution of 2014, they are ready to resist.

Ukraine: Maïdan Spirit

The Supreme Court is now made of a majority of ultra-conservative judges since President Trump's term in office. The court now looks set to overturn the Roe v Wade case which gave women the constitutional right to have an abortion if they so wish or need. This worrying step backwards for women's rights doesn't mean women won't have abortions. It means they'll die trying.

Abortion: A Threatened Right

This worrying step backwards doesn't mean women won't have abortions. It means they'll die trying

Mapping the World

Pianist Maria-João Pires joins the Monte-Carlo Philharmonic Orchestra at the Aix-en-Provence Easter Festival in a concert featuring the music of Mozart, Mendelssohn and Schumann.


Programme:
Felix Mendelssohn - Ein Sommernachtstraum (A Midsummer Night's Dream), Overture, Op. 21
Wolfgang Amadeus Mozart - Piano Concerto No. 9 in E flat major, K. 271

Robert Schumann - Symphony No. 1 in B flat major, "Spring", Op. 38

Aix-en-Provence Easter Festival 2022

Pianist Maria-João Pires joins the Monte-Carlo Philharmonic Orchestra at the Aix-en-Provence Easter Festival in a concert featuring the music of Mozart, Mendelssohn and Schumann.

Maria-João Pires plays Mozart

In 2020, for the 250th anniversary of Beethoven's birth, Philippe Jordan and the Vienna Symphony Orchestra recreated the mythical evening of December 22 1808, when  the composer presented his Sixth Symphony, also known as his Pastoral.

Philippe Jordan recreates the evening of December 22, 1808, when Beethoven presented his Pastoral symphony

Philippe Jordan Conducts Beethoven's Pastoral Symphony

Since its invention in the 19th century, the bicycle has allowed Western women to move around independently. Today, it is the turn of women in Arab countries to discover its power. Though at first glance innocuous and common, the bicycle is unexpectedly feminist.

The Freedom to Cycle

Though at first glance innocuous and common, the bicycle is unexpectedly feminist

Gymnastics

Saudi Arabia is reputed to be one of the richest and most conservative nations on the planet. But how do its citizens live today?

Saudi Arabia: The West

Unknown Arabia

The internationally renowned bassist, singer and composer Avishai Cohen performs in an exclusive concert from the Maillon theatre in Strasbourg. Accompanied by drummer Roni Kaspi and pianist Elchin Shirinov, the jazzman presents his forthcoming album Shifting Sands.

Private Session at the Maillon Theatre, Strasbourg

IThe internationally renowned bassist, singer and composer Avishai Cohen performs from his forthcoming album Shifting Sands.

Avishai Cohen Trio

Live from the Teatro Real in Madrid, an adaptation of Prokofiev’s flamboyant masterpiece by the ever-radical Calixto Bieito.

An adaptation of Sergei Prokofiev’s flamboyant masterpiece by radical director Calixto Bieito.

Prokofiev’s "The Fiery Angel" at the Teatro Real in Madrid

In 2017, Ukrainian journalist Stanislav Aseyev was living and working from the separatist region of Donetsk in eastern Ukraine. Critical of the self-proclaimed republic, he used pseudonyms to protect his identity. But one day he was exposed which led to his imprisonment and torture in the notorious Izolyatsia prison

The story of Ukrainian journalist Stanislav Aseyev who was imprisonment and tortured in the separatist region of Donbas.

To Infinity, and Beyond

Journey into Maths Country