Mathewelten

W krainie matematyki

Voyages au pays des maths

The Land of Mathematics

Viaje al país de las matemáticas

Viaggio nel Paese della Matematica

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...

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Journey into Maths Country

Prime Numbers and the Rieman Hypothesis

The distribution of prime numbers is still a mystery

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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

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

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.

To Infinity, and Beyond

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

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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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?

Ecotopia

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?

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.

Homo Digitalis

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

The Digital Orgasm

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.

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

The Upgraded Brain

A look at three pioneer eco-districts in Europe, set up between 1995 and 2005, to encourage ecological living..

Pioneering Green Neighbourhoods

A look at three pioneer eco-districts in Europe

Urban eco-neighborhoods are multiplying and becoming increasingly large. But is it possible to remain ecological on such a large scale? The Docks of Saint-Ouen (France), Eikenøtt of Gland (Switzerland) and Scharnhauser Park in Ostfildern (Germany) took up the challenge.

Living Differently in the City

The Docks of Saint-Ouen (France), Eikenøtt of Gland (Switzerland) and Scharnhauser Park in Ostfildern (Germany) each try in their own way foster sustainable living

Clichy-Batignolles (Paris, France) and the Eco-Village des Noés (Val-de- Reuil, France) have been awarded the label "One Planet Living" by the WWF, helping the inhabitants to adopt a more sustainable way of life.

An Eco-Village For Every Taste

Helping the inhabitants to adopt a more sustainable way of life

Since antiquity, scientists have tracked down the principles behind the movements of moving things, from planets to athletes. Running champions make sure of basic principles of physics developed by Newton to improve their performance. We take a look at the maths behind the movement. 

Sprinting and Newton's Law

Since antiquity, scientists have tracked down the principles behind the movements of moving things, from planets to athletes

The Mechanics of Strength

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

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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

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

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

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

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

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

The paintings of Vincent Van Gogh are losing their colours. The paints he used were vibrant, but cheap, and degraded within months of painting. It's now impossible to appreciate the true beauty of his works, as his flamboyant flare for colours has slowly turned drab. If nothing is done, the Sunflowers which are still a beautiful gold today could well turn brown. Should we just accept they can't be saved?

Van Gogh's Disappearing Colours

The paintings of Vincent Van Gogh are losing their colours because the pigments used were vibrant but cheap

Gymnastics

Techno, house, garage or hip hop: electronic music is a driving force in pop culture today. Almost forgotten is its origins in the post-war classical avant-garde of Europe, with figures such as Pierre Schaeffer and Karlheinz Stockhausen. This documentary traces the history of electronic music from Europe to the great post-industrial cities of America, with exclusive interviews and little-seen archive footage.

The Sound That Changed Everything

This documentary traces the history of electronic music from Europe to the great post-industrial cities of America, with exclusive interviews and little-seen archive footage.

Electronic Vibrations

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

Why do the works of the Italian painter Caravaggio exude such violence? The answer is to be found in the eventful life of the artist, who just couldn't stay out of trouble and met a sticky end.

Caravaggio, Genius - and Killer?

Caravaggio just couldn't stay out of trouble and met a sticky end

It is impossible for them to stay in Russia. For these Russian citizens opposed to the Kremlin, the outbreak of war in Ukraine and the new laws restricting freedom of expression have forced them to leave everything behind. Their destination: Istanbul, as Turkey did not require a visa. It is a difficult exile with a host country that does not consider them as refugees and a homeland that views them as pariahs.

Russians Seek Refuge in Turkey

Russian Journalists Report

The loss of biodiversity is highly alarming: our planet is currently experiencing the greatest extinction since the age of the dinosaurs. This film documents the extinction of species currently happening around the world. But it also highlights hopeful initiatives as committed men and women on every continent fight to save endangered species and work towards improving biodiversity.

Mankind's Great Challenge

Biodiversity or Extinction

A breakaway region of Moldova that is not recognised internationally, Transnistria is largely pro-Russian. The war in Ukraine has awakened fears that Russia will try to annex the region.

Moldova: Transnistria and Russia

ARTE Reportage

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

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

At Lviv station, a convoy prepares to make its way to Kyiv. The driver in his cabin, is at the front of the train. In the other cars are volunteers and men going into battle. Without even picking up a gun, Evgeni, a train driver, is now on the de facto front line.

Ukraine: Keeping the Trains Running

Without even picking up a gun, Evgeni, a train driver, is now on the de facto front line

Have you ever wondered why pop songs sometimes sound a little too familiar? Welcome to the world of pop-recycling where borrowing, sampling and interpolation are the order of the day. Featuring interviews with Placebo, Ed Sheeran, Charlie XCX and Lauv.

Pop Music: The Great Recycling Business

Have you ever wondered why pop songs sometimes sound a little too familiar? Welcome to the world of pop-recycling. Featuring interviews with Placebo, Ed Sheeran, Charlie XCX and Lauv.

Tracks: Songwriting Special

Thirty years after the end of apartheid, South Africa has still not overcome its many problems: Endemic violence, economic and racial inequalities, state corruption. However, the rainbow nation has a lot to offer: tourism, natural resources and a leadership role on the African continent.

South Africa and its Demons

Mapping the World

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

Patrycja and Eryk have left their native Poland and their hometown of Wrocław. The two had no longer felt welcome in their own country because of growing anti-Semitism. In search of their Jewish identity, they started a new life in Tel Aviv, where they must adjust to a new language, and new jobs. But the young couple is full of energy and confidence.

Patrycja and Eryk have left Poland because of anti-Semitism, and must now make a life for themselves in Israel

Prime Numbers and the Rieman Hypothesis

Journey into Maths Country