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Le théorème de Gödel

S1 E6
·
2021

In this episode, we look at the relationship between math and truth. Math is supposed to be the domain of certainty: either it's provable or it's false. Well, it is not so simple. Because Gödel's theorem proved that there are 'undecidable' propositions, which can neither be proved nor disproved. First limiting result in the history of mathematics...

Levels:
Secondaire 9e année 10e année 11e année 12e année
Subjects:
Mathématiques Algèbre Données
Skills:
Pensée critique Résolution de problèmes
French level:
B1 : Seuil B2 : Avancé ou indépendant
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E1 : La loi de Benford

9 min 2 s
The starting point of this episode of our travels in the land of maths: the trivial setting of a supermarket where a vast mathematical plot seems to be unfolding. Thanks to Benford's law, we discover two ways of measuring the world and another way of seeing things.
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E2 : Flâneries infinitésimales

9 min 43 s
Speed is such a commonplace notion that we have almost forgotten that it was a mathematical idea. However, three or four centuries ago, speed did not exist... or rather, it was very poorly defined. Behind the complexity of reality, it allows us to discover hidden regularities. Behind the agitation of objects and trajectories, it makes…
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E3 : La conjecture de poincaré

9 min 52 s
In this episode of our travels in the land of maths, we stop in the strange world of topology to decipher the famous Poincaré conjecture. Where we will hear about donuts, circles that are also squares and millions of dollars.
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E4 : Sur la route de l'infini

9 min 44 s
In this episode of our travels in the land of maths, we set course for the Infinite. And even beyond, because infinity exists in several sizes. Vertiginous lands where Georg Kantor and his theory of sets will give us a serious help to find our way.
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E5 : Le dilemme du prisonnier

9 min 2 s
The starting point of this episode of our travels in the land of maths: the prison. Two prisoners must choose between cooperation and betrayal without consulting each other. This is the famous dilemma that will take us to the heart of game theory and make us think mathematically about a very philosophical question: is it in our…
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E6 : Le théorème de Gödel

9 min 55 s
In this episode, we look at the relationship between math and truth. Math is supposed to be the domain of certainty: either it's provable or it's false. Well, it is not so simple. Because Gödel's theorem proved that there are 'undecidable' propositions, which can neither be proved nor disproved. First limiting…
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E7 : Le jeu de la vie

9 min 36 s
On the program of this journey: the game of life. A game indeed, but one that allows us to better understand how a complex system can emerge from something simpler. This is called 'emergence' and the story is somewhat reminiscent of the story of our universe. We will also meet different profiles of mathematicians, one of…
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E8 : Les nombres irrationnels

10 min 35 s
This time we go to a much more rugged region than expected: that of numbers. Twenty-five centuries ago, the well-ordered world of natural integers and fractions had to expand to accommodate monsters like pi and v2. A dizzying mathematical expedition where we realize that real life numbers are only the tip of the iceberg.
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E9 : Pique-nique sur le plan complexe

10 min 39 s
Irrational numbers no longer hold any secrets for you? Then let's head for a picnic spot that's a bit complicated to reach. It has been known for a long time that some equations have for solutions numbers that do not exist. Fortunately, a flock of mathematicians has discovered a new domain of 'complex' numbers that…
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E10 : Cap sur l'hypothèse de Riemann

10 min 47 s
End of the trips to the country of maths with a difficult hike. It is better to be strong on the complex plane. Because it is about an unsolved mystery of mathematics, namely: the distribution of prime numbers. Riemann made a hypothesis considered as valid but still not proven, that is to say that it is not a walk in the park. Let&…
    Levels:
    Secondaire 9e année 10e année 11e année 12e année
    Subjects:
    Mathématiques Algèbre Données
    Skills:
    Pensée critique Résolution de problèmes
    French level:
    B1 : Seuil B2 : Avancé ou indépendant