Logic
Explore mathematics articles on the theme of logic.
PodcastKnuth and Conway notations for mind-boggling numbers
When it comes to representing extremely large numbers, the standard operations, including exponentiation, are no longer enough. With considerable imagination, Donald Knuth and John Conway devised notations to overcome this limitation.
PodcastCédric Aubouy, math clown and author of “Je ne sais pas”
Cédric Aubouy, a mathematical clown and founder of the L’île logique company, agreed to meet us to mark the publication of his first novel, Je ne sais pas ou la disparition des mathématiciens.
PodcastEuler–Cramer paradox: Are 9 points enough to define a cubic?
The Euler–Cramer paradox: If nine points seem sufficient to determine a cubic curve, how can two distinct cubics also pass through those same nine points?
PodcastMisleading graphical proofs: the missing square paradox and more
Discover how seemingly rigorous diagrams can fool us: the missing square paradox, the astonishing proof that every triangle is equilateral, and more.
Phi is irrational: a geometric proof | Tangente
Let's see how to prove that φ is irrational.
Littéramath: the mathematical literature site | Tangente
A project highlighting the links between mathematics and literature
Poincaré on mathematical induction | Tangente
"This, then, is mathematical reasoning par excellence, and we must examine it more closely" (La Science et l'Hypothèse, "Sur la nature du raisonnement mathématique").
Proof desperately wanted | Tangente
One hundred thousand results are stated worldwide each year—but how many of them are proved? In number theory, for example, many problems remain unsolved. Some are well known to enthusiasts, others less so...
Lean: a new library of Alexandria | Tangente
Building a digital repository of mathematics—a new "Library of Alexandria for mathematics"—is the wildly ambitious collaborative undertaking on which many mathematicians have embarked.
Proving a program | Tangente
Writing a computer program is one thing. Proving that it actually produces the expected result is another! One major advantage of recursion is that it produces programs whose correctness is easy to prove. There is a link between writing a program and proving it correct.
Conway and quantum free will | Tangente
John Conway joined forces with Simon Kochen to prove the free will theorem. This result calls for a reassessment of quantum mechanics, without necessarily tying it to probability. It casts new light on a paradox highlighted by Einstein.
Disputes and paradoxes | Tangente
Even the greatest mathematicians have fallen into the traps laid by logic and its paradoxes.
Self-reference and fixed points in logic | Tangente
Self-reference is paradoxical and connected with the mathematical notion of a fixed point, the method of successive approximations, and recursive definitions. Together, these connections make this fundamental idea a natural subject for mathematics enthusiasts.
Playing with self-referential numbers | Tangente
Can the digits of a number, or the terms of a number sequence, themselves tell readers about their positions or properties? With a few ingenious constructions, they can!
Paradoxes and self-contradictions in logic | Tangente
A source of amusement, self-reference also lies behind some famous and profound mathematical paradoxes. Logic, our senses and our certainties are all sorely tested. Reflection then takes over… and often leads to wonder!
Raymond Smullyan (1919–2017): logician and magician
An eclectic mathematician, Raymond Smullyan, who died last June, was best known to the general public for his books of mathematical recreations centered on logic.