Amazing Math
Surprising or counterintuitive mathematical results and proofs
Mega primes: A new GIMPS record | Tangente
A quest that may seem far-fetched or pointless to some, but is of the utmost importance for our secret codes, is that of "mega primes" — in other words, prime numbers with more than a million digits.
Did you say "Extraordinary"? Magic square and memory | Tangente
When film puts mathematics in the spotlight, it is often to link it with autism, as in the recent film Le Monde de Nathan (see Tangente 165). When television puts it in the spotlight, it is to showcase feats.
Historical math challenges: the Renaissance | Tangente
Throughout history, one of the driving forces behind mathematical research has been intellectual battles fought through challenges. Some of them have remained famous.
Yesterday's conjectures, today's progress | Tangente
Egyptian fractions, like Einstein's relativity, provide the subject matter for conjectures that have only just been proved. The strange abc conjecture, simple to state, has just been resolved... if the proof put forward by Mochizuki turns out to be correct.
Euler's correspondence with his contemporaries | Tangente
Leonhard Euler maintained an extensive network of correspondents across Enlightenment Europe. His exchanges with Christian Goldbach, of particular interest for number theory, have just been published.
2016, a rich vintage
The entire Tangente editorial team joins in wishing its readers a very happy 2016. The gift it has cooked up for you? A bouquet of properties of the number 2016!
Conjecture, conjecture... something will always come of it
Conjectures are especially famous when they have simple statements and resist mathematicians’ efforts for a long time. They give mathematics an air of mystery and bring great renown to those who solve them, but above all to those who first formulated them, such as Fermat and Goldbach.
Of machines and men: Catalan and Mihailescu | Tangente
Little stories about conjectures.
The engine of mathematics
Mathematical progress owes much to conjectures, large and small, that challenge mathematicians. This was true long before Landon Clay and others offered million-dollar prizes: conjectures are the engine of mathematics.
Tangente Book Prize 2015: results & winners | Tangente
The jury has delivered its verdict. It awarded the Tangente Book Prize to Vincent Borrelli and Jean-Luc Rullière, and also gave a special mention to two great ladies, Stella Baruk and Évelyne Barbin.
John von Neumann: means and excess
The Banach–Tarski paradox claims that, in theory, the pieces of a single loaf can be turned into two loaves. It fell to the protean genius John von Neumann to explain the underlying reason for this mathematical miracle. The notion of amenability that he introduced then spread widely.
Plausible conjectures… that turn out to be false!
We often assume that the only mistakes good mathematicians make are trivial slips caused by momentary inattention, such as errors in simple calculations. Yet some have put forward mathematical conjectures that proved false—sometimes spectacularly so.