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Editorial | Tangente
Iterate, iterate... As the Shadoks proclaimed in their day, only by trying again and again do we eventually succeed. In other words, the more often it fails, the greater the chance that it will work. This may raise a smile, yet iterative processes prove to be as simple as they are effective.
A little etymology
Proofs by induction were given long before this form of reasoning was formalized, let alone named.
A sequence of ideas: Ulam and Recamán | Tangente
Algorithms for constructing integer sequences from a given number are diverse. Many were devised in the 20th century by well-known mathematicians (Ulam, Kaprekar, Sloane...) and sometimes produce surprising results, some of which remain conjectures.
Iterative processes at the heart of mathematics | Tangente
Repeating computational or logical procedures is one of the defining features of mathematical activity. The advent of computing gave fresh impetus to this technique, which has been used since antiquity.
Happy is one who, like a number... | Tangente
Starting with an integer, apply a simple rule to obtain a new number. Repeat the process with the result, and so on... Depending on the pattern followed by this sequence—cyclic, constant from some point onward, and so on—the starting number is described as happy, perfect... But sometimes the pattern is still unknown.
News from the Collatz conjecture
Syracuse... For some, the name evokes a classic song performed by the late Henri Salvador (1917–2008); for mathematics enthusiasts, however, it refers to the Collatz conjecture, whose statement is very simple but which remains unproved to this day. A recent result lends further support to the conjecture.