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.
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Terence Tao has successfully tackled many mathematical conjectures. Here are a few examples.
A number for which, apparently, no definition involves a polynomial with integer coefficients has no reason to be algebraic. But that does not prove it is transcendental! Despite the many theorems on the subject, a great many numbers continue to resist classification.
Évariste Galois is known for his tragic fate, his trailblazing mathematical genius and his profound research in algebra. But before all that, he too was a high-school and university student. Some of Galois’s schoolwork has survived.
Visitors to the Palais de la découverte cannot help being fascinated by the sequence of π's decimal digits in the rotunda devoted to it. The digits seem to occur in no apparent order. Yet they are the result of a calculation!
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