by Nitsa Movshovitz-Hadar (Technion – Israel Institute of Technology)
Did you know? – Over 125,000 new items are added each year, to the international database managed by the American Mathematical Society called MathSciNet®1 A vast majority of these items contain new results, continuously enriching the ever-growing discipline known as Mathematics2. To celebrate these tremendous achievements, all to be credited to the incredible creativity of mathematicians, several valuable awards have been established. This vignette is about a few of the more prestigious ones. It opens with the two that nowadays are often described as the Nobel Prize in mathematics3: the Fields Medal and the Abel Prize.
The Fields Medal
The Fields Medal is one of two awards often described as the Nobel Prize of mathematics. It consists of a gold medal bearing the profile of Archimedes and a cash amount of 15,000 Canadian dollars (or roughly $11,540). It is awarded to 2-4 mathematicians every four years at the opening ceremony of the ICM – International Congress of Mathematicians, to recognize outstanding mathematical achievement for existing work and the promise of future achievement. A candidate’s 40th birthday must not occur before January 1st of the year of the Congress at which the Fields Medals are awarded. (Recall, Andrew Wiles, who proved the long-standing Fermat’s Conjecture, missed it as he was slightly over 40 when he and Taylor took care of the final polish of the proof.4)
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, and at the same time, of course, I take full responsibility for things that are not entirely clear or even incorrect. 
), others consist of an infinite one (such as the integers). The binary operations vary as well (think, for example, about addition-modulo-
defined on the finite set mentioned earlier
, or about addition defined on the integers). The wealth of mathematical groups is so large that there is no chance of classifying even the finite ones of them. Fortunately, there is a special family of finite groups called simple finite groups, which can be classified. It turns out that this special family of finite groups is of great importance because, in some sense, all finite groups can be built from simple finite groups in a way that is somewhat analogous to the fact that all the positive integers can be built from the prime ones. The “enormous theorem,” the subject of this article, gives a complete classification of the simple finite groups. In this way, it provides tools for analyzing the structure and features of all finite groups. The theorem received its “enormous” nickname for some very good reason, to be explained below.
), propuesta por Luther Collatz en 1937. La sucesión de Siracusa ha desafiado a los matemáticos durante décadas. A pesar del enorme número de valores que han sido calculados, a día de hoy se sigue sin conocer si esta sucesión es infinita o si, por el contrario, es finita y termina siempre en 
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