Through his marginal notes in Bachet's edition of Diophantus's books on arithmetic and through his correspondence, the mathematician Pierre de Fermat spurred the study of integers with new results and methods. He both transmitted ideas and drove the subject forward.
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Although the four operations—addition, subtraction, multiplication and division—are studied from elementary school onward, students must wait until their third year of secondary school to discover a fifth: raising a number to a power.
In ancient Egypt, puzzles and problems were already being framed in terms of equations over the integers. Although the methods used to solve them have changed, the underlying question remains the same. These equations would go on to transform mathematics.
One facet of mathematical creativity is finding an original representation of a problem that makes it easy to solve. Thus, an elementary Diophantine equation can be solved by studying trajectories on a billiard table, turning billiards into an effective tool.
As noted on www.diophante.fr, which has just celebrated its 20th anniversary, the Greek mathematician Diophantus left us some remarkable works on arithmetic. A journey into history will reveal his extraordinary talent.
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