Who was Giuseppe Peano?

Giuseppe Peano was an Italian mathematician who made very many valuable contributions to mathematics, having written over 200 books and papers on the subject. Two of his accomplishments for which he is best remembered are the Peano Curve and the Peano Axioms.

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The Peano Curve was the first example of a space-filling curve.

When you first hear about it, it seems very amazing that something like a space-filling curve could even be possible. It means, for example, that you can draw a curve inside of a square, with the curve having zero thickness, and having a starting point and an ending point, and do it in such a way that you pass through every point inside the square!

The Peano Curve is constructed as a limit of an infinite sequence of curves. Each of the curves in the sequence is a continuous image of the unit interval [0,1] and none of them fill the entire unit square. Yet, the uniform convergence of them results in a continuous curve that covers the entire unit square. In fact, seeing how each of the curves in the sequence was constructed, it is possible to figure out which point of the unit interval is mapped to which point of the unit square.

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The Peano Axioms were introduced by Giuseppe Peano in 1889 to provide a rigorous foundation for the natural numbers. This made possible the publication of the three-volume book Principia Mathematica by Whitehead and Russell, which in turn led to Gödel's Incompletenss Theorem.