Giuseppe Peano
1858 - 1932

Have you ever heard of a teacher that did not give his students tests? A famous mathematician did just that. He was Giuseppe Peano and was born in a farmhouse right outside Cuneo, Italy. His father was a farmer and his mother was a homemaker. When he was a child, his uncle, who was a priest, recognized that Peano was a talented student and enrolled him in a high school that prepared him for college. After graduation, he entered the University of Turin where he studied analytic geometry, algebra, calculus, descriptive geometry, analysis, geometry, other advanced classes and finally mechanics. His teachers included D’Ovidio, Genocclu, Bruno, and Siacci. In 1880, Peano graduated as a doctor of mathematics. The University of Turin promptly hired him. Peano published four mathematical papers during the next two years. In 1884, he received his qualification to be a university professor at Turin and taught there throughout the rest of his life. He also taught at the nearby Academic Militaire (Military Academy) from 1895 until 1908. He was elected to the Academy of Sciences at Turin in 1981 and was a speaker at several International Congress of Mathematics. In addition, he was honored by the Italian government with several knighthoods, including the Order of the Crown of Italy.

One of the most famous things he is known for is the five Peano axioms, which defined the natural numbers in terms of a set of elements.

  1. Zero is a number.
  2. If a is a number, the successor of a is a number.
  3. Zero is not the successor of a number.
  4. Two numbers of which the successors are equal are themselves equal.
  5. (Induction Axiom) If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

In 1886, Peano proved that if f(x,y) is continuous then the first order differential equation dy/dx = f(x,6) has a solution. Until then, everyone thought that such curves did not exist. In 1890, he invented “space-filling” curves. These are continuous surjective mappings from [0,1] onto the unit square. In 1891, he started his own mathematics journal called Tivista di matematica, which featured logic and foundations of mathematics. In 1887, he introduced the basic elements of geometric calculus (Geometrical Applications of Infinitesimal Calculus) and gave new definitions for the length of an arc and for the area of a curved surface.

From 1892 to 1908, Peano worked on a project called Formulario Mathematico, which contained all theorems and all methods. It was for professors to use in teaching. However, it was not very well accepted by professors or students. This book was never popular.

One thing that Peano could do really well was to find mistakes in other mathematicians’ work! As you can imagine, that habit made him disliked among his peers. As a teacher, he never gave tests. Do you suppose that made him popular with his students?

Peano created a special language called Interlingua. His plan was that everyone could use this language, but especially the scientific community. Interlingua was based on a very simple form of Latin, French, German, and English, with a greatly simplified grammar. However, Interlingua was not used very much because of the popularity of English. Eventually, it disappeared from use.

The author, Hubert C. Kennedy, has this opinion about Peano: “I am fascinated by his gentle personality, his ability to attract lifelong disciples, his tolerance of human weakness, his perennial optimism. …Peano may not only be classified as a 19th century mathematician and logician, but because of his originality and influence, must be judged one of the great scientists of that century.”1

FOOTNOTE:

1www-groups.dcs,st-and,ac,ukj-history/Mathematicians/Peano.html

Contributed by Susan Eastman

References:

  1. Weisstein, Eric W., “CRC” Concise Encyclopedia of Mathematics”, CRC Press L.L.C., Baco Raton, FL, 1999
  2. http://www.britannica,com/bcom/eb/article/8/0,5716,43508+1+42551,00.html
  3. http://www.geocities,com/Athens/Olympus/2948/pgolba,html
  4. http://www-groups.dcs.st-and.ac.ukj~history/Mathematicians/Peano.html
  5. Encyclopedia Americana, Grolier, Danbury, CT, Vol. 21, p. 573, 1999

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