Giuseppe Peano

Giuseppe Peano (27 August 1858 in Spinetta - 20 April 1932 in Turin) was an Italian mathematician, logician and philosopher, known for his contributions to mathematical logic and the theory of numbers. Peano published more than two hundred books and articles, most on mathematics. Most of his life was dedicated to teaching in Turin.

Personal Data

He was born on a farm near the town of Spinetta near Cuneo in Piedmont. He entered the nearby University of Turin in 1876. He graduated in 1880 with honors and began his academic career.

On January 20, 1891, he married Carola Crosio. He died of a heart attack on April 20, 1932 in Turin.

Milestones and distinctions

• 1881: publication of its first article,
• 1884: publication of Calcolo Differenziale e Principii di Calcolo Integrale
• 1887: publication of Applicazioni Geometriche del Calcolo Infinitesimale
• 1889: appointed first class professor at the Royal Military Academy
• 1890: Special Professor of Infinitesimal Calculus at the University of Turin
• 1891: Member of the Turin Science Academy
• 1893: publication of Lezioni di Analisi Infinitesimale (2 volumes)
• 1895: promoted to regular professor at the University of Turin
• 1901: Knight of the Order of Saints Mauritius and Lazarus
• 1903: announcement Latino sine flexione
• 1905: Knight of the Order of the Crown of Italy, chosen as a corresponding member of the Accademia dei Lincei in Rome, the greatest honor for an Italian scientist
• 1908: publication of Mathematico Form (fifth and final edition of the project Form)
• 1917: Official of the Order of the Crown of Italy
• 1921: Commander of the Order of the Crown of Italy

Career

Aritmetica generale e álgebra elementare, 1902

He began his career as an assistant at the University of Turin in 1880. He was first an assistant to Enrico D'Ovidio and then to Angelo Genocchi, the head of the chair in Infinitesimal Calculus. Due to Genocchi's failing health, Peano began teaching calculus courses after two years of working as a professor's assistant.

His first major work, a textbook on calculus, was attributed to Genocchi and published in 1884. Three years later, Peano published his first book on mathematical logic. This book was the first to use the modern symbols for the union and intersection of sets.

In 1886 he began teaching concurrently at the Royal Military Academy, and was promoted to first-class professor in 1889. The following year, the University of Turin also gave him a full professorship.

The famous space-filling curve or Peano curve appeared in 1890 as a counterexample that he used to show that a continuous curve cannot be enclosed in an arbitrarily small region. This was an early example of what is known as a fractal.

The following year the Form Project began. It was to be an Encyclopedia of Mathematics, containing all the known formulas and theorems of mathematical science using a standard notation invented by him.

In 1897, the first International Congress of Mathematicians was held in Zurich. Peano was a key participant, he presented a paper on mathematical logic. he also began to be busier with the Form to the detriment of his other jobs.

In 1898 he submitted a note to the Academy about the binary number system and its ability to be used to represent the sounds of languages. At one point he became so frustrated with publication delays (because of his demand that the formulas be printed on one line), that he bought a printing press.

Paris was the site of the Second International Conference on Mathematics in 1900. The conference was preceded by the first International Conference on Philosophy where Peano was a member of the steering committee. He presented an article where he posed the question of correctly formed definitions in mathematics, ie "How do you define a definition?". This became one of Peano's main philosophical interests for the rest of his life. At said conference he met Bertrand Russell to whom he gave a copy of the Form . Russell was so impressed with the innovative logical symbols that he left the lecture and returned to study Peano's text.

Peano's disciples presented papers (using Peano's teachings) at mathematical conferences, however Peano did not present any. A resolution was issued for the formation of an "auxiliary international language" that it would make it easier for new mathematical (and commercial) ideas to spread, Peano fully supported that idea.

By 1901 he was at the peak of his mathematical career. He made advances in the areas of analysis, fundamentals, and logic, made many contributions to the teaching of calculus, and contributed to the fields of differential equations and vector analysis. He played a central role in the axiomatization of mathematics and pioneered the development of mathematical logic. By this time he was heavily involved with the Formula project and his professorships began to suffer. In fact, he was so determined he was to teach his new mathematical symbols that no attention was paid to calculus in his courses. As a result, he was dismissed from the Royal Military Academy, but retained his position at the University of Turin.

In 1903 he announced his work on an international auxiliary language called Latino sine flexione ("Latin without inflections", later called Interlingua). This was an important project for him (along with the meeting of collaborators for the Form). The idea was to use a Latin vocabulary, since it was widely known, but to simplify the grammar as much as possible and remove all irregularities and anomalous forms to make it easier to learn. In a brilliant speech, he began by speaking in Latin and, as he described each simplification, he inserted it into the speech so that by the end he was speaking in that new language.

1908 was a great year for Peano, when the fifth and final edition of the Formulario Project, entitled Formulario Mathematico, was published. It contained 4,200 formulas and theorems, all fully stated and most proven. The book received little attention since much of its content was already outdated at the time. The comments and examples were written in Latino sine flexione, which dampened the interest of most mathematicians; however, it remains a significant contribution to the mathematical literature.

Also in 1908 he held the chair of higher analysis in Turin (this appointment only lasted two years). He was elected director of the Academia pro Interlingua . Having previously created the Neutral Language, the Academy chose to abandon it in favor of Peano's Latino sine flexione.

After his mother died in 1910, Peano divided his time between teaching, working on high school-oriented texts (including a mathematics dictionary), and developing and promoting artificial languages of his own and others, becoming a revered member of the international auxiliary language movement. He used his membership in the Accademia dei Lincei to submit articles written by friends and colleagues who were not members (the Accademia recorded and published all articles submitted during sessions).

In 1925 he informally changed his chair from Infinitesimal Calculus to Complementary Mathematics, a field that more suited his style of mathematics. This move became official in 1931. He continued teaching at the University of Turin until the day before his death, on April 20, 1932, when he suffered a heart attack.

It was a man I admired a lot from the moment I first met him in 1900 at the Congress of Philosophy, which dominated by the accuracy of his mind.

Bertrand Russell, 1932