Mathematics of Southern Europe

Summary: Modern Western mathematics was developed in southern Europe and continues to thrive there.

The system of modern mathematics originated in southern Europe, with the ancient Greeks undoubtedly building on traditions already used in Egypt and by the Phoenicians. Like many areas of the world, the nations of southern Europe have had many different boundaries, names, and political alliances throughout history, and so the mathematical contributions of some individuals may be included within the histories of other regions. For example, many nations were member states of the former Soviet Union. The United Nations now includes Albania, Andorra, Bosnia and Herzegovina, Croatia, Gibraltar, Greece, Holy See, Italy, Malta, Montenegro, Portugal, San Marino, Serbia, Slovenia, Spain, and the former Yugoslav Republic of Macedonia in Southern Europe.

Ancient Greeks and Romans

The earliest Greek school of mathematics is ascribed to Thales (c. 640-550 b.c.e.), who came from Miletus, in present-day Turkey, and Pythagoras (c. 569-500 b.c.e.) who hailed from the Mediterranean island of Samos and later moved to Sicily. Archytas, who subscribed to the Pythagorean philosophy and worked on the harmonic mean, was from Tarentum in modern-day Italy. One of the most well-known Greek mathematicians of the ancient world, Euclid of Alexandria (c. 330-260 b.c.e.), was also not from the Greek mainland. He lived in Alexandria, in modern-day Egypt, and his work proved hugely influential to subsequent mathematicians with his detailed hypotheses and proofs. The great mathematician Archimedes of Syracuse (c. 285-212 b.c.e.) also studied in Alexandria but was from Sicily, where he spent most of his life.

These early Greek mathematicians were undoubtedly an influence on the Romans but the Romans themselves were seemingly more interested in applied mathematics especially how it related to engineering and building than in the pure mathematics that was favored by the Greeks. Mathematics was certainly taught in Roman schools and historians have long pondered why Roman mathematicians did not have more influence. This dearth of mathematical advancement has generally been ascribed to the Romans’ lack of a designation for “zero” and their awkward system of numbers, which may have prevented any great advances in theory. The Roman Empire did, however, see a continual flourishing of mathematics in Greece and the Greek diaspora, in particular the city of Alexandria. Anicius Manlius Severinus Boethius (c. 475-525) was a well-known Roman mathematician who worked during the declining years of the Roman Empire.

The Renaissance

The Bishop of Seville, Isidorus Hispalensis (570-636), helped develop mathematics in Spain and there were great advances made in arithmetic with the Moorish invasions of Spain and the incorporation of many of the advances made in the Muslim world. The great trading cities of Genoa and Venice soon established themselves as important centers of finance, as did Florence during the Renaissance. Venice, in particular, because of its geographical position and its connections with the Arab world, saw the importation of many books and manuscripts on Arab mathematics at that stage well advanced in pure mathematics theories compared to Europe. This Arab influence saw Leonardo Pisano Bigollo (c. 1170-1250), the son of an Italian merchant in North Africa, develop theories the most well-known being the Fibonacci numbers, which were termed after his assumed name.

Several centuries later, the advent of the printing press also led to a republication of the works of Greek mathematicians such as Euclid, albeit in Latin translation. Cardinal Bessarion, the former Archbishop of Nicaea, helped bridge the link between Byzantium and Rome, helping to preserve some of the Greek learning that was lost when the city of Constantinople was captured and sacked in 1453. Leonardo da Vinci (1452-1519) developed mathematics theories, testing out some of them in siege machines designed for Cesare Borgia and others. Girolamo Maggi (c. 1523-1572), another Italian mathematician, was involved in designing military defenses in Cyprus. He was captured by the Ottoman Turks and executed in Constantinople but not before writing two major treatises from memory while in prison there.

The Renaissance saw a new interest in mathematics in Italy, with Galileo Galilei (1564-1642) being a well-known mathematician and scientist. He was a great influence on many subsequent mathematicians, including Alessandro Marchetti (1633-1714). Evangelista Torricelli (1608-1647) invented a barometer; Giovanni Ceva (1647-1734) proved Ceva’s theorem in elementary geometry; and the Jesuit Franceso Cetti (1726-1778) helped connect mathematics to other scientific discoveries. Later Italian mathematicians include Giulio Ascoli (1843-1896) who taught in Milan, and Carlo Emilio Bonferroni (1892-1960) who developed the theory of Bonferroni inequalities. The Italian Mathematical Union was established in 1922 by Salvatore Pincherle and others, and its journal, the Bollettino dell’Unione Matematica Italiana, is widely respected around the world.

Professional Associations

Professional associations in the region other than the Italian Mathematical Union include the Bosnian Mathematical Society; the Croatian Mathematical Society; the Cyprus Mathematical Society; the Montenegro Mathematical Society; the Portuguese Society of Mathematics; the Mathematical Society of Serbia; the Mathematics, Physics, and Astronomy Society of Slovenia; and the Royal Spanish Mathematical Society. Mathematicians also gather from all over Europe in the European Mathematical Society. The International Mathematical Olympiad is a competition for high school students that originated in 1959. Albania first participated in 1993, Bosnia and Herzegovina in 1993, Croatia in 1993, Greece in 1975, Italy in 1967, Montenegro in 2007, Portugal in 1989, Serbia in 2006, Slovenia in 1993, Spain in 1983, Yugoslavia in 1963, and the former Yugoslav Republic of Macedonia in 1993. Greece was a host of the competition in 2004, Slovenia in 2006, Spain in 2008, and Yugoslavia in 1967 and 1977.

Bibliography

Field, Judith Veronica. The Invention of Infinity: Mathematics and Art in the Renaissance. New York: Oxford University Press, 1997.

Hodgkin, Luke. A History of Mathematics: From Mesopotamia to Modernity. New York: Oxford University Press, 2005.

Manaresi, Mirella. Mathematics and Culture in Europe: Mathematics in Art, Technology, Cinema, and Theatre. New York: Springer, 2007.