Albrecht Dürer Biography

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World of Mathematics on Albrecht Dürer

Albrecht Dürer was a world-renown German artist who incorporated the use of geometry and other mathematical theories into his woodcuts, illustrations, and other graphic artwork. Dürer also published a series of treatises on the applications of mathematics to art.

Dürer was born in 1471 in Nuremberg, the third of eighteen children of Albrecht Dürer the Elder and his wife Barbara. Dürer the Elder was a master goldsmith and artisan who served as Nuremberg's official assayer of gold. Dürer the Younger attended school for several years as a child, until leaving at age 10 or 12 to learn goldsmithing and jewelry-making from his father. As an apprentice, Dürer mastered drawing and metal working techniques, and his innate talents as an artist were apparent from an early age. A self-portrait made by Dürer at age 13 that is still in existence today shows his remarkably realistic and finely-detailed drawing skills.

At age 15, Dürer began a second apprenticeship with Michael Wolgemut, a successful Nuremberg painter who taught him drafting skills and woodcut illustration. At the advice of Wolgemut and his father, who both recognized Dürer's immense talents, he toured Germany to further develop his craft and study and meet with other German artists. When he returned home in 1494, he entered into an arranged marriage with Agnes Frey, daughter of a wealthy Nuremberg artisan, and used the dowry money to finance his first trip to Italy. It was in Italy that Dürer hoped not only to broaden his artistic horizons, but to learn more about the study of mathematics in order to raise his art and the study of art in general to new levels.

While in Italy, Dürer studied the classical Italian art forms. While there are no records of Dürer meeting personally with any of the famous Italian mathematical figures of the time, there are indications that he followed their work while in Italy and discussed their theories with several Italian artists during his stay. Dürer also did not meet with Leonardo da Vinci, another outspoken proponent of the use mathematics in art, although there is later evidence that he knew of da Vinci's theories and had met at least one of da Vinci's confidants.

When he returned to Nuremberg in 1495, Dürer began an intensive study of the mathematical theories of Euclid, Vitruvius, and the Italians Leone Alberti and Luca Pacioli. Dürer's close friend Willibald Pirckheimer, a well-connected humanist translator and writer fluent in Italian, Greek, and Latin, provided Dürer with ready access to classic mathematical texts and Italian Renaissance literature, and introduced him to many leading figures of both Nuremberg and Italian society.

Dürer set up his own artists workshop in 1496, and began to incorporate many of the mathematical principles he had studied into his woodcuts, sketches, and other works. The influence of Pacioli, in particular, surfaced in many of his works as he incorporated the concepts of perspective and proportion into his artwork. He used compass and ruler to construct proportionate human figures, and geometrical patterns and shapes began to figure prominently in his artwork. Dürer's mathematical influences are also clear in his later works. His application of mathematics to art would continue throughout his career. Dürer's famous 1514 engraving "Melancholia," incorporates the figure of a magic square, which is believed to be the first representation of that mathematical figure seen in Europe.

After a number of commissions for portraits by wealthy, highly-ranked members of German society, Dürer's reputation as a master artist began to grow throughout Germany. By 1500, he was acknowledged as both a well-respected and well-compensated member of the artistic community. Between 1505 and 1507, Dürer visited Italy once again to consult and study with Italian mathematicians. During this trip he is thought to have met with Pacioli and mathematician Jacopo de Barbari. Upon his return to Nuremberg, Dürer began work on a series of books that would explain the mathematical principles of proportion and their applications to art. The books, which formed a treatise entitled Unterweisung der Messung mit dem Zirkel und Richtscheit, (or "Investigation of the Measurement with Circles and Straight Lines of Plane and Solid Figures"), were a blend of artistic instruction and classical and contemporary mathematical theory. They dealt with the construction of curves, polygons, and other geometrical elements; the nature of pyramids, cylinders, and other solids; and the theory of perspective. Dürer published them himself in 1525. Three years later, Dürer was in the final stages of preparing his newest work Four Books on Human Proportion for publication when he died. At age 57, Albrecht Dürer had become one of the world's most famous artists and an important figure in Renaissance mathematics and geometrical theory.