European Renaissance mathematics (c. 1200—1600)

In Europe at the dawn of the Renaissance, most of what is now called school mathematics -- addition, subtraction, multiplication, division, and geometry -- was known to educated people, though the notation was cumbersome: Roman numerals and words were used, but no symbols: no plus sign, no equal sign, and no use of x as an unknown. Most of the mathematics now taught at universities was either known only to the mathematical community in India or had yet to be investigated and developed in Europe.

Through Latin translations of Arabic texts, knowledge of the Hindu-Arabic numerals and other important developments of Islamic and Indian mathematics were brought to Europe. Robert of Chester's translation of Al-Khwarizmi's Al-Jabr wa-al-Muqabilah into Latin in the 12th century was particularly important. The earlier works of Aristotle were redeveloped in Europe, first in Arabic and later in Greek. Of particular importance was the rediscovery of a collection of Aristotle's logical writing, compiled in the 1st century, known as the Organon.

The reawakened desire for new knowledge sparked a renewed interest in mathematics. Fibonacci, in the early 13th century, produced the first significant mathematics in Europe since the time of Eratosthenes, a gap of more than a thousand years. But it was only from the late 16th century that European mathematicians began to make advances without precedent anywhere in the world, so far as is known today.

The first of these was the general solution of cubic equations, generally credited to Scipione del Ferro circa 1510, but first published in Gerolamo Cardano's Ars magna. It was quickly followed by Lodovico Ferrari's solution of the general quartic equation.

From this point on, mathematical developments came swiftly, and combined with advances in science, to their mutual benefit. At this time Treviso arithmetic was first written, and is still regarded as the first mathematics book ever printed. In the landmark year 1543, Copernicus published De revolutionibus, asserting that the Earth traveled around the Sun, and Vesalius published De humani corporis fabrica, treating the human body as a collection of organs.

Driven by the demands of navigation and the growing need for accurate maps of large areas, trigonometry grew to be a major branch of mathematics. Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Regiomontanus' table of sines and cosines was published in 1533.[12]

By century's end, thanks to Regiomontanus (1436—1476) and François Vieta (1540—1603), among others, mathematics was written using Hindu-Arabic numerals and in a form not too different from the elegant notation used today.