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# 16th Century An important figure in the late 15th and early 16th centuries is an Italian Franciscan friar called Luca Pacioli, who published a book on arithmetic, geometry and book-keeping which became quite popular for the mathematical puzzles it contained. In Renaissance Italy of the early 16...

# 16th Century An important figure in the late 15th and early 16th centuries is an Italian Franciscan friar called Luca Pacioli, who published a book on arithmetic, geometry and book-keeping which became quite popular for the mathematical puzzles it contained. In Renaissance Italy of the early 16th century, Bologna University in particular was famed for its intense public mathematics competitions. It was in just such a competition that the unlikely figure of the young, self-taught Niccolò Fontana Tartaglia revealed to the world the formula for solving first one type, and later all types, of cubic equations (equations with terms including $x^3$), an achievement hitherto considered impossible and which had stumped the best mathematicians of China, India and the Islamic world. Building on Tartaglia’s work, another young Italian Lodovico Ferrari, soon devised a similar method to solve quartic equations (equations with terms including $x^4$) and both solutions were published by Gerolamo Cardano. Tartaglia went on to produce other important (although largely ignored) formulas and methods, and Cardano published perhaps the first systematic treatment of probability. # 17th Century The 17th century saw John Napier, and others greatly extend the power of mathematics as a calculatory science with his discovery of logarithms. Pierre de Fermat was a French lawyer and a mathematician who is given credit for early developments that led to infinitesimal calculus. Fermat, together with Pascal, began the mathematical study of probability. Blaise Pascal laid the foundations of the Probability Theory together with Fermat. He invented the Pascaline, an early mechanical calculator. He is also known for the Pascal’s Triangle, a tool for expanding a binomial $(a + b)^n$. Rene Descartes was another notable mathematician of the 17th century. He invented the Cartesian coordinate system, developed analytic geometry and laid the foundation for the development of calculus.