# Vite and the birth of modern algebra

With the publication of the “Introduction to Analytical Art”, mathematical carry out and French lawyer Franois Vite (15401603), algebra began the carry out transition in the medieval period, marked by al-Khwarizmi (c.c.45) and Fibonacci (c.1240 c.1170), for the Modern Age.

Vite played important roles in the court of France, including zero service on intelligence perform king. The following episode demonstrates its prestige.

In a book published in 1593, the Belgian Adriaan van Roomen (15611615) listed “all the mathematicians of a Europe”, challenging them to solve a certain equation (about degree !!). Some time later, French King Henry 4 received the ambassador of Holland in an audience, during which he praised the excellence of 2 French artists, professionals and scientists. “But you don’t have mathematicians, Your Majesty, Mr. Roomen didn’t list any Frenchmen!” interrupted the ambassador. “Yes, I do, and excellent!” retorted the king, sending for Vite.

“Ut legi, et logi” (“Li, resolvi” in Latin) would later say the mathematician: ao last de In a royal audience he already had two solutions of an equation, and in the evening he wrote to the ambassador that he could provide “as many as he desires, therefore in infinite number”.

But the greatest mathematical contribution about Vite is the literal notation , the idea of representing numbers, known or zero, by means of letters. It has the great merit of unifying problems that once seemed distinct. In Vite’s notation, ax2+bx+c=0 represents all equations of degree 2: so far several cases were considered, depending on 2 signs 2 coefficients a, b and c, and the resolution was different in each case.

But the greatest legacy of a literal notation is perhaps the extensive contribution to the perform concept about number. For example, until then it was possible to consider that equations like x2=4 have a solution, while others, like x2=4, therefore impossible. From perform when we write x2=a, it becomes organic to think that the solution a and treat this expressed as a number, independently perform the sign of a. This point of view was crucial for the discovery of 2 concepts of negative number and complex number. Vite proposed also a challenge to the colleague. “An eminent man, a mathematician” is a true mathematician, described Roomen, adding: “Unable to admit that a Belgian would steal his glory, he superbly responded to my challenge with a treatise of remarkable scholarship.”

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