History of equations

Already in the 16TH century BC, the Egyptians solving everyday problems that had to do with the distribution of food, crops and materials that were equivalent to solve simple algebraic equations of first degree; as the algebraic notation did not exist, they used an approximate iterative method, called the “method of false position’.

The principles of our era Chinese mathematicians wrote the book the nine chapters on the mathematical art, which raised various methods for solving algebraic equations of first and second degree, as well as systems of two equations with two unknowns.

The Greek mathematician Diophantus of Alexandria published his Arithmetica in the 3RD century trying to first and second degree equations; He was one of the first to use symbols to represent equations. It also raised the equations solver with entire solutions, called Diophantine equations in his honor.
After the “dark age” medieval, the study of algebraic equations experiences a boost. In the 15TH century were the order of the day public mathematical challenges, with prizes to the winner; Thus, a famous challenge faced two mathematicians to solve equations of the third degree, the winner was Niccolò Fontana Tartaglia, expert bonesetter.

About mid-16TH-century Italian Girolamo Cardano and Rafael Bombelli mathematicians discovered to solve all equations of second, third and fourth graders, the use of imaginary numbers was essential. Cardano, staunch enemy of Tartaglia, also found methods of solving equations of fourth grade.

In the same century, the French mathematician Rene Descartes popularized the modern algebraic notation, in which the constants are represented by the first letters of the alphabet, a, b, c,… and the variables or unknowns by the latter, x, y and z.

At this time outlining problems of equations that only have been resolved today, some recently; among them Fermat’s last theorem, one of the most famous theorems of mathematics, which was not proven until 1995 by Andrew Wiles and Richard Taylor.
In the 17TH century, Isaac Newton and Gottfried Leibniz published the first methods of solving differential equations appearing in dynamics problems. The first book about these equations was probably on the constructions of differential equations of first degree, Gabriele Manfredi (1707). During the 18TH century, illustrious mathematicians Leonhard Euler, Daniel Bernoulli, Joseph Lagrange and Pierre Simon Laplace published findings on ordinary differential equations and equations in partial derivatives.
Despite all the efforts of former times, algebraic fifth grade and higher equations were reluctant to be resolved; It was only achieved in particular cases, but was not a general solution. At the beginning of the 19TH century, Niels Henrik Abel proved there is no resolvable equations; in particular, he showed that a general formula there is for solving the equation of fifth grade; then Évariste Galois showed, using his theory of groups, that the same can be said of any equation of degree equal to or greater than five.

During the 19TH century, the physical sciences used in its formulation differential partial differential equations or integral equations, as in the case of the electrodynamics of James Clerk Maxwell, the Hamiltonian mechanics or fluid mechanics. The routine use of these equations and solution methods led to the creation of a new specialty, mathematical physics.

In the 20TH century, mathematical physics continued to expand its field of action; Erwin Schrödinger, Wolfgang Ernst Pauli and Paul Dirac formulated equations with complex functions to quantum mechanics. Albert Einstein used tensor equations for his General relativity. The equations also have a wide range of applications in economic theory.

Since the majority of equations that arise in practice are very difficult or even impossible to solve analytically, it is common to use numerical methods for finding approximate roots. The development of information technology makes it possible to currently meet at reasonable times equations of thousands and even millions of variables using numerical algorithms.