Leonhard Euler and pure mathematics

Leonhard Euler and pure mathematics

Leonhard Euler was a mathematician of Swiss origin whose most important works focused on pure mathematics, a field of study that he helped found.

Euler was born in Basel on April 15, 1707 and studied at the University of this city with the Swiss mathematician Johann Bernoulli, graduating at age 16.

In 1727, at the invitation of the Empress of Russia Catherine I, she became a member of the faculty of the St. Petersburg Academy of Sciences. He was appointed professor of physics in 1730 and mathematics in 1733.

In 1741 he was a professor of mathematics at the Academy of Sciences of Berlin at the request of the King of Prussia, Frederick the Great. Euler returned to St. Petersburg in 1766, where he remained until his death.

Although hampered by a partial loss of vision before his 30th birthday and almost total blindness at the end of his life, Euler produced numerous important mathematical works, as well as mathematical and scientific reviews.

In his Introduction to Infinity Analysis (1748), Euler performed the first complete analytical treatment of algebra, equation theory, trigonometry and analytical geometry. In this work he discussed the development of series of functions and formulated the rule by which only infinite convergent series can be properly evaluated.

He also addressed three-dimensional surfaces and showed that conic sections are represented by the general equation of second degree in two dimensions. Other works dealt with calculus (including the calculus of variations), number theory, graph theory, imaginary numbers and determined and indeterminate algebra.

Euler, although mainly a mathematician, also made contributions to astronomy, mechanics, optics and acoustics. Among his works are Institutions of differential calculus (1755), Institutions of integral calculus (1768-1770) and Introduction to algebra (1770).

Euler had a prodigious memory; he remembered the powers, until the sixth, of the first 100 prime numbers, and the entire Aeneid. He made mental calculations that other mathematicians performed with difficulty on paper.

Euler's mathematical productivity was extraordinary. We find his name in all branches of mathematics: There are Euler's formulas, Euler's polynomials, Euler's constants, Eulerian integrals and Euler's lines. In spite of all this he married and had thirteen children, always being attentive to the welfare of the family; He raised his children and grandchildren.

Leonhard Euler died on September 18, 1783 in St. Petersburg, Russia. He was one of the most brilliant mathematicians in history and it is estimated that his complete works could occupy between 60 and 80 volumes.

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