One of the pioneers to be known in the field of mathematics from the 18^{th} Century is Leonhard Euler. He was born in Berlin, Switzerland, to pastor of the Reformed church, Paul Euler on April 15, 1707. Being a pastor himself, Paul wished his son to become a pastor too. But Paul’s friend and a great Swiss mathematician, Johann Bernoulli, identified Euler’s capability of achieving great success in mathematics. He spent a lot of time studying/under the mentorship of Johann’s son, Daniel Bernoulli.

Euler did his masters from University of Basel. After moving to Russia in 1727, he served the Russian Navy as a medical lieutenant till 1730. The same year he joined St. Petersburg Academy of Sciences as a Physics Professor with the help of his friend Daniel Bernoulli who headed the Mathematics department there. Then a year later took over Daniel’s position after his death.

Major publications by Euler were made during his chairmanship in this academy. His first book titled as Mechanica, covered his analysis of Newtonian dynamics in mathematical form. His other works covered fields of integral calculus, geometry, logarithmic functions, optics, mechanics etc.

Many of the notations that are used in mathematics today became popular due to Euler’s efforts. Some of these include;

SYMBOL | NAME | PURPOSE/FUNCTION/USE |

π | Pi | Ratio of a circle’s circumference to its diameter |

∑ | Sigma | Sum of all numbers |

sin, cos, tan | Sine, cosine, tangent | Trigonometric functions |

f(x) |
Function of x |
‘f ‘is the function of variable ‘x’ |

i |
Unit imaginary number | Square root of negative one (-1) |

e |
Base of natural logarthm |

In 1735, Euler also worked on the Basel Theory that was proposed early in 1644 and confirmed the sum of a specific zeta function to be. This result was different by what Daniel Bernoulli had provided earlier. The same year, he made another progression in mathematics by solving the Seven Bridges of Königsberg Problem that had remained unsolved by many scientists for many years, thus introducing the concept of graphs. In result of his untiring efforts, Euler loss sight in his one eye in 1735.

In 1741, Euler got the opportunity of joining the Berlin Academy of Science and Beaux Arts upon invitation from Frederick the Great. From this year untill 1766; Euler made numerous contributions to mathematics through his articles, books and publications. Some of his works include;

**Calculus: **

Many formulae and solutions of differentiation and integration were discovered by Euler. He presented them in his publications *Institutiones calculi differentialis* in 1755 and *Institutiones calculi integralis* in 1768–70 that allowed many future mathematicians to use them in various applications such as, calculating work done by a force, finding geometric solutions etc.

**Algebra:**

He used scientific reasoning for the fundamental processes occurring, proved the binomial theorem and addressed the problems put forth by Fermat and solved them. His book Anleitung zur Algebra published in 1770 in two volumes contains a lot of his algebraic work.

**Geometry:**

He presented properties of Euler line, Euler’s circle and many other geometrical phenomenons.

**Trigonometry: **

He developed a famous relation which we now know as the Euler’s Identity. He also gave the concept of imaginary logarithms of negative numbers and infinite logarithms for complex numbers.

**Astronomy:**

Much of Euler’s work can also be found in astronomy amongst which three books are of great significance. In these he addressed the problem of three bodies. He referred the motion of a body with its three axes that are parallel to one another. This discovery by Euler led to the construction of Lunar Tables by Mayer. Euler’s books on astronomy include,

- Theoria Motuum Planetarum et Cometarum in 1744
- Theoria Motus Lunaris in 1753
- Theoria Motuum Lunae in 1772

**Optics:**

Euler also made prominent discoveries in optics in 1746. He then got his book published in three volumes by the name of Dioptrica.

Euler died in St. Petersburg on September 18, 1783 and the cause of death was said to be brain hemorrhage. Even after his death, Euler received great respect from the whole of mathematical society especially the Mathematical Association of America. *Leonhardi Euleri Opera Omnia is a compilation of all of Euler’s work and has multiple volumes. *