Leonhard Euler

Leonhard Euler was a Swiss polymath who made major contributions to many areas of science and mathematics. Born on April 15, 1707, and passing away on September 18, 1783, Euler was active as a mathematician, physicist, astronomer, and engineer. He founded the studies of graph theory and topology, and made influential discoveries in many branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus.

Euler is also known for introducing much of the modern mathematical terminology and notation that we use today. He popularized the Greek letter π to represent the ratio of a circle’s circumference to its diameter, and he was the first to use the letter i to express the imaginary unit √-1. Euler also introduced the notation f(x) for functions, the Greek letter Σ for summations, and Δ for finite differences. His work helped shape the way we study and apply mathematics.

In addition to his work in pure mathematics, Euler made important contributions to applied mathematics and engineering. His studies of ships improved navigation, and his work on optics helped in the design of microscopes and telescopes. Euler also reformulated Isaac Newton’s laws of motion to better explain the movement of solid objects, and he laid the foundations for many areas of physics and engineering.

Euler is regarded as one of the most prolific contributors to mathematics and science, and he is often called the greatest mathematician of the 18th century. He wrote over 866 publications, and his work continues to influence mathematicians and scientists around the world. Even after his death, other famous mathematicians like Pierre-Simon Laplace and Carl Friedrich Gauss praised Euler’s importance, with Gauss saying that studying Euler’s works was the best school for learning mathematics.

Early life

Leonhard Euler was born in Basel, Switzerland, on April 15, 1707. He was the oldest of four children in a family with a strong background in learning. Soon after his birth, his family moved to Riehen, where his father worked as a pastor.

From a young age, Euler showed a talent for mathematics. He studied at the University of Basel at just 13 years old. There, he was guided by Johann Bernoulli, a famous mathematician who helped him learn through challenging books and weekly meetings. With Bernoulli’s support, Euler chose to pursue mathematics instead of following his father’s path into the church.

Career

Leonhard Euler began his career at the Imperial Russian Academy of Sciences in Saint Petersburg. After moving there in 1727, he worked closely with Daniel Bernoulli and took on various roles, including a position in the mathematics department. He later joined the Russian Navy as a medic before focusing fully on mathematics.

Euler then spent 25 years in Berlin, where he produced many important works, such as his text on functions. During this time, he also tutored a princess and wrote many letters explaining science in simple terms. In 1766, he returned to Saint Petersburg, where he continued his mathematical work until his death.

Personal life

Leonhard Euler married Katharina Gsell, the daughter of a painter, in 1734. They bought a house near the Neva River. After Katharina passed away, Euler married her half-sister, Salome Abigail Gsell. They had 13 children together, but only five lived past childhood. Euler was known for his memory and kindness, even after he lost his sight.

Euler’s eyesight got worse over time. He lost most of the vision in his right eye in 1738 and later in his left eye as well. Even with poor vision, he kept working hard and produced many mathematical papers.

Contributions to science

Main article: Contributions of Leonhard Euler to mathematics

Leonhard Euler made major contributions to many areas of mathematics and science. He worked on geometry, calculus, trigonometry, algebra, and number theory, as well as physics and astronomy. His works fill many volumes, and his ideas influenced many fields. Euler introduced important mathematical notations we still use today.

Euler helped develop calculus and used it to solve problems in physics. He created new ways to represent mathematical ideas with symbols, like using "f(x)" for functions and the letter "e" for a special number. He also worked on solving complex math problems involving infinite sums and special numbers. His work connected different areas of math and science, making new discoveries possible.

Personal philosophy and religious beliefs

Euler was a devout Christian throughout his life and believed the Bible was inspired. He wrote about his beliefs in letters and a book defending the Bible against critics.

Euler disagreed with the ideas of some other philosophers, calling their views "heathen and atheistic." There is a popular, though likely made-up, story about Euler using a mathematical formula to convince a philosopher named Diderot that God exists. While this story is amusing, it is not true and was likely first told by another writer later on.

Legacy

Main article: List of topics named after Leonhard Euler

Leonhard Euler is remembered as one of the greatest mathematicians of all time. Many people think he was the most productive thinker in math and science. He is often placed among the top mathematicians in history, right below famous names like Carl Friedrich Gauss, Isaac Newton, and Archimedes.

Euler appeared on Swiss money and stamps, and an asteroid was named after him to honor his amazing contributions to math.

Selected bibliography

Leonhard Euler wrote many important books and papers. Some of his well-known works include:

• Mechanica (1736)
• Introductio in analysin infinitorum (1748) (Introduction to Analysis of the Infinite)
• Institutiones calculi differentialis (1755) (Foundations of differential calculus)
• Vollständige Anleitung zur Algebra (1765) (Elements of Algebra)
• Institutiones calculi integralis (1768–1770) (Foundations of integral calculus)
• Letters to a German Princess (1768–1772)

Euler’s work has been carefully collected and organized. The Euler Archive, which began at Dartmouth College, is now hosted by the University of the Pacific. The Swiss Academy of Sciences started the Euler Commission to publish all of Euler’s works in a series called Opera Omnia. This huge project has published many volumes organizing Euler’s mathematics, science, and letters.