Born: 15 April 1707 · Basel, Swiss Confederacy

Died: 18 September 1783 (aged 76) [OS: 7 September 1783] · Saint Petersburg, Russian Empire

Education: University of Basel (MPhil)

Spouses: Katharina Gsell · (m. 1734; died 1773) · Salome Abigail Gsell · (m. 1776)

Children: 13, including Johann

Known for: Contributions · namesakes

Fields: Mathematics · Physics

Institutions: Imperial Russian Academy of Sciences · Berlin Academy

Major contributions of Leonhard Euler  include:

• Founded graph theory and studies of topology.

• Developed the theory of trigonometric and logarithmic functions.

• Introduced mathematical notation still in use today.

• Used the letter "e" for the base of the natural logarithm (Euler's number).

• Influenced graph theory, calculus, trigonometry, geometry, algebra, physics, music theory, and astronomy.

Problem/events that influence Leonhard Euler's  mathematical ideas:

Leonhard Euler’s mathematical ideas were shaped by several pivotal events and influences throughout his life. Growing up in Basel, Switzerland, he was introduced to mathematics early, largely due to his father, a pastor and amateur mathematician, who supported his education. Euler also thrived in the intellectually rich environment of 18th-century Europe, where he had access to interactions with leading scientists and mathematicians of his time.

At the University of Basel, Euler studied under prominent mathematician Johann Bernoulli, whose mentorship played a significant role in Euler’s development. Euler's exposure to the works of mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz broadened his understanding and laid the foundation for his later groundbreaking contributions.

During his time in St. Petersburg, Russia, and later in Berlin, Euler collaborated with leading scientific figures, further extending his influence. Despite personal challenges, such as losing his sight later in life, Euler remained remarkably productive. His ability to develop efficient mathematical methods was enhanced by these difficulties. Euler’s deep interest in solving real-world problems in physics, mechanics, and astronomy drove him to create vital mathematical tools, such as Euler’s formula and Euler’s identity. These experiences, combined with his unrelenting curiosity, played a critical role in shaping Euler’s transformative impact on mathematics.

His Impact on the modern mathematics:

Leonhard Euler’s impact on modern mathematics is immense and continues to shape various fields today. His contributions to calculus, graph theory, number theory, and topology have laid the groundwork for many modern mathematical concepts. Euler’s formula, eiπ+1=0e^{i\pi} + 1 = 0, is one of the most famous equations in mathematics, linking five key mathematical constants and influencing areas like complex analysis, physics, and engineering.

In graph theory, Euler introduced concepts such as the Eulerian path and Eulerian circuit, which are essential to modern network theory and computer science. His work in number theory, including the Euler’s totient function and the distribution of prime numbers, has significant applications in modern cryptography and algorithm design.

Euler’s work in fluid dynamics, mechanics, and astronomy also played a pivotal role in advancing physics and engineering. Moreover, his introduction of mathematical notation, including the function notation f(x)f(x) and the summation symbol Σ\Sigma, has become integral to the way mathematics is written and studied today. Euler's ideas and methods continue to influence mathematics, science, and technology, cementing his legacy as one of the most important figures in the history of mathematics.