Leonhard Euler, born on April 15, 1707, in Basel, Switzerland, was one of the most influential mathematicians and physicists in history. He was the first of six children born to Paul Euler, a pastor, and Marguerite Brucker, the daughter of a pastor. Euler's early education was conducted at home by his father, who had studied theology and had some training in mathematics from Jacob Bernoulli, a renowned mathematician.
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| Portrait of Leonhard Euler by Emanuel Handmann 1753 |
Euler entered the University of Basel at the age of 13. He earned his Master’s degree in Philosophy in 1723 with a dissertation comparing the philosophies of Descartes and Newton. Under the mentorship of Johann Bernoulli, Euler was encouraged to pursue his passion for mathematics despite his father's initial wish for him to become a pastor. Bernoulli recognized Euler’s exceptional talent and provided him with advanced mathematical problems to solve, fostering his mathematical abilities.
In 1727, Euler moved to St. Petersburg, Russia, joining the St. Petersburg Academy of Sciences at the invitation of Daniel Bernoulli, Johann's son. Initially, Euler was appointed to the physiology department, but he soon transferred to the mathematics department. He quickly established himself as a leading mathematician with his work on differential calculus and the theory of numbers.
Euler married Katharina Gsell in 1734. They had 13 children, though only five survived to adulthood. Euler’s family life was marked by both joy and tragedy, and he continued his work even amidst personal challenges. In 1738, Euler lost the sight in his right eye due to a fever, a condition that worsened over time.
In 1741, Euler accepted an invitation from Frederick the Great to join the Berlin Academy of Sciences. He spent 25 years in Berlin, where he published over 380 works and contributed to the development of several scientific disciplines. In 1766, Euler returned to St. Petersburg at the invitation of Catherine the Great. Despite losing his eyesight completely in 1766, Euler continued to work with the help of his assistants and maintained his prolific output until his death on September 18, 1783.
Fun Facts
1. Prolific Writer: Euler published over 850 papers and books during his lifetime, making him one of the most prolific mathematicians in history. His collected works fill more than 70 volumes, covering various topics in mathematics, physics, astronomy, and engineering.
2. Blind Mathematician: Euler lost the sight in his right eye in 1738 and became completely blind in 1766. Remarkably, his productivity did not decline after losing his eyesight. He developed a remarkable ability to perform complex calculations in his head and dictated his work to scribes.
3. Family Man: Euler was a devoted family man with 13 children, though only five survived to adulthood. He often worked with children playing around him, demonstrating his ability to concentrate amidst noise.
4. Memorable Legacy: Euler’s work laid the foundation for many areas of modern mathematics, and numerous concepts, theorems, and formulas bear his name, such as Euler’s number (e), Euler’s angles, Euler’s circuit, and Euler’s polyhedron formula.
Quotes
1. "Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different."
2. "To those who ask what the infinitely small quantity in mathematics is, I answer that it is actually zero. Hence, there are not so many mysteries hidden in this concept as they are usually believed to be."
3. "For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear."
4. "Nothing takes place in the world whose meaning is not that of some maximum or minimum."
Works
Leonhard Euler’s contributions span a wide array of disciplines. Here are some of his most notable works:
Mathematics
1. Introductio in analysin infinitorum (1748): Euler's seminal work in which he introduced the concept of a function and laid the foundation for the study of complex analysis. This work also contains his famous identity involving exponential and trigonometric functions.
2. Institutiones calculi differentialis (1755): A comprehensive work on differential calculus that systematically presented the foundations of differential calculus, including the notation and methods still used today.
3. Institutiones calculi integralis (1768-1770): A significant multi-volume work on integral calculus. Euler’s contributions to integral calculus were extensive and include the development of many integration techniques.
4. Mechanica (1736): Euler’s two-volume work on classical mechanics, where he systematically formulated the principles of Newtonian mechanics using differential equations.
5. Elements of Algebra (1770): Euler’s work aimed at a broad audience, introducing many into the study of algebra. This book remains one of the most popular and accessible books on the subject.
6. Letters to a German Princess (1768-1772): A series of letters written by Euler to the Princess of Anhalt-Dessau, in which he explained various scientific and philosophical topics in an accessible manner. These letters were widely read and contributed to Euler’s reputation as a great educator.
Physics and Astronomy
1. Theoria motus corporum solidorum seu rigidorum (1765): Euler’s work on the rotation of rigid bodies, introducing Euler’s equations for the motion of a rigid body. These equations form the foundation of rotational dynamics.
2. Euler’s Disk: Euler contributed significantly to the study of rigid body dynamics, including the analysis of the motion of a spinning disk, now commonly referred to as Euler’s Disk.
3. Opticks: Euler made substantial contributions to the wave theory of light and optics, developing theories that enhanced the understanding of light and vision.
4. Lunar Theory: Euler made significant contributions to the understanding of the Moon’s motion, developing methods to improve the accuracy of lunar tables used in navigation.
Engineering
1. Euler-Bernoulli Beam Theory: Euler, in collaboration with Daniel Bernoulli, formulated the Euler-Bernoulli beam equation, fundamental to structural engineering. This equation describes the relationship between the bending of a beam and the applied load.
2. Ship Design: Euler worked on improving the design and stability of ships, contributing to the field of naval architecture.
3. Hydrodynamics: Euler’s work in fluid dynamics includes the formulation of the Euler equations, which describe the flow of inviscid fluids.
Graph Theory
1. Seven Bridges of Königsberg (1736): Euler’s solution to the problem of the Seven Bridges of Königsberg laid the foundation for graph theory. He proved that it was impossible to walk through the city crossing each bridge only once, introducing the concept of Eulerian paths.
2. Eulerian Circuits: Euler’s work on the Königsberg problem led to the development of Eulerian circuits, paths that visit every edge of a graph exactly once.
3. Graph Theory and Topology: Euler's work in this field also laid the groundwork for topology, a branch of mathematics that studies properties of space that are preserved under continuous transformations.
Leonhard Euler’s contributions to science and mathematics are monumental. His work continues to influence and inspire mathematicians, scientists, and engineers. Euler’s legacy is a testament to his brilliance and his ability to overcome personal challenges to contribute profoundly to human knowledge. His remarkable productivity, even in the face of significant personal and health challenges, underscores his extraordinary dedication and intellectual prowess. Euler's works remain a cornerstone of mathematical and scientific education and research, cementing his status as one of the greatest mathematicians of all time.