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.
2. Child Prodigy: Euler enrolled at the University of Basel at the age of 13 and earned his Master’s degree in Philosophy by 16.
3. Multifaceted Genius: Besides mathematics, Euler made significant contributions to physics, astronomy, logic, and engineering.
4. Eccentricity: Euler’s work often demonstrated a unique blend of deep theoretical insights and practical problem-solving, reflecting his versatile genius and broad intellectual curiosity.
5. Blind Mathematician: Euler lost the sight in his right eye in 1738 and became completely blind in 1766. Despite this, his productivity did not diminish, and he continued to work with the help of assistants.
6. Family Man: Euler was a devoted family man with 13 children, though only five survived to adulthood. He often worked with his children playing around him.
7. Eulerian Numbers: Euler’s work on permutations and combinatorics led to the introduction of Eulerian numbers, important in the study of combinatorial mathematics.
8. Eulerian Path: Euler’s work on the Seven Bridges of Königsberg problem laid the foundation for graph theory and introduced the concept of Eulerian paths.
9. Teacher and Mentor: Euler was an influential teacher and mentor. He tutored students from various backgrounds and wrote educational books to make complex topics accessible.
10. Mechanica: Euler’s "Mechanica" formulated the principles of Newtonian mechanics using differential equations, providing a systematic framework for classical mechanics.
11. Euler’s Totient Function: Euler introduced the totient function, which counts the integers up to a given integer that are coprime to it, a crucial function in number theory.
12. Military Engineer: Euler worked as a military engineer in the Russian army and helped design fortifications.
13. Multilingual: Euler was fluent in several languages, including Latin, French, German, and Russian.
14. Memoir Writer: Euler wrote a memoir detailing his scientific and mathematical discoveries, contributing significantly to the historical record.
15. Personal Hardships: Despite many personal hardships, including the deaths of several children and his wife, Euler maintained his scientific work and productivity.
16. Euler’s Angles: Euler developed the concept of Euler angles, which describe the orientation of a rigid body in three-dimensional space.
17. Pioneered Calculus: Euler’s work laid the foundation for many aspects of modern calculus, both differential and integral.
18. Correspondent: Euler maintained correspondence with many leading scientists and mathematicians of his time, sharing ideas and collaborating on research.
19. Lunar Theory: Euler made significant contributions to the understanding of the Moon’s motion, improving the accuracy of lunar tables used in navigation.
20. Euler’s Disk: He studied the dynamics of rotating objects, leading to the analysis of what is now known as Euler’s Disk.
21. Euler-Bernoulli Beam Theory: In collaboration with Daniel Bernoulli, Euler developed the Euler-Bernoulli beam equation, fundamental in structural engineering.
22. Publications in Russian: Euler published many of his works in Russian during his time at the St. Petersburg Academy of Sciences.
23. Institutiones: Euler’s major works, "Institutiones calculi differentialis" and "Institutiones calculi integralis," systematized the fields of differential and integral calculus.
24. Letters to a Princess: Euler’s "Letters to a German Princess" made complex scientific concepts accessible to a broader audience and were widely read.
25. Graph Theory Pioneer: Euler’s solution to the Seven Bridges of Königsberg problem is considered the first theorem of graph theory, a foundational element of modern computer science.