Leonhard Euler (pronounced "oiler")
1707 - 1783

Leonhard Euler was born in Basel, Switzerland, the first of six children in a minister's family. (Wheeler, 1995) His father was a Calvinist preacher and worked with young Euler in the area of mathematics and even managed to have Leonhard study with the renown Johann Bernoulli. (Dunham, 1990) Like most preacher's kids, Euler has no desire to follow the steps of his father as a minister. His interest was with numbers. As an aside, some see a mathematical connection with the Bible. Jesus Christ, the central figure in Christianity told a mathematical problem in the form of a biblical story. He told of a shepherd who had one hundred sheep and lost one. The shepherd then counted ninety and nine. That's basic mathematics. However, in spite of his upbringing, Euler's attraction to mathematics was more powerful than the calling to ministry so he sought to develop his mathematical skills more so than his biblical knowledge. At age 13 he entered the University of Basel and received his Master's Degree at age 16. He even broadened his studies to include astronomy, medicine, languages, and physics. (Wheeler, 1995)

Early in his career, Euler lost sight in one of his eyes, possibly from observing the sun without taking proper precaution, in his study of astronomy. (Reimer, 1992) After completing most of his formal studies, Euler became a well-traveled individual and experienced culture far beyond his modest upbringing in Switzerland. Before he was appointed to the St. Petersburg Academy in Russia in 1727, he published his first formal mathematical paper at age 19 regarding the optimum placement of a ship's mast, even though he had never seen a sea-going vessel! (Dunham, 1990) For this same treatise, he won a prize from the Paris Academy of Sciences. (Burton, 1998) In 1741, Euler left St. Petersburg to take a position in the Berlin Academy under Frederick the Great before he eventually returned to St. Petersburg during the reign of Catherine the Great. He lost sight in his other eye due to a cataract, and at age 50 was completely blind until his death in 1783. (Reimer, 1992) Euler was so highly regarded that even without sight he was still able to continue his incredible calculations and mathematical assertions.

Euler was described by his contemporaries and peers, one of which was Isaac Newton, who he collaborated with over the famous equation F = ma, as a kind and generous man who enjoyed the simple pleasures of life. His simple pleasures included growing vegetables in his garden and telling stories of his 13 children and playing with his many grandchildren. (Dunham, 1990) He is possibly the most prolific writer in mathematics history. He is credited with revising all the branches of mathematics, which included filling in details, adding proofs, and arranging everything into a consistent form. (Reimer, 1992) He applied mathematics to shipbuilding, geodesy, astronomy, ballistics, optics and a variety of other areas. ( Cooke, 1997) He is also credited with writing the definite textbooks of calculus. It has been said that calculus professors today simply teach the things that Euler presented hundreds of years ago. In 1748 he wrote Introductio in analysin infinitorium a two-volume work which thoroughly discussed analytical geometry in two and three dimensions, infinite series, and the foundations of a systematic theory of algebraic functions. Other works include, Institutiones calculi differentialis and Institutiones calculi integralis written from 1768 to 1774. (Cooke,1997) Euler wrote and dictated over 700 books and papers in his lifetime. (Burton, 123)

Euler's most notable work was his Opera omnia. This work is contained in 73 volumes of collected papers and 886 books and articles. His writings contain papers on acoustics, engineering, mechanics, astronomy, and even a three-volume treatise on optical devices such as telescopes and microscopes. (Dunham, 1990) His writings on optical devices tend to be ironic considering that the last 25 years of his life, Euler was blind. While no one theorem can sum up the work of Leonhard Euler, he is remembered for his ability to solve problems involving series, such as:

Not only did he work with series, but also proved that any even perfect number must have the form specified by Euclid. The riddle of the perfect even number N was solved by Euler when he determined that if N is an even perfect number, then there exists a positive integer n such that,

He also made great strides in attempts to understand Fermat's Theorem. Euler's generalization of Fermat's theorem which is defined, "For n > 1, let (n) denote the number of positive integers not exceeding n that are relatively prime to n."

For this generalization, the notation (n) became known as Euler's Phi Function. (Burton, 123)

Modern mathematics owes a great deal to the efforts of Leonhard Euler. Not only did he make enormous strides in the study of advanced mathematics, he also is credited with some "little things" that just cannot be overlooked. He was the first to establish a consistency with the use of letters of the alphabet. Lowercase letters represented the sides of a triangle and uppercase letters represented the opposite angles. He standardized the use of the letter e to represent the base system of natural logarithms. Euler's work also established the use of the Greek letter for the ratio of circumference to diameter in a circle. (Reimer, 1992) He was also the first to use circles to show the relationship of sets, but instead of calling them Euler Circles, they are identified as Venn Diagrams. (Price, Rath, Leschensky, 1992) His many contributions have helped to formulate and mold today's curriculum and methods in many mathematical fields. (Wheeler, 1995)

Thank you Leonhard Euler!

Contributed by John Stockstill


  1. Burton, D. (1998) Elementary Number Theory. St. Louis: The McGraw -Hill Companies, Inc.
  2. Cooke, R. (1997) The History of Mathematics. New York: John Wiley and Sons, Inc.
  3. Dunham, W. (1990) Journey Through Genius. New York: John Wiley and Sons.
  4. Price, J., Rath, J.N., Leschensky, W. (1992) Pre-Algebra, a transition to algebra. Lake Forest: Macmillan / McGraw - Hill Publishing Company.
  5. Reimer, W., Reimer, L. (1992) Historical connections in mathematics. Fresno: AIMS Educational Foundation.
  6. Wheeler, E.R., Wheeler, R.E. (1995) Modern Mathematics for Elementary School Teachers. New York: Brooks / Cole Publishing Company.

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