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Mathematics

The Life and Times of Leonhard Euler

Once, or maybe twice, every century there comes a mind that was seemingly methodically placed on this plane, with the simple purpose of reinventing the way the entire world sees even trivial, everyday occurrences. Sometimes this thinker is a philosopher, as in someone like Henry David Throeau–very often however, with specific examples of Roman and Greek thinkers, this person comes from the mathematics or science discipline. This is certainly the case with brilliant 18th century mathematician Leonhard Euler, who arguably contributed more to modern mathematics than anyone else in history.

Born in Basel, Switzerland on April 15, 1707, Leonhard Euler was born the son of a Calvinist pastor, and originally studied theology and Hebrew himself. Attending the University of Basel, his life’s plan was originally to follow his father into a member of the Church. In 1724, he graduated from the institution, where he had been “privately tutored” by the world renowned mathematician John Bernoulli. In fact, it was this man himself that single-handedly convinced Euler’s father to allow Euler to pursue mathematics as a career, a testament to the brilliance of even the early mind of Leonhard Euler (Golba, 2007).

One of the most unique things about the Swiss mathematician is the sheer amount of works he compiled. There was never any precedence for the amount of work, papers, and thesis’ he compiled, and there has never been anyone comparable since. Mathematician William Dunham wrote in 1994:

To date there are well over 70 volumes on the shelves (but            who’s counting?) and             new ones will appear sporadically well into the twenty-first century. As a typical    volume runs to 500 large pages and weighs about 4 pounds, the overall bulk of   his Opera Omnia stands at more than 300 pounds! No other mathematician          can match this poundage.

There have been many mathematicians, theorists, and scientists in history, both before and after Euler–men such as Issac Newton and Albert Einstein, and even their genius could match the work of Leonhard Euler (Leonard Euler, 2012).

It is interesting to note the sheer work ethic when considering Mr. Euler’s various contributions. In 1727 he moved to St. Petersburg to take a position, and eventually head of mathematics, at the Academy of Sciences in Russia. While at the institution, he participated in a contest to solve a math problem. All other mathematicians took months to solve the problem; Euler, on the other hand, stayed up for three days straight and solved the equation–an act that literally cost him the vision in one of his eyes (Wachsmuth, 2007).

He then moved to Berlin where his works could be less impeded than they were under the czar in Russia. This was a time where Russia and Prussia were at constant war, and, during the conflict, Euler’s personal home was destroyed. He was held in such high regard by both governments that he was compensated for his home and all personal items. This is not the only example of the clear respect Euler commanded within the international community, however. Euler was not in the favor of the Prussian King, Frederick the Great, and was thus passed up for the position of President of The Academy of Sciences in Berlin. Instead, D’Alembert, a French mathematician, was offered the prestigious position. He, strictly out of respect for Euler, declined to take the position at all (Wachsmuth, 2007).

One of the major contributions Leonhard Euler has made to modern mathematics is in the legacy left behind in the textbooks he wrote. Euler himself was a fan of children, and helped to standardize many of the mathematical symbols and formulas we now take for granted. Some examples of these include the formula for complex functions, the symbol for imaginary numbers, or i, as well as the symbol for pi, again helped to be made standard at 3.14 (Wachsmuth, 2007).

Another major contribution to math founded by Leonhard Euler is increased studies in Euclidean Geometry. His creation of a new theorem rocked the foundation of the mathematics world, as the field had previously been looked upon as completed. The theorem, which has to do with a new way to find the center of a circle within a triangle, was truly innovative (Leonard Euler, 2012).

Perhaps the most considerable innovation Leonhard Euler presented to the world of mathematics is the concept of trigonometric functions. Before Euler, there was absolutely no understanding as to how the angles of a triangle related to its sides. In this way, he also became responsible for the “imaginary logarithms of negative numbers”, proving that every complex number has an infinite number of logarithms (Boyer, 2013).

Euler was interested in more than just mathematics on this planet. He was known, especially after 1753, as one of the foremost experts on theories of lunar motion, and more specifically what was known as the “three-body problem”; defined as the relationships and interaction between the Earth, Sun, and Moon. He was able to do adequate calculations to assist the British Navy in creating lunar charts, at this point with no sight at all. All equations were imagined, and solved within Euler’s incredible mind (Boyer, 2013).

Euler was able to think on a plane much differently from most people. His mathematical genius did not simply deal with complex numbers and imaginary numbers, but the theory behind these numbers. Called integers, Leonhard Euler spent much of his life’s work exploring the ideas behind the numbers. In his experimentation with whole numbers, or integers, he discovered the law of quadratic reciprocity. This, in essence, started modern number theory and the way mathematics is looked at today (Boyer, 2013).

Specifically, without this contribution in particular, the explosion of algebraic theory of later generations would never have been possible. Leonhard Euler laid the foundation for any further research and development into real numbers by explaining quadratic reciprocity to the world (Boyer, 2013).

This is only the tip of the proverbial iceberg when it comes to the study of Leonhard Euler’s contributions to mathematics as a whole. With regards to mechanics, “Euler angles” are “angles that specify the orientation of a rigid body”, taken from his discoveries in trigonometry (“Leonhard Euler”, 2013).

His discoveries truly do span every single aspect of mathematics. Euler’s theorem, with regards to math and physics for example, states that every single rotation has an axis in which to rotate on. In addition, he also adopted equations for determining the motion of fluids. His most popular “Euler’s formula” is widely taught and recognized as defining exponents of imaginary numbers in trigonometric terms. These principles are still taught to this day, hundreds of years after his death (“Leonhard Euler”, 2013)

There is another example of what is known as “Euler’s formula” in the terms of mathematics. It seems that when one’s body of work encompasses the vast regions that Euler’s did there is bound to be more than one theorem bearing one’s name. This theorem “gives the values of the Riemann zeta function at positive, even integers, in terms of Bernouilli numbers” (“Leonhard Euler”, 2013).

In fact, there exists both a Euler number system, and a Eularian number system, which are completely different. The number system named directly for the mathematician has to do with the math involved in architecture; Euler extensively studied bridges across what is now Germany, and applied this numerical system to their further study; a discipline now known as a form of “topology” (“Leonhard Euler”, 2013).

Leonhard Euler was perhaps the most active and diverse mathematician the world has ever seen. In addition, he also had one of the most prolific minds the world has ever seen. The stories of his ability to work with children running at his feet is legendary, and in the case of Euler, his minds’ capacity was further enhanced with the loss of his sight. His ability to do incredibly difficult calculations in his head is a story best told by the “contemporary mathematician Condorcet”, in his retelling of a situation where students of Eulers’, while working on a problem, came to the same answer up to the fiftieth decimal place. Euler then “recomputed” the problem in his head, visionless, and provided his students with an answer on the spot.

Mind’s such as Leonhard Euler’s are truly timeless.

Resources

Boyer, Carl. “Leonhard Euler (Swiss Mathematician).” Encyclopedia Britannica Online.            Encyclopedia Britannica, n.d. Web. 18 Apr. 2013.

“Leonhard Euler.” LEONHARD EULER. N.p., 2013. Web. 18 Apr. 2013.

“Leonhard Euler.” Mathematicians. N.p., 2012. Web. 18 Apr. 2013.

“List of Discoveries by Leonhard Euler.” Euler, Leonhard. Thefreedictionary,com, n.d.                        <http://encyclopedia2.thefreedictionary.com/List+of+discoveries+by+Leonhard+         Euler>.