Euler's Contributions to the Modern Day Mathematics Essay

Introduction

Leonhard Euler was born in1707 and died in 1783. Euler, a Swiss, is considered as a founder of pure mathematics. Most importantly is that Euler also contributed to quite a number of discoveries, for example, infinitesimal calculus and graph theory among others. Besides, he introduced several modern mathematical terminologies that are used currently. Notations for mathematical analysis and mathematical notations are some of his works. He also worked on principles of fluid dynamics, optics and astronomy as well as music theory. Euler is regarded as an 18th century mathematician and is equally considered the best in history. It is important to state that Euler's mathematical works can fill approximately 70 quarto volumes, which is relatively higher compared to the publication of other mathematicians of his time (Bair et al., 2017). History indicates that Euler (mathematician) spent a considerable amount of time as an adult in Saint Petersburg, Berlin and Prussia. Because of his mathematical ability, he managed to earn the prize of Johann Bernoulli, who was one of the mathematicians in entire Europe. Euler also worked with Saint Petersburg Academy, which saw him succeed Daniel Bernoulli as the chair of mathematics. According to Bair et al.(2017), Euler, perfected the concepts of integral calculus, created the theory of log functions and made analytical operations more simpler that brought a completely new insights in the field of mathematics. Records indicate that in the year 1735 Euler lost sight of one eye, and later also became a member of the Berlin Academy in which he served for nearly 20 years.

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Euler's contributions to the modern day mathematics

It is important to note that Euler was accountable for the majority of modern mathematical terminology as well as notations which are still used today. His works spanned around the fields of geometry, calculus, lunar theory, trigonometry and number theory. Euler was the first mathematician to introduce the notation for the function f (x), which has been used in modern notation for several trigonometric functions. He is also known for the letter e to imply base of a natural logarithm. Moreover, Euler popularized the Greek word to denote the ratio of a circle's circumference to its diameter. In addition, Euler also made some contributions to complex analysis, the Euler identity eip = -1 equation, combines calculus as well as trigonometry. He also discovered eix = cosx + isinx which state that for any real number x, the exponential function should be satisfied. Euler's identity revolves around constants such as I, 1, 0 which are the most essential elements in modern mathematic today. Beyer (2018), noted that Euler's mathematical discoveries were equally based on the calculations of infinite sums, it was known as a Basel problem after a failed trial by Bernoulli's, this concept involved the summing of the reciprocals of squares of all the natural numbers, 112 + 122 + 132 + 142.This discovery has made the current mathematicians to the infinite series equals to the infinite product of prime numbers. When it comes to number theory, Euler was able to show the relationship between in prime distributions, in which his analysis revealed the connection in Riemann zeta and prime numbers commonly called the Euler product formula for zeta functions.

Explain how this mathematics may have influenced modern day life or how it has affected historical events in the World

In the year 1735, Leonhard Euler solved a mathematical and logical challenge, called the Seven Bridges of Konigsberg Problem, which for several years has disturbed scholars as well as engineers. In offering a solution, Euler laid the foundations of graph theory and showed the relevance of mathematics concepts on the overall topology (Qi, Wang & Guo, 2018). The city prominently referred to today as Kaliningrad in Russia, was put on the two waterways of Pregel River, and established two incredible islands which were associated with one another and the terrain by the seven bridges. The major challenge was to find a route which could enable the city to cross the each bridge at one given time. Even though from his analysis, Euler noted that the problem had no solution, but in giving different insights of a route crossing landmasses, he was able to reformulate the problem. He replaced each particular mainland with the help of an abstract node, while for each bridge he used an abstract connection. With graphical representation of the problem, Euler was able to conclude that the land masses were touched by an odd number of bridges; hence the formation of a walk traversing each bridge could lead to contradictions. And if the city had lesser bridges and equally even number of bridges on each piece, then the solution would be possible.

Discover the importance of mathematics

Generally, mathematics is an application of a given matter in a defined manner. Firstly, mathematics makes our daily lives enjoyable and easier, math puzzles and riddles allow one to be alert and open-minded in addressing issues. Secondly, since the current modern world focuses more on innovations and skill developments, mathematics offers us with an approach that promotes rationality in thinking; hence it is a tool that encourages growth and developments.

References

Bair, J., Blaszczyk, P., Ely, R., Henry, V., Kanovei, V., Katz, K. U. & Schaps, D. M. (2017). Interpreting the infinitesimal mathematics of Leibniz and Euler. Journal for general philosophy of science, 48(2), 195-238.

Beyer, W. H. (2018). Handbook of Mathematical Science. CRC press.

Qi, F., Wang, J. L., & Guo, B. N. (2018). Simplifying differential equations concerning degenerate Bernoulli and Euler numbers, Trans. A. Razmadze Math. Inst. 171 (2017), no. 3, in press. ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.12078.10566.