Leonhard Euler (Source: Wikimedia)

Leonhard Euler is a name as worthy of recognition as Albert Einstein, Stephen Hawking, Isaac Newton, and Pythagoras. The last four names are present in sci-math textbooks at every level.

However, Leonhard Euler, the most brilliant and the most proliferous mathematician of all time, remains invisible.

He is the person behind Euler’s constant, Euler’s polyhedron formula, the Euler line of a triangle, Euler’s equations of motion, Eulerian graphs, Euler’s pentagonal formula for partitions, and Euler’s number, to name a few. His influence is undying; today, 311 years after his birth, his contributions are everywhere, yet the details would extend beyond the scope of this article. Perhaps we should heed Pierre-Simon Laplace when he says,

Read Euler, read Euler, he is the master of us all.”

Leonhard Euler was born in Basel, Switzerland, in 1707, to a Calvinist pastor, Paul Euler. Although he showed prodigious talent for mathematics, his father was determined that he should study theology and pursue a career in the Church. Euler dutifully obeyed and studied theology and Hebrew at the University of Basel.

Basel was also home to the Bernoulli family, famous for their mathematical prowess—producing eight of Europe’s most extraordinary minds within only three generations. Daniel and Nikolaus Bernoulli, close friends of Euler, realized his potential in mathematics and convinced Paul Euler that his son was meant to calculate, not preach. Therefore, Leonhard soon left Switzerland and spent a good portion of his career in Berlin, under Frederick the Great of Prussia, and in Russia under Catherine the Great, where he spent his final years. Euler’s work ranged from infinite series, geometry, logarithms, calculus, and mechanics to optics, calculating paths of celestial bodies, motion of the moon, and sailing of ships.

He solved one problem after another with so much ease that the French academician Francois Arago remarked,

“Euler calculated without apparent effort, as men breathe or as eagles sustain themselves in the wind.”

Much of the mathematical notation today—including e, i, f(x), , and the use of a, b and c as constants and x,y and z as unknowns—was either created, popularized or standardized by Euler. Therefore, Euler’s work is at the root of almost every equation, formula, or other relationship used in mathematics, from the simplest to the most complex, from the algebra in your homework to the next groundbreaking discovery in math.

Rather than using mathematics to explore abstract concepts, rulers like Frederick and Catherine were interested in exploiting mathematics to solve practical problems, and employed the best minds to do so. Consequently, during his career, he tackled a plethora of real life problems, ranging from finance to acoustics, and from navigation to irrigation.

However, the practical world of problem solving did not dull Euler’s mathematical skills.

Instead, each new task inspired him to pioneer ingenious mathematics.His passion drove him to write several papers in a single day, and it is said that between the first and second calls for dinner, he would attempt to dash off a complete calculation worthy of publication. Not a moment was wasted, and even when he was cradling an infant in one hand, Euler would be outlining a proof with the other.

Basel Problem: Euler’s First Major Triumph in The World of Mathematics

In 1735, Euler showed that the sum of reciprocals of the square of all positive real numbers converges to:\frac{\pi ^{2}}{6}

\frac{1}{1}+\frac{1}{4}+\frac{1}{9}+\frac{1}{25}+\frac{1}{36}+.....=\frac{\pi ^{2}}{6}This problem had eluded mathematicians of the likes of Bernoulli for decades. Hence, this discovery sealed Euler’s reputation among mathematicians.

Euler’s Identity: The Most Beautiful Equation in Mathematics

In a masterstroke, Euler weaved together three unrelated threads of mathematics into one fabric. π (the ratio of a circle’s circumference to its diameter), e (the base of natural logarithms), and the imaginary number i (the square root of -1), are all distinct concepts, yet by combining them in Euler’s Identity, he combines arithmetic, calculus, trigonometry and complex analysis into one equation filled with cosmic beauty.e^{i\pi } + 1=0

In 1988, the journal Mathematical Intelligencer asked its readers to list the most beautiful equations in mathematics. Three of the top five nominees had been discovered by Euler, and the equation above won the first place.  David Percy of the University of Salford said:

Euler’s identity is amazing because it is simple to look at and yet incredibly profound. What appeals to me is that this equality connects some incredibly complicated and seemingly unrelated concepts in a surprisingly concise form

In late 1730s, Euler became partially blind due to his intensive work on cartography.

After almost 3 more decades, at the age of 59, Euler became totally blind.

For someone as resolute as him, this was no challenge. With the help of his brilliant memory, he continued working on various topics and produced almost half of his life’s work (about 430 books and articles) after this tragedy. Beethoven is well known for composing some of his best works when he was completely deaf, but it is a tragedy that Euler’s work during his blindness does not have the same level of recognition.

In his eulogy to Euler, Marquis de Condorcet writes:

“On the 7th of September 1783, after amusing himself with calculating on a slate the laws of the ascending motion of air balloons, the recent discovery of which was then making a noise all over Europe, he dined with Mr. Lexell and his family, talked of Herschel’s planet (Uranus), and of the calculations which determine its orbit. A little after, he called his grandchild, and fell a playing with him as he drank tea, when suddenly the pipe, which he held in his hand, dropped from it, and he ceased to calculate and to breathe. The great Euler was no more.”

Like a clock that works from the moment it starts ticking to the moment it stops, never wasting a second in between, Leonhard Euler worked incessantly, and perhaps never wasted a day in his life.

Before his death at in 1783, he had written more than 800 papers and books on pure and applied mathematics.

His collected works fill 25,000 pages in 79 volumes—more than anybody in the field. The Saint Petersburg Academy continued to publish Euler’s unpublished work for nearly 50 years after his demise. Mathematics would not be what it is today if it weren’t for Leonhard Euler’s revolutionary work. Whether you measure greatness by the quality of one’s work or the quantity, Euler is undoubtedly the greatest mathematician ever.

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