LEONHARD EULER: BIOGRAPHY, CONTRIBUTIONS, WORKS, QUOTES - CULTURE VOCABULARY - 2025

Leonhard Paul Euler (1707-1783) is considered the leading mathematician of the 18th century and one of the most prolific and eminent of all time. This Swiss-born mathematician is recognized as one of the original fathers of pure mathematics, and made a decisive contribution in the areas of theory, calculus, graphing and mechanics.

He was also a physicist and a philosopher; his ability and alertness have led him to be compared with minds of the stature of the father of physics, Albert Einstein. According to historians who have studied his work, it can be said that Euler was light-tempered and unsophisticated, even simple tastes, but he was very tenacious and hard-working.

Leonhard Euler, one of the most outstanding mathematicians in history. Source: Jakob Emanuel Handmann

His religious training led him to the field of philosophy under that approach. Despite this, it is known that he did not have a solid knowledge or proper handling of rhetoric, something that some of his philosophical competitors took advantage of to organize debates on topics such as metaphysics, debates of which he was rarely successful.

As with other brilliant minds in history, his works and theories are still being published and studied. Even many authors agree that today some of their proposals are fundamental parts that make the search engines that we use every day to surf the internet much faster.

Euler's extensive work made it possible for him to have a marked influence on different branches of knowledge. For example, among the most relevant contributions of this scientist stands out the discovery of several mathematical constants, all of them in common use today.

Likewise, he also developed important advances in the fields of astronomy, physics and mechanics, and even in the field of optics, in which he proposed a theory that differed from that presented by Isaac Newton.

Biography

Early years

Leonhard Euler was born on April 15, 1707 in Basel, Switzerland. He was the son of the marriage between Pastor Paul Euler, a man who belonged to a theological system called "Calvinism"; and Marguerite Brucker, who was the daughter of another pastor in the same stream.

From an early age, he surprised parents and close associates - such as the Bernoulli family, of which the father was intimately known - with his abilities in early learning and the skills to quickly solve basic arithmetic problems.

Her formal education began in Basel despite the rest of the family living in the nearby town of Riehen, where her family decided to move shortly after giving birth to Leonhard. He was the eldest of three children, he had two younger sisters named Anna María and María Magdalena. Euler had a quiet and peaceful childhood.

Brilliant and prominent from the start, and under the care lavished on his maternal grandmother, Euler managed to enter the University of Basel at the young age of 13. In 1723, when he was only 16 years old, he obtained the title of Master of Philosophy.

Influenced by his father - who had the hope of ordaining him as pastor of his Church as well - Euler studied Hebrew, Greek and theology with determination.

Paul's good friend, Johann Bernoulli, convinced him to allow him not to follow in his footsteps given the exceptional conditions he constantly demonstrated in relation to numbers and mathematics in general.

Adolescence

Completely devoted to studies, he turned 19 when he completed his doctorate; His thesis, De Sono, was about the propagation of sound.

When he was 20 years old, he entered a contest through which the French Academy of Sciences required the contestants to locate the optimal place to place the mast of a boat.

He did not win the contest at that time (then he won it more than a dozen times), but he was only beaten by who in the end was known as the father of naval architecture, the French mathematician, astronomer and geophysicist Pierre Bourguer.

Arrival in Russia

At that time, at the beginning of 1727, Euler was called from the Russian Academy of Sciences (located in Saint Petersburg) to fill the position that became vacant after the death of one of the sons of Johann Bernoulli, an old friend of the father of Euler.

He did not come immediately, as his priority was to obtain a place as a Physics professor at his university. He was unsuccessful in this endeavor, so he arrived in Russia on May 17, 1727.

Euler quickly worked closely with Daniel Bernoulli and was promoted from the Medical Department to another position in the Department of Mathematics.

It is important to note that at that time the Academy had ample resources and freedoms for its researchers due to the intention of the nation to raise its educational level and reduce the wide range that existed compared to the nations of the West.

Catherine I of Russia was the person who mainly promoted this idea of ​​increasing educational levels. Upon the arrival of Leonhard to the country, Catherine died at the age of 43, leaving Peter II of Russia, who at that time was 12 years old, on the throne.

This fatal event aroused suspicions in the Russian nobility about the legitimate intentions of the foreign scientists summoned to the Academy, which caused them to cut most of the budget dedicated to them.

Death of Pedro II and nuptials

As a result of this situation, economic adversities settled on Euler and Bernoulli, and only slightly improved when Pedro II died. By the age of 24 Euler had already climbed ranks and became a Physics professor at the Academy.

In 1731 he established himself as director of the Department of Mathematics of the Academy after his colleague Daniel Bernoulli returned to his native Basel, as a result of the climate of tension that still existed on the part of the nobility.

The stay in Russia ceased to be lonely for Euler, since on January 7, 1734 he married Katharina Gsell, daughter of a Swiss painter from the Academy named Georg Gsell and of the also painter Dorothea M. Graff.

The Euler-Gsell couple had 13 children, of which only five survived. Of them Johann Euler stood out, who became a member of the Berlin Academy thanks to his knowledge of mathematics and astronomy.

From Russia to Germany

The political instability in Russia was palpable. Concerned for his integrity and that of his family, he decided to travel to Berlin on June 19, 1741 to settle there and be able to work at the Academy of that city. His stay in Germany lasted 25 years, during which he wrote most of the treatises and works of his life.

It was in Germany that he wrote and published the works Introductio in analysin infinitorum and Institutiones Calculi Differentialis, of 1748 and 1755 respectively. These were two of the most important works that this scientist wrote in the course of his career as a researcher.

With a broad inclination to philosophy, Euler spent part of his time writing more than 200 letters to Princess Anhalt-Dessau, who was under his tutelage at the time.

In these letters -which were later compiled, published and considered the most widely read work of the Swiss mathematician- Leonhard Euler extended himself with teacher-student confidence on various topics, among which philosophy, religion, physics and mathematics stood out., among other matters.

Consolidation of your beliefs

In the multiple and extensive letters that Leonhard Euler tried to convey to Princess Anhalt-Dessau, his student and mentee, you can see a Euler of deep Christian faith, committed to the concepts proclaimed by the Bible and its literal interpretation.

Perhaps that is why he was critical of philosophical currents such as monism, which proposed and argued that everything in the universe was made up of a single and primary substance, which meant that everything was matter and only matter. He was also opposed to the opposite extreme of this current, idealism, according to which this primary substance was the spirit.

Any philosophical current that was at odds with his literal vision of the Christian holy text was considered by Euler as atheistic, pagan and not worthy of being spread. Such was Leonhard Euler's dedication to Christianity and its parameters.

Euler the Cyclops

Before his arrival in Germany, and thanks to the deplorable world health situation during the century, Euler suffered from several diseases. One of these in particular occurred in 1735 and almost ended his life; The consequences of these diseases caused that in 1738 he almost completely lost the vision in his right eye.

His passage through Germany did not change the luck of his sight; his right eye gradually deteriorated, to the point that the king himself referred to him as "the cyclops." Years later his sight was punished again: this time the cataracts took over his left eye, leaving him practically blind.

None of that set him back in his productive career; on the contrary, it gave him a new impetus, thereby increasing the well-earned respect that the scientific community around him had for him. There came a time when Leonhard Euler dictated the results of calculations that he mentally produced to his assistant, almost as if he could see them.

Return to russia

Despite all his contributions and contributions to the Berlin Academy, and in general to the science of the time, at the end of 1766 Euler had to leave the city that hosted him for 25 years.

The reason for this was that King Frederick II had never finished getting along with the "mathematical cyclops"; He criticized it for its simplicity and the little grace it brought to halls full of nobles.

The economic, social and political situation in Russia had undergone a fortunate change and the mathematician did not hesitate to accept a job invitation at the Saint Petersburg Academy of Sciences. However, his second stay in Russia was full of unfortunate events.

In 1771 he almost lost his life in a raging fire that consumed his house to its very foundations. Just two years later, in 1773, his wife Katharina, a woman with whom he shared his life for 40 years, lost his life.

Second nuptials and death

The loneliness into which he fell disappeared in 1776, the year in which he married Salome Abigail Gsell, half-sister of his first wife. This woman accompanied him until his last days.

His death occurred in Saint Petersburg as a result of a sudden stroke, on September 18, 1783. His mortal remains were buried along with those of his first wife and today they rest in the Alexander Nevsky Monastery.

Contributions

Historically, Euler is considered the person with the most publications, studies and treatises made to date. It is estimated that only a limited 10% of all his works have been studied.

Their contributions touch so many areas that their influence reaches our days. For example, Sudoku, a popular entertainment that requires ordering a string of numbers in a specific way, is believed to be due to calculations of probabilities addressed by it.

All areas and any possible branch of mathematics were touched by this Swiss scientist. Geometry, calculus, trigonometry, number theory, algebra, and even set diagrams, so widely used in education today, have their main driver in Leonhard Euler.

The function and mathematical notation

Euler was the first to propose that a result or magnitude of any operation is a "function" of another if the first value depends on the value of the second.

He denoted this nomenclature as f (x), where one is the "function" and the other the "argument." Thus, the time “A” (dependent variable) that it takes a vehicle to travel an established distance “d” will depend on the speed “v” (independent variable) of the vehicle.

He also introduced the now called "e number" or "Euler number", which connected John Napier's logarithmic functions with exponential functions.

Euler popularized the use of the symbol π. He was also the first to use the Greek letter ∑ as an indication of a sum of factors and the letter “i” as a reference to the imaginary unit.

Logarithms and e number

Euler established the use of the "number e", whose value is 2.71828. This value became one of the most important irrational numbers. This mathematical constant is defined as the base of natural logarithms and part of equations of compound interest.

He also discovered how to express various logarithmic functions with the use of power series. With this discovery he managed to express the arc tangent function and surprised by solving a problem (the Basel problem), in which he asked to find the exact sum of the inverses of the squares of the positive integers of an infinite series.

Calculus and applied mathematics

This mathematician introduced new ways of facing and solving fourth degree equations. He deduced the way to calculate integrals with complex limits and managed to find a way to calculate variations.

One of the most relevant achievements of Leonhard Euler was the use of mathematics, the mathematical analysis of real life situations, to solve the problems that arose.

In this case, mathematics aims to give a logical, orderly and possible answer to everyday problems in, for example, the social sciences or finance.

Engineering, mechanics, physics and astronomy

His main contribution in the field of engineering was the analysis of the composite and decomposed forces that affect vertical structures and cause their deformation or buckling. These studies are collected in the so-called Euler's law. This law describes for the first time the radius line and specific properties, the fundamental basis of engineering.

Astronomy also felt the impulse of the contributions of Euler, since with his work he contributed to the more precise calculation of distances of celestial bodies, the calculation of the orbits of planets in their space journey and the calculation of the trajectory and path of comets. He concluded that all planets orbit the Sun in an elliptical path.

To be sure, Euler's influence was extremely broad; He also put his knowledge to work for solving mechanical problems. In this sense, he was the one who used the vector symbol to notice acceleration and velocity, and used the concepts of mass and particle.

Other areas in which he had influence

The field of optics was also part of the topics in which Euler left his contribution. He had a different theory than the one put forward by his colleague Isaac Newton; for Euler, light propagated in the form of waves. He studied the mechanics of the flow of an ideal imaginary fluid, and created Euler's equations in this area.

Plays

During his lifetime, Leonhard Euler wrote up to 800 pages a year at his most productive age. It is known that the vast majority of his work is still not shared with the world and is waiting to be reproduced under the title of Opera Ommia, an ambitious project that aims to bring to light all the texts produced by this scientist.

There are almost 400 articles on philosophical and / or mathematical topics written by this mathematician. Among his entire collection, his most relevant works are listed below:

- Mechanica, sive motus scientia analytica expósita (1736)

- Tentamen novae theoriae musicae (1739).

- Solutio problematis ad geometriam situs pertinentis (1741).

- Methodus invent curved lines maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti (1744).

- Introductio in analysin infinitorum (1748).

- Institutiones Calculi Differentialis (1755).

- Theoria motus corporum solidorum seu rigidorum (1765).

- Institutiones Calculi Integralis (1768 - 1770).

- Vollständige Anleitung zur Algebra (1770).

- Lettres à une Princesse d'Allemagne (Letters to a German princess) (1768 - 1772).

It is estimated that, if his complete work was published, it would occupy between 60 and 80 volumes. The arduous process of complete publication of his work began in 1911, and 76 volumes have been published to date.

Quotes

History has always perpetuated the word of those characters who, due to their achievements, contributions to humanity and deep thought, earned such a right. Leonhard Euler could not be the exception.

Many phrases articulated by this famous Swiss mathematician passed through generations to this day. Some of the most famous are listed below:

- "Since the texture of the Universe is the most perfect and the work of a very wise Creator, nothing happens in the Universe without obeying some rule of maximum or minimum."

- "Better than our judgment, we must trust the algebraic calculation."

- "Although the aim is to penetrate into the intimate mystery of nature and from there to learn the true causes of phenomena, it may happen, nevertheless, that a certain fictitious hypothesis may be enough to explain many phenomena."

- “For those who ask what is the smallest quantity in mathematics, the answer is zero. Therefore, there are not so many hidden mysteries in this concept, since it is generally believed that there are ”.

- "Mathematicians have tried in vain, until now, to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery that the human mind will never solve."

- "Of course, when the actual causes are too obscure, but the final causes are more easily determined, the problem is commonly solved by the indirect method."

- “The type of knowledge that only relies on observations and has not yet been proven must be carefully distinguished from the truth; you win by induction, as we say. However, we have seen cases in which mere induction led to error ”.

Leonhard Euler was well ahead of his time, and an example of this is the quote we mention below. He could not prove certain numbers and / or equations, not because it was impossible to do so but because he did not have the appropriate tools that were invented with the passage of time, and Euler was very aware of this:

- “In fact, it would be a considerable invention to have a machine capable of imitating speech, with its sounds and articulations. … I think it's not impossible ”.

References

1. "Leonhard Euler" in Wikipedia. Retrieved on February 20, 2019 from Wikipedia: es.wikipedia.org
2. "Leonard Euler" at the University of Granada. Retrieved on February 20, 2019 from the University of Granada: ugr.es
3. "The enigma solved 300 years ago by the mathematician Leonhard Euler that today allows us to access the internet" on BBC London. Retrieved on February 20, 2019 from BBC - News - World: bbc.com
4. "Leonhard Euler" in Encyclopaedia Britannica. Retrieved on February 20, 2019 from Encyclopaedia Britannica: britannica.com
5. "Phrases of Leonhard Euler" in Phrases and Thoughts. Retrieved on February 20, 2019 from Frases y Pensamientos: frasesypensamientos.com.ar