Leonhard Euler


Leonhard Euler was one of top mathematicians of the eighteenth century and the greatest mathematician to come out of Switzerland.

He made numerous contributions to almost every mathematics field and was the most prolific mathematics writer of all time. It was said that “Euler calculated without apparent effort, as men breathe….”

He was dubbed “Analysis Incarnate” by his peers for his incredible ability.

Leonhard Euler was born in Basel, Switzerland, on April 15, 1707. His father, a Calvinist pastor and former mathematician, planned the life of a clergyman for his son and originally Leonhard followed that path.

He graduated from the University of Basel in 1724 where he studied theology and Hebrew. During his time at the school, however, he was privately tutored in mathematics by Johann Bernoulli.

Johann was so impressed by his pupil’s ability that he convinced Euler’s father to allow Leonhard to become a mathematician.

Euler took up a position at the Academy of Sciences in St. Petersburg, Russia, in 1727 and became the professor of mathematics six years later.

During his stay, he was married and would over his lifetime have thirteen children, five of which would survive to adulthood. While in Russia, he lost sight in one eye after working day and night for three days to solve a problem.

The question, which was a public contest, took all the other mathematicians involved months to figure out. He also discovered that the Czar’s government was far from democratic as he was followed by secret police. He looked for a way out.

He found it in 1741, when he moved his family to Berlin to take over as director of mathematics at the Academy of Sciences under Frederick the Great.

While in Prussia, his home was destroyed by invading Russian armies, but he was held in such high esteem by both countries that he was compensated for more than he lost. He also frustrated Frederick’s mother to no end by refusing to engage in conversation.

When she finally asked him for a reason, he responded: “Madam, it is because I have just come from a country where every person who speaks in hanged.”

He also could not handle the intrigues and feuds that plagued the Academy. When the previous president died, Euler should have been the obvious successor except for the fact that Frederick disliked him.

The monarch asked D’Alembert, a French mathematician, to take the position. D’Alembert, who saw the injustice, refused on the basis that no one could be placed above Euler. However, it became clear it was time for Leonhard to find a new home.

Meanwhile, Russia had come under the rule of the more liberal Catherine the Great. In 1766, he returned to St. Petersburg and became the director of the Academy.

Soon afterwards, he went completely blind but continued his mathematical work by dictating to a secretary. His house burned down in 1771 and his life was saved only by the heroic efforts of a servant to carry him out of the flames.

He died of a stroke on September 7, 1783. Appropriately to this simple mathematician, his final words were simply “I die.”

Euler was especially famous from his writings. Simply put, he produced more scholarly work on mathematics than anyone.

It was said that he could produce an entire new mathematical paper in about thirty minutes and had huge piles of his works lying on his desk.

Even more impressive, Euler contemplated new problems not in quiet privacy but in the presence of his young children. It was not uncommon to find “Analysis Incarnate” ruminating over a new subject with a child on his lap.

Though Euler is best remembered for his contributions to mathematics, he was involved in some extent in almost all fields.

Especially close to his heart was philosophy. While in Berlin, he would constantly get involved in philosophical debates, especially with Voltaire. Unfortunately, Euler’s philosophical ability was limited and he often blundered to the amusement of all involved.

However, when he returned to Russia, he got his revenge. Catherine the Great had invited to her court the famous French philosopher Diderot, who to the chagrin of the czarina, attempted to convert her subjects to atheism.

She asked Euler to quiet him. One day in the court, the French philosopher, who had no mathematical knowledge, was informed that someone had a mathematical proof of the existence of God.

He asked to hear it. Euler then stepped forward and stated: “Sir, a+b/n=x, hence God exists; reply!” Diderot had no idea what Euler was talking about. However, he did understand the chorus of laughter that followed and soon after returned to France.

Euler’s contributions to every mathematical field that existed at the time. He standardized modern mathematics notation when he used symbols such as f(x), e, , i and in his textbooks.

He was the first person to represent trigonometric values as ratios and prove that e is an irrational number. His invention of the calculus of variations led to the general method to solve max and min value problems.

In physics, he developed the general equations for hydrodynamics and for motion. He was also one of the first people to recognize that infinite series had to be convergent to be used safely.

Possibly his most impressive work was his approximation of the three-body problem of the sun, earth and moon, which he solved while completely blind and performing all the computations in his head.

Among his other endeavors were proofs of Fermat’s final theorem for cubes and quads, the use of calculus in mechanics and the computation of logs for negative and imaginary numbers.

Cultivating creativity


One powerful way to live a more creative life is to cultivate the art of solving problems — this art helps you of looking more deeply at everything we experience with an open, inquisitive spirit. Creative people are intensely observant, paying careful attention to everything they think and hear. They realize that their environments – the people they talk to, the places they go, the things they read or hear on the radio or TV – can lead their thinking in fresh, exciting directions, which can lead to new ideas and opportunities.

Geniuses are just ordinary people who stumble on a knack or way of thinking that enables them to think and learn more effectively and creatively than others.

When you closely examine how “geniuses” like Newton or Archimedes thought, they didn’t simply sit under trees or in baths until their enlightenment: they used some very powerful and practical tools to create order out of their thoughts and find answers to problems that few people ever thought to solve.

  • Clear your head when faced with a challenging problem.
  • Generate more than one workable solution to your problem.
  • Think creatively.
  • Think productively instead of re-productively.
  • Give you clear methodology that will make solving problems straight forward and stress free.

First, here are some of the common factors of the world’s great thinkers:

  • The idea generation was in pictures and images rather than words. Einstein and da Vinci drew diagrams instead of writing words and sentences.
  • Their thinking was unrestrained nothing was consigned to the bin until it had been fully investigated.
  • They treated thoughts as things.
  • Ideas were explored using association.
  • They looked at ideas from different perspectives.
  • They were prolific and recorded everything.
  • They fuelled their imaginations with knowledge.
  • Their thinking was focused.
  • They were passionate and determined about discovery.
  • They made mistakes but instead of seeing them as failures, saw them instead as “ways of how not to do it”.
  • They saw potential in everything.
  • They saw mistakes and unexpected surprise results as valuable opportunities to learn from.
  • They never gave up.

Consider this definition of “problem”: a problem is an external event perceived as a mental, physical, emotional or intellectual threat to the individual/s concerned. Chances are, your problem only became “a problem” when you became personally involved causing your perception of an event to shift before that, it was just an event, when you perceived that you were potentially threatened by it, the event became a problem.

Everything (including problems) starts in your head. Using your imagination and thinking processes constructively while you solve problems gives your mind the “stuff” it needs to be productive (create new solutions) as distinct from re-productive (create more of the old which is what probably landed you with the problem in the first place).

One of the most reliable ways of solving a problem is the “systems” strategy.

This method does not allow you to add complications that do not exist and it ensures the facts are gathered without the hindrance of destructive emotion (the first indication that an event is turning into a problem).

Seeing the entire system (i.e. the problem and everything associated with it) enhances insight into a problem and allows you to deal with the real issue. Most often, when solutions don’t work it’s because they are the solution to a perceived problem, not the real one.

To develop this strategy, I recommend that you get in the habit of asking open-ended questions that help you to look more deeply at your daily encounters and experiences:

  • How can I use this?
  • What lessons or insights can I learn from this experience?
  • What does this mean in the context of my current creative challenge or the projects I’m working on?

Creative people realize that most ideas aren’t totally new, but are adaptations of what has worked in another market, industry or field of study. History is full of examples, from Alexander Graham Bell modeling the telephone after the way the human ear operated to George de Mestral, who used the concept of plant burrs sticking to his dog’s fur to envision Velcro fasteners. Taking ideas from other environments and adapting them for use in your situation is one of the best ways of developing novel solutions.

Your brain is equipped with the awesome capability of making associations between seemingly disparate pieces of information. It’s part of what makes us human beings so incessantly creative. To help ensure that your brain has a rich pile of creative “raw material” from which to draw, try to seek out unique inputs, knowledge and experiences:

  • Read a book or magazine that you don’t normally read. Reading broadly, from a variety of sources, brings your brain into contact with new ideas and concepts, and can be a trigger to your imagination.
  • Discuss your problem with people from entirely different backgrounds. You may be amazed at the ideas and insights these discussions will provoke.
  • Take a trip abroad and immerse yourself in another culture. International travel is one of the most mind-expanding experiences that I know of. Your senses are heightened as you experience new practices, customs and beliefs – creating a fertile field in your mind for new ideas to grow.
  • As you consider the problems and challenges you face, be on the lookout for analogous situations in other industries or fields. How did someone else solve a similar problem? What elements of their solution can you adapt to your situation?

In short, cultivating these strategies are one of the most practical ways in which you can become more creative in your daily life.