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Born in 1879 in Württemberg, Germany, and died in 1955 in Princeton, New Jersey, Albert Einstein is undoubtedly **one of the greatest scientific figures **in the world.

Renowned for his various theses (including his best known **theory of special relativity and the theory of general relativity**), he received the Nobel Prize in Physics in 1921 and contributed to many advances in various fields, including cosmology, mechanics or quantum physics.

Much more than a brilliant scientist, Time magazine even named him personality of the 20th century.

In this article, we wanted to focus on what Albert Einstein brought to mathematics.

Let us pinpoint a moment in the history of mathematics and look in more detail at how the work of this scientific genius has changed how we learn maths.

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## Albert Einstein: A Lover of Nature

Legend says that Albert Einstein was a very bad student and was told he did not have what it takes to do well in maths class.

Believe it or not, that turned out to be further from the truth.

In actual fact, young Albert Einstein was a genius, as precocious as he was talented.

First in his class at school, **he adored learning mathematics and **maths revision.

Consequently, he refused to learn all subjects he deemed unnecessary. This meant waving goodbye to human sciences and modern languages, for example.

During his time at university, he became friends with a mathematician, Marcel Grossmann, who went on to help him prove his greatest theories. He was able to bring **his expertise and in-depth knowledge in non-Euclidean geometry to the table**.

Albert Einstein, a self-taught scientist, educated himself in the sciences that fascinated him. This allowed him to work on topics such as **celestial mechanics** and **nuclear physics**.

Recognised by his peers in 1909, it is from this date onward that he devoted himself entirely to research.

In fact we can define Albert Einstein as a lover of nature, in the sense that his objective was to understand its mechanisms.

As such, in his early years, he was convinced that only the study of physics would allow him to achieve this objective. By taking a step back from mathematics, he established **for the first time the notion of relativity** in this field.

For him, mathematics can not be certain when it relates to reality. Hence his theories of special and general relativity.

In fact, Einstein's post-mortum highlighted some unusual features that might help to explain how he became one of the greatest scientific geniuses the world has ever known.

## Maths Lessons: the Theory of Special Relativity

In 1905 for the first time Albert Einstein voiced the equation which made him famous throughout the world.

The famous formula **E = MC²**.

More importantly, what does this mean and why did it bring him glory and esteem?

In fact, this equation explains that a mass (M) multiplied by the velocity of the squared light (C²) produces a certain amount of energy (E) called mass energy.This implies that the faster a body moves, the more energy it releases.

But this idea did not come to him suddenly. It took him a whole thought process to come up with this equation for special relativity.

Everything begins with the assumption made by our learned ancestors that an object in motion has a velocity which corresponds to its normal velocity but also to that observed by an external observer.

By taking up the work of two 19th century physicists (Morley and Michelson), Albert Einstein made this amazing discovery that in fact **the laws of physics are the same everywhere**. And all of that, regardless of the reference. More surprisingly, **the movement would slow down time**.

An interesting example to illustrate this is that of space travelers moving at the speed of light, which would return to Earth after a year.While the latter have aged a year (the duration of their journey), the Earth would have undergone a much greater aging. In simpler terms: it has been proven that by moving at the speed of light, 1 second for you would be equal to approximately 1 minute for a motionless observer.

Albert Einstein's genius was to resonate on a much grander scale than on a human one. Indeed, on Earth, the speed of human movement is too low to observe even the slightest variation of time. Yet, taking as his starting point the speed of light, he had set up the notion of relativity in physics and **questioned the absolute nature of space and time**.

Thus, from this original postulate, he deduced that the velocity of a matter (as small as it may be) can cause great damage if it is launched at a great pace (using the famous equation E = MC²). The military and nuclear scientists quickly understood how to use this type of invention, and thus the atomic bomb was born. Today, we have learned how to tame this discovery to develop nuclear energy.

Thus, by creating a "simple" mathematical formula (a product), Albert Einstein changed the face of the world. We all remember the tragedies of Hiroshima and Nagasaki.

But this mathematical equation also allowed us to make** tremendous advances in understanding the workings of our universe**.

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## Learning Maths: the Theory of General Relativity

In 1915, after restricted relativity, Albert Einstein published a new theory on gravitation: **general relativity**.

Working from Isaac Newton's thesis (the law of universal gravitation which shows the fall of bodies and the displacement of the stars), Albert Einstein established a new postulate. He put aside the concept of gravitational force and explained that** every movement of an object is determined by the configuration of space-time**.

According to him, rather than the Sun pulling the Earth around it, Albert Einstein explains that the Sun actually creates a disruption of space-time. It is this anomaly that forces the Earth to evolve around the Sun.

Put simply, if we imagine a stretched sheet (symbolizing our galaxy or our universe) and in the middle of it we put a stone (our Sun). Under the force of this stone, the sheet will twist and deform.

Now, roll a marble from the edge of this sheet to the center, in any direction, and study its trajectory. What is interesting is that at the beginning, the ball will move in a continuous straight line. Then, as it enters the dip created by our stone, it will change direction and begin to turn around, thus making a curved trajectory. You see now that the marble symbolises a star (our beautiful planet Earth for example).

With this type of hypothesis, Albert Einstein explained to us that each body moves in a straight line in space-time. Regardless of its destination, it is only when it encounters an anomaly in the configuration of space-time that it will begin to modify its trajectory, making a curve around the object at the origin of this anomaly. Of course, this will take much longer than a simple ball turning around a stone in the center of a tablecloth. **We're talking about elements that are difficult for our human minds to comprehend**.

Difficult but not impossible since Albert Einstein came up with the mathematical equations and formulas that can accurately calculate the curvature of space-time created as a result.

Obviously, we are talking here of an infinitely complex system, still requiring years and years of research. For now, we have discovered what happens with an isolated star. Imagine on the scale of the galaxy, even of the universe, with its infinities of stars each producing their own strength. It's enough to make you dizzy.

Returning to our original subject, we can conclude that with this theory, **Albert Einstein questions the fifth postulate of Euclidean geometry** (see essential maths vocabulary) explaining that by placing a point outside a straight line there is only one parallel to this line.

Through his love of physics and desire to have a better understanding of how our universe works, he came to change our contemporary view of mathematics.

## Help with Maths: Gravitational Waves

Predicted by Albert Einstein in 1916, gravitational waves have just been detected using American instruments.

### Albert Einstein: a fortune-teller of science

In short, this offered a new way for astronomers to explore the corners of the universe.

"This is one of the most spectacular tests of Einstein's theory," said astrophysicist Zoltan Haiman (Columbia University), who did not participate in the research effort.

For him: "it looks like a new window to the universe". It will lead to plenty of scientific applications.

### The distortion of space and time

According to Einstein's theory, every object with a mass distorts the curvature of space and time.

To illustrate this we use the image of a bowling ball that bouncing on a trampoline. It moves space and time.

In space, this generates waves that radiate at the speed of light.

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### Tedious research

The research work was long and tedious. More than 1000 researchers in fifteen countries.

In terms of numbers, more than a billion dollars was spent over the last thirty years.

Researchers have detected gravitational tremors around spiral black holes around 1.3 billion light years from Earth.

To do this, they used a very elaborate measuring device: the LIGO instrument (Laser Interferometer Gravitational-wave Observatory).

This instrument is capable of detecting remarkably small vibrations, in other words, gravitational waves.

Once the gravitational wave signal was detected, scientists converted it into sound waves and were able to listen to the sounds of two black holes in fusion.

"This discovery will allow us to learn more about the fusion of black holes, neutron stars and other exotic astronomical phenomena that raise so many questions about the evolution of our universe," said France Córdova (Director Of the NSF).

## Albert Einstein, the Maths Tutor

From 1909 Einstein accepted various teaching positions in Europe.

Nazi Germany removed his citizenship in 1933 because he was a Jew.

So he moved to the United States and started teaching a maths help class at Princeton University.

In 1988, the American Society of Civil Engineers created the Albert Einstein Award for Science to recognise and reward the outstanding achievements in the field of erosion control, sedimentation and/or navigation

In 1947, he expressed his passion for teaching maths in these words:

"It is the essential role of the teacher to awaken the joy of working and knowing."

Having the right maths tutor can play big role in how you understand and enjoy the subject.

## Maths Help to Better Understand the Universe Around Us

Among the many mathematics articles that this genius has published during its life-time, we can distinctly recall the article on differential geometry and the one on field equations, written with the help of his mathematician friend, Marcel Grossmann. It is this knowledge which enabled him to bring to light the theory of restricted relativity and the theory of general relativity.

Much more than just a mathematician or physicist, **Albert Einstein's goal was to gain a better understanding of the universe that surrounds us**. For this he used mathematics and physics (a discipline derived from mathematics, let us bear in mind) to bring to light certain theories that to this today form the basics of this subject.

Here is another argument in favour of explaining the world through mathematics.

Thus, although it is easy to link Albert Einstein mathematics, we can only thank him for the outstanding legacy that this great man has left scientists of future generations.

The links between:

However, Einstein was mentally frustrated because he never managed to explain electromagnetism. He spent the last 25 years of his life trying in vain to develop a unified field theory. The latter would have explain all the natural forces.

He was afraid that if he could not find the answer, no one would. Learn about many other mathematical misconceptions in the world.

To finish, I'll leave you with some of his best quotes:

"Imagination is more important than knowledge."

"It is the human, free and creative person who shapes the beautiful and the sublime, while the masses remain entangled in an infernal round of imbecility and stupidity."

"The most beautiful thing we can experience is the mysterious. He to whom this emotion is a stranger, his eyes are closed."

“Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That's relativity.”

An incredible figure of the last century who, single-handedly, participated in the evolution of math!

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