Albert Einstein is arguably one of the most influential scientists in human history. His work continues to guide astronomers, physicists, mathematicians to study everything from gravitational waves to Mercury's orbit.
Einstein's equation that helped explain special relativity, that is, E = mc^2 – is well-known even in those circles where physics is not popular or not understood. Einstein is also known for his theory of general relativity (an explanation of gravity).
Einstein's work on the photoelectric effect (which explains the behaviour of electrons under certain circumstances) earned him a Nobel Prize in Physics in 1921. He was still working on a way to unify all the forces of the universe in a single theory, or a theory of everything, at the time of his death.
Albert Einstein: The Man Behind the Math
Einstein was born on March 14, 1879, in Ulm, Germany, a town that bears a small commemorative plaque where his house used to stand (it was destroyed during World War II). Einstein's father, Hermann, ran an electrochemical factory and his mother Pauline took care of Albert and his younger sister, Maria. The family moved to Munich shortly after his birth, and later to Italy
By his own admission, two "wonders" deeply affected Einstein's early years, according to Hans-Josef Küpper, an Albert Einstein scholar. Young Einstein encountered his first wonder — a compass — at age 5. He was mystified that invisible forces could deflect the needle. This would lead to a lifelong fascination with unseen forces. The second wonder came at age 12 when he discovered a book of geometry, which he worshipped, calling it his "holy geometry book."
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Contrary to popular belief, young Albert was a good student, excelling in physics and mathematics. However, Einstein was a rebel of sorts and despised the authoritarian attitude of some of his teachers, dropping out of school at 16.
Later, Einstein took an entrance exam for the Swiss Federal Polytechnic School in Zurich. While his performances in physics and math were excellent, his subpar marks in other areas prevented him from passing the exam. The aspiring physicist took additional courses to close the gap in his knowledge and was admitted to Swiss Polytechnic in 1896. In 1901, received his diploma to teach physics and mathematics.
Mathematical creativity was fundamental in Einstein’s contributions.
At the time he was conceiving the General Theory of Relativity, he needed knowledge of more modern mathematics, including concepts like tensor calculus and Riemannian geometry, the latter developed by the mathematical genius Bernhard Riemann, a professor in Göttingen. These were the essential tools for shaping Einstein’s thoughts. Specifically, non-Euclidean geometries seemed almost tailored to Relativity. Mathematical concepts are like Vocabulary of the subject, it is important to understand the concepts of the subject.
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Einstein's Greatest Discoveries
Theory of Special Relativity
Albert Einstein developed his theory of special relativity in 1905, and it came to form the basis of modern physics. The theory explains how space and time are linked for objects that are moving at a consistent speed in a straight line. One of its most famous aspects concerns objects moving at the speed of light.
In simple terms, as an object approaches the speed of light, its mass becomes infinite and it is unable to go any faster than light travels. This cosmic speed limit has been a subject of much discussion in physics, and even in science fiction, as people think about how to travel across vast distances.
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Theory of General Relativity
The theory reflected Einstein's understanding of how gravity affects the fabric of space-time. Einstein published his theory in 1915 as an expansion of his theory of special relativity. Einstein spent the decade between the two publications determining that particularly massive objects warp the fabric of space-time, a distortion that manifests as gravity.
The theory holds that what we perceive as the force of gravity arises from the curvature of space and time. Einstein proposed that objects such as the Sun and the Earth change this geometry. Einstein’s theory is the best description of how gravity works.
The mathematical equations of Einstein's general theory of relativity are currently the most accurate way to predict gravitational interactions, replacing those developed by Isaac Newton several centuries prior.
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Einstein Field Equations
While Einstein is primarily remembered for his contributions to physics, he also made contributions to mathematics. He contributed several equations to calculus and geometry, ten of which are called the Einstein Field Equations. He first published these equations in 1915. One of these equations demonstrates how stress-energy inflicts curvature of space-time.
The Einstein Field Equations are ten equations that describe gravity as a result of spacetime being curved by mass and energy. is determined by the curvature of space and time at a particular point in space and time, and is equated with the energy and momentum at that point. The solutions to these equations are the components of the metric tensor , which specifies the spacetime geometry. The inertial trajectories of particles can then be found using the geodesic equation.
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Einstein's Take on Gravitational Waves
Gravitational waves are 'ripples' in space-time caused by some of the most violent and energetic processes in the Universe. Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity.
Einstein's mathematics showed that massive accelerating objects (such as neutron stars or black holes orbiting each other) would disrupt space-time in such a way that 'waves' of undulating space-time would propagate in all directions away from the source.
Einstein predicted that cosmic ripples would travel at the speed of light, carrying with them information about their origins, as well as clues to the nature of gravity itself. The first proof of the existence of gravitational waves arrived in 1974, 20 years after Einstein's death.
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Albert Einstein: The Teacher
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 recognize and reward the outstanding achievements in the field of erosion control, sedimentation, and/or navigation
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Among the many mathematics articles that Einstein published during his lifetime, the 2 articles on differential geometry and field equations, written with the help of his mathematician friend, Marcel Grossmann, had the greatest impact on contemporary mathematics.
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) to shed light on theories that have come to form the basis of the disciplines.
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