Essay Example: Mathematical Sciences

Mathematical sciences play a major role in the development of nearly all aspects of everyday life with many scientific models and digital communications using Mathematics to accomplish different tasks. Mathematics brings out different hidden patterns that are effective in helping to understand the world that surrounds us these days. It has developed historically with new inventions being realized in the progress of years and the use of abstraction, calculations, and measurements being a key element for most scientific studies in the world. Many scientists and mathematicians led to the innovation of mathematics and science through the creation of theories that helped to develop their areas of specialization. Albert Einstein is known to be one of the most famous mathematical and scientific innovators in the world, and his theories provided a different outlook on both math and science.

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Biography

Albert Einstein was born in 1879 in Germany, and until his death in 1955, he was considered the most influential physicist and mathematician in the 20th century. He attended a high school in Switzerland that was run by Jost Winteler (PBS 1). Einstein later studied at the Swiss Federal Institute of Technology, mostly due to the way he performed well in Physics and Mathematics in his exam of entry (PBS 1). After he graduated, he faced a lot of challenges by being unable to find academic positions because he had alienated most of his professors for not attending class most of the time.

During his days in school, he had chosen to study independently for the better part of his college years. In 1902, he was employed as a clerk in Swiss, and while he worked there, he was able to begin an exploration of ideas which he had been unable to implement when he was studying at the institute of Technology (PBS 1). This exploration made him cement his theory on the principle of relativity, and with his career taking new turns, he was able to study physics.

Impact of Albert Einstein on the Mathematical and Scientific Community

In 1905, he was successful in publishing five German papers of Physics. The first paper focused on the study of the motion of particles that are suspended in different liquids. He labeled the concept of the Brownian motion, which supported the atomic theory, which stated that all existing matter is composed of tiny molecules and atoms (PBS 1). This study prompted him to develop a formula in Mathematics that he used to describe the motion of the particles that were visible was caused by the motion of liquid molecules that were invisible to people (PBS 1).

The second paper focused on the photoelectric effect, where he argued about how metal releases electrons in the presence of light. The main ideas that were used to describe this idea focused more on Max Planck with the use of quanta that was the first theory away from the work of Planck (PBS 1). In the third paper, he developed the special theory of relativity, and in 1921, he won the physics Nobel Prize because he was able to explain the aspect of the photoelectric effect. The theory of relativity stated that time, mass, and weight are not constant. When these three aspects move at high speeds, they do not remain the same as they get compressed (PBS 1).

The fourth paper showed mass-energy equivalence where the speed of light has an ability to remain constant because energy is equal to mass multiplied by the square of the speed of light. He summarized this concept with the formula E=mc2 (Gates 1). His work was not without barriers as most of his work was disregarded by the scientific community at that time, and he was targeted by the German Nazi Party, which made him become an immigrant in the United States. He also renounced his former citizenship and acquired Swiss citizenship as the new century began. Einstein contributed a lot to the development of atomic energy and the unified field theory.

Mathematical Contributions

While most of Einstein's contributions were in Physics, he also made a lot of contributions to Mathematics by creating different equations for geometry and calculus, with ten of them being named the Einstein Field Equations (Gates 1). He published these equations for the first time in 1915, with one of them demonstrating the way that stress energy inflicted curvature for space-time. During his early years in the research field, Einstein was not sure whether to major in Mathematics or Physics as he was not confident that mathematics was more essential than physics.

Mathematical creativity was essential for the contributions that Einstein made, especially when he was conceiving the theory of relativity. The theory required that he had a clear knowledge of more modern mathematics, such as Riemannian geometry and tensor calculus (Gates 1). The Riemannian geometry was developed by Bernhard Riemann, who was a professor in Gottingen. Einstein needed the geometric theories of many scientists and their complete toolboxes so that he could be able to handle the sophisticated creation he was about to perform in Mathematics. He used the help of many other mathematicians such as Levi-Civita, who helped to correct any errors that occurred in his writings.

Einstein had thought about Mathematics and machinery design from a young age, mostly because he was surrounded by people who majored in those fields, especially his father. Due to the failure that his father experienced in his business venture, which was as a result of alternating currents beating the direct current, Einstein was inspired to begin his inventions for different Mathematical and Physics concepts (Gates 1). At the age of 16, he had the first concept thinking that created a breakthrough for him. He was looking at a mirror, and he wondered what his view would be like if he was traveling at a speed equivalent to that which light travels at which made it be labeled as Einstein's Mirror (Gates 1).

Confirmation by Sir Arthur Eddington

The five papers that he produced in 1905 made him famous in the Academia model, and by the year 1908, he was a top scientist that was recognized by many people. By the year 1911, Einstein had created the theory of general relativity, where he calculated the concept of light from a distant star being bent by the gravity of the sun (Gates 1). This concept remained unconfirmed until Sir Arthur Eddington confirmed it in 1919 during a solar eclipse.

The confirmation made Einstein to be known worldwide as a household name from that time onwards. The contribution he made to theoretical physics by discovering the photoelectric effect laws and leading to the development of the quantum theory (Simon 1). He collaborated with a friend who was a medical student by the name Max Talmud in exploring his path to learning philosophy and mathematics.

Einstein came up with a new equation known as Einstein's field equation in 1915 and is targeted to replace Newton's law of gravity. The theory was completed and published one year later, but physicists and mathematicians like Ludwig Flamm and Karl Schwarzschild tried to create solutions that would refute the field equations before it was published (Simon 1). Einstein also described gravity as a geometry property of space-time that led to the predictions of certain phenomena such as bending of light and wormholes. One year later, Einstein explained the theory of anti-gravity force, which he named the cosmological constant. He did this in an effort to show the behavior of the universe while avoiding to lose the belief of Newtonian infinite (Simon 1).

He established Euclid's Elements that were tailored towards relativity. These elements revolutionized geometry when scientists thought about Euclid's fifth postulate. The principle behind Euclid's elements stated the axioms by Euclid that showed when a straight line and a certain point outside it was displayed. Only one parallel line was able to cross that particular point (Simon 1). The negation of the postulate led to the establishment of hyperbolic geometry that showed the presence of infinite parallel line numbers and spherical geometry, which stated that there were no parallel lines in the postulate.

Einstein also led to the theory that nuclear energy is founded on atomic nuclei are created from neutrons and protons with the mass of the nucleus being smaller than that of protons and neutrons together (Simon 1). His theory of relativity of the year 1915 showed a similarity between mass and energy, which required mathematics to calculate the energy that was required to be added to the nucleus so that it could split.

He argued about quantum mechanics and the uncertainty principle with a focus on one equation that helped explain all-natural forces. While he was still at work in the patent office, Einstein discovered that the space-time fabric supports ripples and has an ability to bend depending on the force of gravity (Simon 1). To achieve this projection, he used the Riemannian geometry, and this helped to solve a problem that many physicists had been unable to solve since the death of Newton.

The super field supergravity concept, which was a successor of general relativity, was created form the motivation of Einstein's works before his death. His legacy did not die with him as the supergravity concept was established to lead to a growth of geometry properties that are used until now (de Leon 1). Most of the mathematics concepts that were created by Einstein were accurate descriptions of things that were hidden in nature. Most of his mathematical approaches offered the opportunity for humanity's unification dream. They were so revolutionary to a point where they challenged all doctrines established in natural sciences and led to an alteration of the style in which ordinary people saw the world they lived in.

Disagreements with Scientists

Throughout his inventions and studies, Einstein disagreed with many of his scientific colleagues, and in the time of the Nazi Germany wars, he went against the scientist's motives and wrote to the German government with a vivid description of the shameful steps of the other scientists (de Leon 1). One of the other three signatories of the document sent to the German government was arrested and jailed, but Einstein was not. This instance showed the first power display of the new strength he had achieved from his scientific and mathematical inventions and the ability it had given him to not only protect himself but also to enable him to speak when others could not.

However, an attempt on his life by the government led by Hitler made him finish one of his speeches in the Netherlands under heavy protection from bodyguards (de Leon 1). While in his new country, he attempted to prove the electromagnetism and gravity concepts, which were dissimilar indicators for a single phenomenon that was fundamental in the growth of his scientific concerns in cosmology and physics.

He was a major figure in the Manhattan Project because he warned President Roosevelt about the advances of Germany in nuclear researches with a possibility of them creating an atomic bomb that they would use in war (de Leon 1). He, however, was not given any role in the project due to his reluctance and the radicalism he got from other scientists and governments due to his works. Einstein used his physics knowledge and intuition with a resort to mathematics to create a theory that no one has been able to match six decades after his death.

Einstein died in 1955 at the age of 76 due to an abdominal aortic aneurysm. His brain was removed by a pathologist by the name Thomas Stoltz Harvey during his autopsy, and it was preserved for future studies as he had wished before his death (de Leon 1).