# Mathematics and Eugene Catalan Essay

The first mathematician I will be writing about is Eugene Charles Catalan. I picked him, because he is one of the top 100 most known mathematicians in the world. Eugene Catalan, was born in Bruges or more commonly known as Belgium, on May 30, 1814. He traveled to Paris where he pursued his mathematical dreams. Later on in 1841, he received his degree in mathematics. Eugene Catalan studied mathematics and design in a university located in Paris. Eventually, he became an architect, just like his father.

At the age of 15, he tutored and taught his fellow students how to solve geometry problems in school.

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As he grew older, he traveled to attend Ecole Polytechnique due to his outstanding aptitudes in mathematics. In 1833, he was eventually expelled for his political activities. 2 years later, he was able to resume his studies and graduated in 16th place and acquired a post at College de Chalons sur Marne. In 1846, Catalan was told to take charge of teaching higher mathematics at the College de Charlemagne because of his outstanding skills with numbers and math.

Later on in his career, Eugene published books about continued fractions and number theory, which is still used today.

Through all of his hard work, Eugene Catalan is recognized because of his accomplishments. Many people studying math know about “Catalan numbers,” which obviously came from him. Another accomplishment he has made in the mathematical area is being able to dissect a polygon into triangles by means of non-intersecting diagonals. He was not the first to accomplish this, but no one has a more elegant style than he does. The “Catalan minimal surface” is also one of his major accomplishments that he studied around 1855. It relates to another one of his titles called “Catalan’s minimal curve. However, the most famous theory of all is the “Catalan Conjecture” made in 1844 in a letter he sent to one of his friends’ journal. It read: I beg you, sir, to please announce in your journal the following theorem that I believe true although I have not yet succeeded in completely proving it; perhaps others will be more successful. Two consecutive whole numbers, other than 8 and 9, cannot be consecutive powers; otherwise said, the equation xm – yn = 1 in which the unknowns are positive integers only admits a single solution. Solving this “conjecture” was awfully slow.

In 1850, a man named Victor Lebesgue that no solution existed when n = 2. Catalan also wrote few popular texts that ran in different editions. He wrote: Elements de geometrie (1843); the two volume work Traite elementaire de geometrie descriptive (1850-52) which ran to 5 editions; Theoremes et problemes de geometrie elementaire (1852) which ran to 6 editions, and many more that are known worldwide. Eugene Catalan made a huge impact in the mathematical world, and contributed with his unbelievable theories and mind puzzling ideas.

His accomplishments has helped us today by learning more about his ways of solving numbers and shapes in an “elegant” way. Pierre Simon de Laplace I chose Pierre Simon de Laplace as my second mathematician so I can travel way back in history and find out more about mathematics. Laplace was born on the 23rd of March, 1749, and passed away March 5, 1827. Laplace was a famous French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics.

Pierre Simon de Laplace probably made a much larger impact on the world of math than Eugene Catalan did. In his five volume Mecanique Celeste, he translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. Many do not know that the Bayesian interpretation of probability was mainly developed by Laplace. The “Laplacian differential operator” which is widely used in applied mathematics, is also named after him. He was great in the world of mathematics.

However, as an astronomer, he restarted and developed the nebular hypothesis of the origin of the solar system, as well as become one of the first scientists to explain the existence of black holes and the notion of gravitational collapse. Back to his math skills. He worked on continued fractions, descriptive geometry, number theory and combinatronics, which is a branch of mathematics concerning the study of countable discrete structures. Laplace also developed celestial mechanics, the study of movement of celestial bodies under gravitational forces.

He also created a probability theory, an area in math that investigates the likelihood of occurrence of random events in order to foreshadow the behavior of defined systems. He also studied spheroids to invent an ice calorimeter and to help prove that respiration was a form of combustion. As an astronomer, he used Isaac Newton’s theories of gravitation to the solar system and tried to solve the puzzle of Jupiter’s shrinking orbit. In 1796, Laplace published The System of the World, in which he detailed the findings in celestial mechanics.

He is referred to as one of the greatest mathematicians and scientists of all time. Sometimes, people refer to him as the “French Newton” or the “Newton of France. ” He has greatly contributed to the world because of his astronomical abilities as well as his mathematical theories. Without him, we would not be able to fully understand the physics of the world and how gravity works with everything that is put on earth and made by man. Without him, mathematics would not be beautifully translated in a way that makes it simple for many students to understand (his way of doing mathematics).

Many other scientists today surely follow his steps and use his studies to further understand what is going on in outer space, as well as on the activities on earth. Elena Cornaro Piscopia Elena Cornaro Piscopia, 1 of two of the female mathematicians I will be talking about was born on June 5, 1646 and died on July 26, 1684. I picked Piscopia because I do not know much about women mathematicians. The ones I remember most are Einstein, Newton, and Laplace and they are all male. Piscopia is known for being the first woman to earn a doctoral degree.

At a young age, Elena was personally educated by his father, who was a public official. Piscopia was a very, very talented lady. She was a mathematician, theologian, and a philosopher. When she was seven, she began to study with tutors in Latin, Greek, music, theology, and mathematics. She eventually learned Hebrew, Arabic, Chaldaic, and also French, English, and Spanish. At the age of 17, she could sing, compose, and play instruments such as the violin, harp and harpsichord. All of her achievements attracted many including clerics, royals, as well as scientists.

Many people all over the world, came to Venice to be able to speak with her. Not only was she the first woman to earn a doctoral degree, she was the first woman to apply in theology in Italy. By 1678, she earned a master’s and doctorate degree in philosophy. Her examination was so interesting to people that the venue had to be changed: to accommodate the crowds of students and other individuals who came from all across the world to witness the historic event. These events usually occur in the university’s “great hall” because there were so many visitors.

Instead, they gathered at the more spacious cathedral of the Blessed Vigrin in Padua. She was granted the highest honor of all: She was named professor of Mathematics at the University of Padua. After receiving her degree, Piscopia devoted her life to charity. She found her place in the Venetian society and refused several important marriages. During the final years of her life, she focused on helping educate the poor as well as ministering them. Later on, she became a math teacher in the University, but sadly died on 1684.

The University of Padua has created a statue of her to honor and thank her for her great accomplishments. She is also remembered her in the United States by the stained glass window at Vassar College which show her defending her theses at the Cathedral of Padua. Elena Piscopia impacted both the mathematical world and the world the we live in because of her smart math skills, and her caring personality. Her accomplishments have helped many today by motivating many people (not only women) to pursue their goals as well as help other by using our own skills, similar to what Piscopia did in her time.

Until today, she is opening up more opportunities as well as motivating many people with her examples. Mary Fairfax Somerville Born on December 26, 1780, Mary Fairfax Somerville was in a family that stood high on economic standing. I chose Mary Somerville because she was one of the choices I had that was a little later than Elena Piscopia’s generation. However, she had the same treatment in education similar to the normal girls. Mary studied her first arithmetic at the age of thirteen, when her mother took a small flat for the winter months in Edinburgh and she was enrolled briefly in a writing school there.

Eventually, she attended a boarding school for girls in Musselburgh (unhappily). She eventually ended up studying algebra due to constant encounters with “weird” math symbols. In 1804 at the age of 24, Mary married her cousin, Captain Samuel Greig. 21 years later, 1825, Mary began her scientific investigations. She experimented on “magnetism. ” Immediately, she submitted her paper and called it “The Magnetic Properties of the Violet Rays of the Solar System” to the Royal Society. Her paper/research attracted people and eventually became the first paper by a woman to be read by the Royal Society.

Although her paper later on became refuted by the investigations of other, it distinguished her as a skilled scientific writer respected by many people. As she grew older, she published her second book in 1834. Her book talked about physical phenomena and its connection with physical sciences. Her books earned her a job at the Royal Society, giving her 200 pounds per year from the King of England and she also received honorary memberships from well known scientific organizations, including eleven Italian scientific societies between 1840 and 1857. She lived to complete two more works before her death in Naples in 1872.

Her last scientific book, Molecular and Microscopic Science, was published in 1869 when she was 89 years old. Her published book was a summary of the most recent discoveries in chemistry and physics. Although Mary did not have as much accomplishments like the other three mathematicians, she created books that filled many with great knowledge about physics, chemisty, as well as mathematics. Somerville went through many hardships due to the death of many of her loved ones. However, she has helped us today similar to the other mathematicians I wrote about.