Georg Simon Ohm
By: Amy Dixon
Georg Simon Ohm was born to Johann Wolfgang Ohm and Maria Elizabeth Beck in 1787 in Erlangen. His father, Johann Wolfgang, was a self-taught man in mathematics, physics, chemistry, and philosophy brought this knowledge to his children. Georg Simon learned more science from his father than he did at Erlangen Gymnasium. Ohm entered the University of Erlangen but lost funding for it by his father after three semesters because Georg was too interested in student life. He then became a mathematics teacher in a school in Gottstadt bei Nydau. Ohm wished to go with Karl Christian von Lagsdrof to the University of Heidlelberg to continue his mathematics education, but Lagsdrof suggested that Ohm teach himself. Ohm studied Euler, Laplace, Lacroix, Lagrange, Legendre, Laplace, Biot, and Poisson and taught himself much mathematics. He eventually received a doctorate from Erlangen and started working towards his lifetime goal of gaining a high position in a university.
Ohm taught math and physics at a poor school in Bamberg where he wrote an elementary book on teaching geometry. In 1817, He became a physics and math teacher at the Jesuit Gymnasium of Cologne where he had access to a laboratory and began experiments after the discovery of electromagnetism by Oersted. Ohm began to seriously experiment and publish after he realized it would be what it would take to reach his life goal. His first paper was written in 1825, which describes the decrease in electromagnetic force produced by an increased wire length. He also wrote two papers that expanded Fourier’s study of heat conduction that gave a mathematical description of conduction in circuits.
Ohm is famous for his study of electricity. The famous Ohm’s law which gives the relationship between voltage, current, and resistance and is displayed by the equation V=IR, where V is voltage, I is current, and R is resistance. His law was published in 1827 in the famous book Die galvanische Kette, mathematisch bearbeitet. This book was different from most scientific books at that time because it began with a mathematical background for understanding the work and therefore he did not have much support for his ideas. Resistance is when collisions between the electrons and the atoms of the conductor interfere with the flow of electrons. Resistance is proportional to length and inversely proportional to the cross-section of a wire. The Ohm which is the unit for resistance was named in honor of Ohm’s work. Ohm also did work with sound. He applied the work of the French mathematician Baron Jean Baptiste Joseph Fourier to sound in 1822. In 1843 he gave the principle of physiological acoustics explaining that a human ear hears sounds in specific tones.
Ohm ended up becoming a member of the Royal Society in 1842. His lifetime goal was finally achieved when he became the chair of physics at the University of Munich in 1852. Georg Simon Ohm died two years after gaining the chair of physics. His works with electricity has greatly helped with electronic advances without them many things we use today might not exist.
Anna Johnson was a woman who was very blessed, and suffered great hard ship throughout her life. Anna was born in the United States, however she was of a Swedish decent. In the United States she was allowed to receive a wonderful education. She attended private school while she was young and then continued her education at the University of South Dakota. It was there that she began a promising career in Mathematics, which was strongly encouraged by her mathematics professor, Alexander Pell. Anna finished her undergraduate degree in 1903 and then decided to continue with her master degree. Anna went on to obtain two master’s degrees from the University of Iowa. She remained there to study under Bocher and Osgood until she was awarded the Alice Feeman Palmer Fellowship from Wellesley College, which allowed her to study for one year at Gottingen University and work on her doctorate while she was there. Anna gained the opportunity while at Gottingen to attend lectures under Hilbert, Klien, Minkowski, Herglots, and Schwarzschild. Much of the knowledge that she obtained came from the influence of Hilbert, though she did not always agree with him. While she was studying in Gottingen, Germany her former professor Alexander Pell, 25 years her senior, traveled there to wed her. Anna returned to the United States with her husband and taught courses in the theory of functions and differential equations. However she soon went back to Gottingen to complete her doctorate. Unfortunately she had a disagreement with Hilbert, one of her professors, and returned to Chicago without an awarded degree. Thankfully she did received her Ph.D as a student of Eliakim Moore. Her thesis was Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations, which was the one originally formed in Gottingen. After Gaining her Ph.D she taught at Mount Hoyoke College and Bryn Mawr. It was during this time that her husband Alexander Pell died. Four years after his death she became the head of mathematics and then a full professor a year later. During this period of her life Anna received one of the greatest honors in the Mathematical society. She was the first woman to give the Colloquium Lectures at the American Mathematical Society. Anna soon married Arthur Wheeler. While she was married to him they lived at Princeton where she taught part-time. Sadly he also died only a few years later. Anna then decided to return to full time work at Bryn Mawr along with her good friend Emmy Noether. To Anna’s dismay her good friend also died only two years later. However, Anna did not let this stop her. She had lost two husbands, a wonderful friend, and also her parents but she still continued to work and better herself until 1948 when she retired. The bulk of Anna’s work fell under integral equations with a focus on infinite dimensional linear spaces. However in today’s society her work is not much appreciated because her findings have become more of a general theory.
Story of John Forbes Nash Jr.
By: Trevor Hardy
John Forbes Nash Jr. was born in 1928 in the Bluefield Sanatorium of Bluefield, West Virginia. As a child, Johnny was more into books than playing with others. While his sister and cousins played the normal childhood games, Nash would read or play by himself with airplanes and matchbox cars. Virginia, his mother, made sure that he received proper schooling. She did what she could to encourage his education.
Nash entered Bluefield College in 1941. There he enrolled in many math and science courses. Here is where he began to show his abilities in math. He hadn’t thought of making a career out of mathematics until John Synge, Head of the Math Department at the Carnegie Institute of Technology, noticed his mathematical skills. Synge, along with other math professors, tried to convince Nash to become a professional mathematician.
Despite the peer abuse Johnny suffered for being “different”, he received a BA and an MA in mathematics in 1948. He then decided to further his studies at Princeton. Here he became interested in pure mathematics, such as topology, algebraic geometry, game theory, and logic. Nash did not attend lectures nor did he hit the books. Instead he decided to develop the topics on his own. While studying for his doctorate, Nash wrote a paper that would later win him Nobel Prize.
After receiving his doctorate, he continued his work on pure mathematics while attempting to teach. During this time, especially at the Massachusetts Institute of Technology (MIT), he started having problems with his personal life. One problem that seemed to plague him was his homosexual tendencies. He would sometimes climb into bed with other boys and in 1954, while working for the RAND Corporation, Nash was arrested in a police operation to find homosexuals. He was then fired from RAND. All the while, he has had a child with Eleanor Stier. She was pressuring him to marry her, yet Nash was not interested. Nash found interest in Alicia Larde, a student at MIT. They soon begun to see each other regularly and were soon married. This is when his mental problems started to get bad.
He went through a period of being enrolled in hospitals for treatment and temporary recovery. Alicia eventually divorced John, but she continued to help him with his problem. He went through a period of time where he thought that Russian Communists were chasing after him because he was helping his government decode there encrypted messages. Later, Nash was diagnosed with schizophrenia. He recovered in 1990 from the disease he has been plagued with since 1959. In the year 2001, Ron Howard directed a film in which Russell Crowe played John Nash in a movie about his life.
Karl Gustav Jacob Jacobi
By: Jason Eldridge
Karl Gustav Jacob Jacobi was a great mathematician in the nineteenth century. He was born in Potsdam, Germany on December 10, 1804 and died in Berlin, Germany on February 18, 1851. His father was a banker and his family was very prosperous, yielding three boys and one girl, Karl being the second born brother. The eldest son became a physicist, the youngest son followed his father’s footsteps to become a banker, and Karl went on to study mathematics.
Jacobi was very smart, especially for his age, and some consider him to have been a child prodigy. An uncle on his mother’s side of the family gave his early education to him. Karl later attended school in Potsdam where he quickly outgrew the first year class and was moved to the final year class. By the time he was twelve years old Jacobi had already met the academic requirements needed to attend a university. However, the University of Berlin wouldn’t accept anybody under the age of sixteen. He stayed at the same school in Potsdam for four years until he finally entered the university in 1821.
Germany’s standards for education in mathematics was very poor at the time so Karl had to study and learn on his own, reading the works of Euler and Lagrange. He became a professor at University of Berlin and then later at the University of Konigsberg. Jacobi made major discoveries in number theory, and more importantly discovered fundamental advances in the theory of elliptic functions. He had a unique teaching technique for his time, by letting students learn by the seminar method. This helped give him the reputation of being an excellent professor and attracted many students to the University of Konigsberg. Karl continued to form new postulates and theorems while gaining a reputation as a great teacher.
In 1834 Jacobi proved that the ratio of periods is imaginary if a single-valued function of one variable is doubly periodic. He also played an important part in furthering research on partial differential equations of the first order and applied them to the fields of differential equations and dynamics. His book Fundamenta Nova Theoria Functionum Elliptcarum introduced his newly found concept of hyperelliptic functions. Karl studied determinants and now has a functional determinant named after him, called the Jacobian. He continued advancing mathematic properties and formulas until he became ill in 1842. However, Karl recovered, and by 1842 he was lecturing on analytical mechanics at the University of Berlin.
In January 1851 Karl Jacobi contracted influenza, also called the common flu virus. While trying to recover from this he also contracted smallpox and died only a matter of days later. Although he lived a relatively short life, only forty-seven years, Jacobi had a large impact on our society. He made huge advancements in fundamental theories and equations, both building on great mathematicians from the past and leading the way for others in the future. As if all these accomplishments weren’t enough, Karl Jacobi was also considered to be one of the most inspiring teachers of his time.
Mary Ellen Rudin
By: Kamilah Whipple
Mary Ellen Rudin was born on December 7, 1924 in the small town of Hillsboro, Texas. Her father, Joe Jefferson Estill, was a civil engineer and her mother, Irene Shook, was a high school English teacher. She became interested in mathematics at the University of Texas, where she obtained her Ph.D. She then taught at Duke University until 1953. Later, she married fellow mathematician, Walter Rudin, both moving on to teach at the University of Rochester. She became the first to hold the Grace Chisholm Young Professorship at Wisconsin. She held professorships in New Zealand, Mexico, and China. Mary was a working woman who maintained a vibrant family life, raising four children; Catherine, born in 1954; Eleanor, born in 1955; Jefferson, born in 1961; and Charles Michael, born in 1964. She is quoted as saying, “I have never minded doing mathematics lying on the sofa in the middle of the living room with her children climbing all me. I feel more comfortable and confident when I’m in the middle of things, and to do mathematics you have to feel comfortable and confident.”
Mary was the product of the “Moore Method.” She registered for the class of professor, R.L. Moore because of the short lines for mathematics registration. He used no textbooks or lectures in his classes. Each day, he came in and wrote definitions and statements on the board. His students would then try and prove the true ones, and find counterexamples for the false ones. Mary’s own work centered upon set-theoretic topology with an emphasis on the construction of counter examples, producing around 70 research papers on the subject. She is perhaps, best known, for using box products to construct an example of a normal Hausdorff space whose Cartesian product with an interval is not normal. She received the Prize of Nieuw Archiet voor Wiskunde (Mathematical Society of the Netherlands) in 1963. She was Vice-President of the American Mathematical Society (AMS) from 1980 to 1981. She has been Governor of the Mathematical Association of America, elected a Fellow of the American Academy of Arts and Sciences, and elected to the Hungarian Academy of Science. She was also invited to be the Emmy Noether Lecturer for the Association for Women in Mathematics, where she lectured on Paracompactness
When asked how she does mathematics, she responds, "I draw little pictures and try this thing and that thing. I'm interested in how ideas fit together. Actually I'm very geometric in my thinking. I'm not really interested in numbers." And how does mathematical talent show itself? "It's in pattern recognition."
Albert Einstein
By: John Allen
Albert Einstein was born in Ulm, Wiirttemberg, Germany on March 14, 1879. Around 1886 he began his school career in Munich. He was also taught violin from age six to thirteen, along with a religious education at home where he was taught Judaism. Two years later he entered the Luitpold Gymnasium and after this his religious education was given at school. He studied mathematics, in particular calculus, beginning around 1891.
In 1894 Albert’s family moved to Milan, but he remained in Munich. In 1895 Einstein failed an examination that would have allowed him to study for a diploma as an electrical engineer at the Eidgenossische Technische Hochschule in Zurich. Albert renounced his German citizenship in 1896 and would remain stateless for a number of years. It wasn’t until 1899 that he would even apply for Swiss citizenship. He was granted citizenship in 1901.
After failing the entrance exam to ETH, he attended a secondary school at Aarau in hopes that he could eventually enter ETH in Zurich. Einstein did succeed in entering ETH and graduated in 1900 as a teacher of mathematics and physics. Several of Einstein’s classmates had obtained positions as assistants at ETH in Zurich, but Einstein had not impressed enough people and was still writing around to universities in 1901 in hope of finding a job. Meanwhile, he was able to avoid Swiss military service on the grounds that he had flat feet and varicose veins. In mid 1901 he was able to gain a temporary job as a teacher, teaching mathematics at the Technical High School in Winterthur. Einstein then gained another temporary teaching position in a private school in Schaffhausen. Albert was then recommended to the director of the patent office in Bern where he was appointed as a technical expert third class.
Albert worked in the patent office from 1902 to 1909. He held a temporary post when he was first appointed, but by 1904 the position was made permanent and in 1906 he was promoted to technical expert second class. While he was in the Bern patent office he completed numerous theoretical physics publications that he wrote in his spare time without the benefit of close contact with scientific literature or colleagues.
Einstein then earned a doctorate from the University of Zurich in 1905 for a thesis On a new determination of molecular dimensions. In the first of his three papers he examined the phenomenon discovered by Max Planck. Einstein used Planck’s quantum hypothesis to describe the electromagnetic radiation of light. His second paper in 1905 proposed what is now called the special theory of relativity. Then, in 1905, he showed how mass and energy were equivalent. After 1905 he continued working in the areas described by his papers and made important contributions to the quantum theory.
By 1908, Einstein became a lecturer at the University of Bern after submitting a thesis. The following year he became a professor of physics at the University of Zurich after resigning from Bern and his job at the patent office. He was finally recognized as a leading scientific thinker. He was appointed a full professorship at the Karl-Ferdinand University in Prague in 1911. In 1912 he began a new phase of gravitational research with the help of a friend named Marcel Grossmann. Einstein called his new work the general theory of relativity. During this period, he moved from Prague to Zurich in 1912 to take up a chair at the Eidgenossische Technische Hochschule in Zurich. He returned to Germany in 1914, but did not apply for German citizenship. He accepted a research position at the Prussian Academy of Sciences together with a chair (without teaching duties) at the University of Berlin. He was also offered the directorship of the Kaiser Wilhelm Institute of Physics in Berlin.
Einstein greatly gained popularity for his new Theory of Relativity and his lectures were disrupted by demonstrations that were anti-Jewish in 1920. By 1921, he made his first visit to the United States so that he could raise funds for the planned Hebrew University of Jerusalem. He received the Barnard Medal during his visit and gave several lectures on relativity. Albert received the Nobel Prize in 1921, but not for his relativity theory, but for his earlier work on the photoelectric effect. He was later given several more awards such as the Copley Medal of the Royal Society in 1925 and the Gold Medal of the Royal Astronomical Society in 1926.
Einstein’s life had been extremely hectic and he had to pay the price in 1928 with a physical collapse brought on due to overwork. He made a full recovery but had to take things easy throughout 1928.
By 1930 Einstein was back to the United States and in 1932 he was offered a post at Princeton. The idea was that Einstein would spend seven months a year in Berlin and five months at Princeton. Albert left Germany in December 1932 for the United States and the following month the Nazis came to power in Germany and Einstein would never return.
In the years to come he was offered numerous academic posts around the world, but finally decided to stay at Princeton. The arrangement was made permanent in 1935 and he applied for permanent residency in the United States. In 1940 he became a citizen of the United States, but chose to retain his Swiss citizenship. He made many contributions to peach during his life. In 1944 he made a contribution to the war effort by hand writing his 1905 paper on special relativity and put it up for auction. It raised six million dollars, the manuscript now being in the Library of Congress.
In 1949 Einstein was unwell. A short spell in the hospital helped him to recover but he began to prepare for death by drawing up his will in 1950. One more major event was to take place in his life though. The first president of Israel died in 1952 and the Israeli government offered the post of second president to Einstein. He refused the offer.
One week before he died he signed his last letter to Bertrand Russell in which he agreed that his name should go on a manifesto urging all nations to give up nuclear weapons. Einstein died on April 18, 1955 and was cremated at Trenton, New Jersey. His ashes were scattered at an unknown place.
Pythagoras of Samos
By: Stuart Nickerson
Pythagoras of Samos is one of the first early mathematicians and astronomers. He lived from around 560 to 480 B.C. in Greece. He had a school for other highly dedicated intellectuals which served as his team. He headed this team and they called themselves the Pythagoreans. Little is known about the Pythagoreans because they followed a code of secrecy, and we have nothing of Pythagoras’s writings.
According to early bibliographies Pythagoras’s interest in mathematics and astronomy was influenced by Thales and Anaximander. Thales suggested that Pythagoras travel to Egypt to learn more about the subject. Anaximander lectured about geometry and cosmology. Pythagoras attended these lectures and gained an interest in the subject. After arriving in Egypt, Pythagoras had discussions with the temple priests. He was later admitted as a brother after completing the rites. These customs and codes that Pythagoras learned in Egypt would later influence how he ran his school in Italy and Samos.
Pythagoras returned to Samos and set up a school called the Semicircle. The Samians did not accept Pythagoras’s school and methods of teaching. Left with only one option, he left his home and went to southern Italy around 518 B.C. He was able to found a school in Croton. This is where Pythagoras was able to setup is elite team of followers and form the Pythagoreans.
The Pythagoreans believed that all things could be explained by numbers. Math, music, and astronomy are all derived from numbers. They noticed that when vibrating strings could produce harmonious tones when the strings were are in lengths of whole numbers. They also knew that any triangle whose sides where 3:4:5 was a right triangle where the square of the hypotenuse is equal to the sum of squares of both sides. Even though philosophers in Babylonia are heavily suspected of knowing this too, the Pythagoreans are credited with giving us the Pythagorean theorem.
The Pythagoreans were also accomplished astronomers. They believed in the celestial spheres which meant that the planets were thought to produce a harmony which was called the music of the spheres. This meant that they thought that the Earth was in motion. They also thought that the Earth was round. Naturally, they used math or more accurately geometry to prove this. They were able to look at the shadow of the earth on the moon during a lunar eclipse. A shadow looks like the object that is making the shadow. It just has a different size. They saw earth’s shadow and assumed that the Earth was round. They had no decisive evidence to prove this, so they were not taken very seriously. The Pythagoreans were able to help setup a basis for Aristotle to get his start.
In conclusion, Pythagoras was one of the first mathematical minds. Even though no documents remain from Pythagoras or the Pythagoreans, we have bibliographies from other figures who point out the achievements of the Pythagoreans. After learning from his mentors, Pythagoras setup a school that gave us the Pythagorean theorem and helped with early astronomy. His achievements helped pave the way for other great men such as Aristotle.