Name: Thales of Miletus

History Notebook

Prof. Goulet

Laura Robinson (Toomey)

Name: Thales of Miletus

Dates: 624- 546 BC

Geographic location: Mostly Greece but traveled to both Egypt and Babylon

Biography: Born in Miletus in 624, Thales is highly regarded in ancient Greek culture and was considered one of the sacred seven sages. He traveled extensively and was said to have measured the height of the pyramids by comparing them with the lengths of human shadows. He was also considered a great philosopher and believed that water was essential to life. He died at an old age during an athletic event from heat exhaustion.

Contribution to math/science: Thales is credited with inventing deductive mathematics. He was credited with several important such as the vertical angles of two intersecting lines are equal and ASA theorem for triangles. He also established The Ionian School of Greek Astronomy and was able to predict the year of the solar eclipse.

Reference/s:

Name: Eratosthenes

Dates: 276 BC – 194 BC

Geographic location: Born in Cyrene, North Africa (now Shah hat, Libya) Died in Alexandria, Egypt

Biography: Born in Cyrene, Eratosthenes studied under many scholars who were also from this region. One of these scholars, Callimachus brought him to Alexandria as a tutor to the son of the ruler Ptolemy III. When Callimachus died, Eratosthenes took over his position as the librarian of the great library at Alexandria, a position he held until his death in 194 BC.

Contribution to math/science: Created with accurately estimating the circumference of the earth using shadows and angles. He also developed a method for finding prime numbers. In geography he was able to determine the source of the Nile River to be lakes and that heavy rain affected its behavior and made very accurate sketches of the Nile.

Reference/s:

Name: Euclid

Dates: 325 BC –265 BC

Geographic location: Alexandria

Biography: Not much is known about his life. Most comments are deduced from his many works. It is believed that he studied at Plato’s Academy because he knew the geometry of Eudoxus and Theaetetus.

Contribution to math/science: The Elements, a set of thirteen books, which describe several areas of mathematics, begins with five postulates that become the basis for what is now known as Euclidian Geometry.

Reference/s:

Name: Pythagoras

Dates: 569 BC-about 475 BC

Geographic location: Samos, Ionia

Biography: Not much is know about his life. Supposedly he traveled with his father, seeing Syria and Italy. He was influenced by Pherekydes, Thales and Anaximander. The latter two had a great influence on his study of mathematics and encouraged him to travel to Egypt, which Pythagoras did in 535 BC. Here he studied in the temples and learned many of the belief he would impose on his own societies. When Egypt was invaded, he was taken prisoner and brought to Babylon around 525 BC. Eventually he returned to Samos and traveled to Crete. He later founded a philosophical and religious school in southern Italy in Croton. The society was made up of two circles: the inner, who followed strict guidelines of diet (they were vegetarians), code (they had no personal possessions), dress and secrecy, known as the mathematikoi, and the outer who only participated during the day, were allowed to have personal possessions and were known as the akousmatics. There is much speculation on the death of Pythagoras. Some believed he committed suicide after one of his societies was attacked in 508 BC. Others believe that he lived well beyond this dying around 480 BC

Contribution to math/science: Pythagoras is created with the discovery of irrationals, identifying the five regular solids, constructing figures of a given area and geometrical and the sum of angles in a triangle are equal to two right angles. The Pythagorean theorem for which he is most famous for was actually known to the Babylonians 1000 years earlier but he was able to do a proof of it.

Reference/s:

Name: Descartes

Dates: March 31, 1596- Feb 11, 1650

Geographic location: France , Holland

Biography: He began school at the age of eight at the Jesuit College of La Fleche in Anjou. He then went to the University of Poitiers in Paris and received a laws degree and enlisted in military school at Breda. He traveled extensively throughout Europe finally settling down in Holland. He died in Stockholm after developing pneumonia.

Contribution to math/science: Found the application for algebra in geometry, which led to the development of Cartesian geometry. He also tried to work on relationships between the Universe and mathematics.

Reference/s:

Name: Archimedes

Dates:287 BC -212 BC

Geographic location:Syracuse, Sicily

Biography: Not much is known of his life. His father was an astronomer and Archimedes traveled to Egypt and worked with the mathematicians at Alexandria. He loved geometry and pure mathematics. Roman soldiers in the capture of Syracuse killed him.

Contribution to math/science: The Archimedes screw, a pump, many war inventions, a compound pulley. He was able to find an accurate approximation of pi, discovered fundamental theorems of concerning the center of gravity of plane figures. Discovered many geometric relationships

Reference/s:

Name: the birth of Algebra

Dates: 800 AD, 1400 AD

Geographic location: Baghdad, Europe

Biography: The first written account of solving problems with unknowns occurs around 800 AD in a work by Muhammad ibn-Musa al-Khwarizmi. Later on in the 1400’s the development of symbolic algebra began. Nicholas Chuquet gives abbreviations to words like addition and subtraction. This continues with Cardano who introduces the equal sign and finally Francois Viete introduces using letters for unknowns.

Reference/s:

Name: Apollonius

Dates: about 262 BC-about 190 BC

Geographic location: Perga, Alexandria

Biography: Born in Perga (now part of Turkey), he traveled to Alexandria to study under the followers of Euclid.

Contribution to math/science: His famous books the Conics introduced the concepts of parabolas, hyperbolas, and ellipses. It was made of eight books, seven of which survive today in some form. He was also a founder of Greek mathematical astronomy.

Reference/s:

Name: Pierre Fermat

Dates: Aug 17, 1601- Jan 12, 1665

Geographic location: France

Biography: Born to a wealthy leather merchant, Fermat had one brother and two sisters. He attended the University of Toulouse, then to Bordeaux and finally to Orleans where he received a degree in civil law. He eventually became an official in Toulouse and spent the remainder of his life there. It was during his years at the University that Fermat began his mathematical career and throughout his life he had a very deep dialogue with other mathematicians through letters. Some of these included Carcavi, Mersenne and Descartes. Fermat and Descartes were actually in bitter debates over each man’s works. Descartes was able to damage Fermat’s creditability. For period of time Fermat was out of touch with his counterparts in Paris. Eventually Blaise Pascal contacted him for help with his theories on probability

Contribution to math/science: Developed many theories and theorems in the area of Number Theory, With Pascal set up the theory for Probability, developed many challenging problems, developed the idea that light always follows the shortest path, his greatest theorem Fermat’s Last Theorem baffled mathematicians for years.

Reference/s:

Name: Kepler

Dates: Dec 27, 1571 - Nov 15, 1630

Geographic location: Germany

Biography: Kepler grew up in his grandfather’s Inn after his father was killed during a war in the Netherlands. He was schooled at a local school and then enrolled in the seminary then onto the University of Tulingen. Being very religious, he felt that man should be able to understand the universe since it was created by God and man was created in God’s image. It was at the university that he developed an interest in mathematics and astronomy. He wanted to create a mathematical model that actually represented the movement of the planets and brought back to light the Copernican system. He eventually became the Imperial Mathematician. He went through a difficult period around 1611. First his seven-year-old son died and then his wife Barbara. The Emperor had to abdicate to his brother who was not tolerant of Protestant forcing Kepler and his children to move to Linz from Prague. Here he remarried and began his work on the Rudolphine Tables. He died after a short illness while in Regensburg to collect money for the tables.

Contribution to math/science: Discovered three laws of planetary motion that are a basis in Astronomy. Pushed for the acceptance of the Copernican model of the Universe. Published astronomical tables that used his first two laws called the Rudolphine Tables and proved to be accurate for many decades. And gave the first proof for how logarithms worked.

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Name: John Harrison

Dates:1693-1776

Geographic location: England

Biography: Born to a carpenter and from an early age took an interest to clocks. He married his first wife, Elizabeth, in 1718. She died just eight years later and he remarried within six months, to another Elizabeth. He had little formal education but he did have mechanical insight and talent. His first mechanical achievement was developing a clock that required no oil. He and his brother James tested the limits of what they could do with clocks. He used this ingenuity to help him solve the longitudinal problem. For many years the government council on the problem refused to believe an uneducated commoner had solved the problem. It took an act of Parliament to have John Harrison recognized as the solver of the longitudinal problem.

Contribution to math/science: Created a time piece to help sailors locate their position and prevented ships from running aground

Reference/s:

Name: Gaston Julia

Dates: 1893- 1978

Geographic location: France

Biography: Born in Algeria during the French occupation, he showed a great interest in math and music during his youth. At the age of 20 he served in the French army during WW1. During a battle Gaston was wounded and lost his nose. Despite several surgeries to correct the injury, he was forced to wear a leather strap across his face for the rest of his life. He became a professor at the Ecole Polytechnique in Paris.

Contribution to math/science:His most famous achievement was paper that described a rational function f and its subsequent iteration. It eventually became known as the Julia set of fractals and was brought back to the forefront by Benoit Mandelbrot.

Reference/s:

Name: Gauss

Dates: April 1777 -Feb 1855

Geographic location: Germany

Biography: From his early schooling, those who meet Gauss could see his genius. At eleven Gauss began his education at the Gymnasium and with a stipend from the Duke of Brunswick entered the Brunswick Collegium Carolinum in 1792 where he made many discoveries. By 1795 he was studying at Gottingen University. He received a degree from Brunswick in 1799. In 1805 he married Johanna Ostoff and due to the death of his benefactor he left Brunswick to take a post as the director of the Gottingen observatory. In 1807 his father, wife and son died. He married the following to a friend of his wife, Minna and had three children.

Contribution to math/science: Wrote book devoted to number Theory, correctly predicted the location of “new” planet, Ceres. He continued to work on the motion of celestial bodies and the relation to differential equations, conic sections and elliptical orbits, invented the heliotrope to be used in surveying, proved the existence of two poles. Able to construct a 17-gon with ruler and compass.

Reference/s:

Name: Riemann

Dates:Sept 1826 - July 1866

Geographic location: Germany, Italy

Biography: One of six children, Riemann began school in 1840 at the Lyceum, then to the Gymnasium at Luneburg and finally attending the University of Gottingen where he began to study theology but with his father’s permission later changed to math. He moved to Berlin University in 1847 to study under Steiner, Jacobi, Eisenstein and Dirichlet, the last becoming a great influence for him. It was here that he worked out his general theory on complex variables. He moved back to Gottingen in 1849 to work on his PhD thesis under the supervision of Gauss. Gauss recommended him for a post and within a few years he was appointed professor. When his mentor Dirichlet died, Riemann was appointed chair of mathematics at Gottingen and was elected to the Berlin Academy of Sciences. In 1862 after his marriage to Elise Koch he caught a severe cold that developed into tuberculosis and moved to Italy because of the warmer climate. He traveled between Italy and Gottingen for the remaining years of his life, dying leaving his last work unfinished.

Contribution to math/science: He introduced topography into Complex functions, worked on determining behavior of trigonometric series. Introduced ideas about geometry in the real world, Introduced the idea of Riemann space and relationship to abelian functions, introduced the Riemann hypothesis

Reference/s:

Name: Lobachevsky

Dates:Dec 1792 -Feb 1856

Geographic location: Russia

Biography: At the age of seven, Lobachevsky, his mother and brothers, moved to Kazan, Russia on the Siberian border after the death of his father. Here he began school in 1802 at the Kazan Gymnasium followed by the Kazan State University where he began to study medicine but later turned to mathematics and physics. Here he also met Martin Bartels, a math professor who would greatly influence his career. By 1811, Lobachevsky received his Master’s degree and by 1814 he was appointed a lectureship followed by an appointment to full professor in 1822. He eventually became rector of the university. Throughout his career, he encouraged the improvement of education at all levels. He bought equipment to improve the labs and pressed for higher levels of scientific research. He finally retired in 1846 but due to the heavy workload, his health had taken a serious toll. Not long after retiring his eldest son died and Lobachevsky became blind from his illness.

Contribution to math/science: Lobachevsky began some of the study of other types of geometry that existed if Euclid’s fifth postulate did not hold. He published an early work on hyperbolic geometry, which was widely disputed but eventually accepted. He also found a way to approximate the roots of algebraic equations.

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Name: Benoit Mandelbrot

Dates:Nov 1924- Present

Geographic location: Poland, France, United States

Biography: Born to family of academic tradition, Mandelbrot was introduced to math by his uncles. After his family moved to France he attended the Lycee Rolin in Paris but with the beginning of WWII his family moved around and he was mainly self–taught in this period, which he now attribute much of his success to. In 1944 he began his study at Ecole Polytechnique. Once he finished here he traveled to the US and studied at both the California Institute of Technology and Princeton. He was also granted a PhD from the University of Paris. He returned to France in 1955 and married Aliette Kagan. He then returned to the US to work for IBM and became a professor at Yale. In June of 1999 he received the Honorary Degree of Doctor of Science from the University of St. Andrew’s.

Contribution to math/science: Introduce the existence of fractals in everyday life. Related them to the basis for chaotic systems

Reference/s:

Name: Lewis Richardson

Dates:Oct 1881- Sept 1953

Geographic location: England, Scotland

Biography: Born to a Quaker family, Richardson was a pacifist his entire life. He attended Newcastle Preparatory School, Bootham in York the Durham College of Science, and finally King’s college, Cambridge, graduating with a first class degree in the Natural Science Tripos in 1903. He held many with the Meteorological offices and at several Universities. He married Dorothy Garnett in 1909 and they adopted three children. When WWI broke out he declared himself a conscientious objector, which excluded him from further University post. He did join the Friend’s Ambulance service. Once the war was over the Meteorological office became part of the military so he resigned his position. Worked at several colleges but finally retired at 59 to concentrate on his research.

Contribution to math/science: Developed differential equations that would be later used to predict weather. Study the mathematical relationship in the causes of war

Reference/s:

Name: Albert Einstein

Dates:March 1879 -April 1955

Geographic location: Germany, Switzerland, United States

Biography: Einstein began his schooling around 1886 in Munich and was in the Luitpold Gymnasium around 1891, which was the point that he began studying mathematics. He failed the entrance exam for the ETH in Zurich and then attended secondary school in Aarau using this route to get in. He did finally get in and graduated in 1900 as a teacher of mathematics and physics. At this point he found it difficult to find a position but did land some temporary posts at private schools. Through the help of a friend’s father, he was able to get a job at the patent office in Bern as technical expert third class. Here worked here from 1902 –1909. During this time he receive his doctorate from the University of Zurich. In 1908 he became a lecturer at the University of Bern and finally a professor the following year at the University of Zurich. At this post he resigned his job at the patent office. In 1911 he became full professor at the Karl-Ferdinand University in Prague. He moved from Prague to Zurich in 1912 to take up a chair at the Eidgenössische Technische Hochschule in Zurich. When his predictions became true regarding a British eclipse he became idolized by the media. Einstein received the Nobel Prize in 1921 for his work on photoelectric effect. During the twenties he traveled extensively around the world. He did have a physical collapse but once he recovered he returned to his travels. He was offered a post at Princeton in 1932. In 1940 he became a US citizen and retained his Swiss citizenship. By 1949 his health was in decline and he passed away April 18, 1955. Even though he always moving around, Einstein did have a family. He married Mileva Maric in 1903 and they had a daughter and two sons; their marriage was dissolved in 1919 and in the same year he married his cousin, Elsa Löwenthal, who died in 1936.