Albert Einstein

Born: March 14, 1879, in Ulm, Kingdom of Wrttemberg, German EmpireDied: April 18, 1955 (at age 76) in Princeton, New JerseyNationality: GermanFamous For: Father of the Atomic Age. Many contributions to science that transformed the modern worldAwards: Nobel Prize in Physics (1921), Time Magazines Person of the Century (1999)

The renowned physicist, is remembered for his theories on nuclear power, and his revolutionary concept concerning nature of light. Nonetheless, his innovative ideas were misunderstood and he was regularly criticized for his involvement in politics as well as social issues. He has made significant contributions to the field of mathematics, physics, and science.

Einsteins Early YearsAlbert Einstein was born on March 14, 1879, at Ulm, Germany. Six weeks later, he moved to Munich with his family where he later started his schooling at Luitpold Gymnasium. Later, his family moved to Milan, Italy, and Albert continued his schooling in Switzerland.Einsteins Contribution to MathematicsWhile Einstein was remembered for his contributions to physics, he also made contributions in 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.

Einstein: The World CitizenDuring the early part of the 20th century, Einstein became internationally renowned. He received several awards in medicine, science, and philosophy from numerous universities across the world. His tour to any corner of the world became the national event; reporters followed him everywhere he went. Though regretting his public life, Albert capitalized on his popularity to further his political and social

Einsteins Personal LifeIn 1903, Einstein married Mileva Maric. They had two sons and one daughter. But in 1919, they divorced and he married Elsa Lwenthal in that same year. He died in 1955 at his home in New Jersey.

Isaac Newton

Born: Dec 25, 1642, in Woolsthorpe-by-Colsterworth, Lincolnshire, EnglandDied: March 20, 1727 (at age 84), in Kensington, Middlesex, England, Great BritainNationality: EnglishFamous For: Newtons method for estimating roots of a function

Isaac Newton is one of the most celebrated andrecognized mathematiciansand physicists in world history. Known for his discovery of gravity, Newton remains to this day a very influential figure from the Age of Enlightenment.

Newtons Early YearsIsaac Newton was born in Lincolnshire on Christmas Day of 1642. His father died before Newton was born and his mother remarried. Newtons early years were spent with his maternal grandmother. The time he did spend with his mother was very tumultuous since he did not like his stepfather at all.Until he was 17 years old, Newton was a student at The Kings School in Grantham. He did not leave the school on pleasant terms. Reunited with his mother, Newton tried his hand at being a farmer. This was a very unhappy with his new profession and he would re-enroll in school. Newton became a standout in school and scored very high in his studies.

Newtons University YearsNewton became a student at Trinity College in Cambridge where he studied the official curriculum based on Aristotle. He also expanded his learning to include the study of the great philosopher Ren Descartes. He invested a great deal of time pursuing his love for astronomy and he spent time learning about the lives and work of many famous astronomers.One of Newtons best known early achievements while in school was his discovery of the generalized binomial theorem. This theorem set the stage for an expanded mathematical system which would be advanced calculus. Ironically, he was not considered all that great of a student when he was enrolled in college. When he graduated, he invested a great deal of time in self-study. During this period of self-study, he focused on physics, calculus, and the laws of gravity.

Newtons Contributions to MathematicsNewton went on to publish a very influential work titledThe Principiaand it centered on infinitesimal calculus in geometric form. His work on cubicle curves in relation to the Euclidean plane was quite revolutionary for its time. As with his other studies, the work set the stage for amazing inroads in math and science when others built upon the groundwork he created.Newton made many discoveries in areas related to optics, the theory of finite differences, and innovative applications in geometry. Based on his very unique work, he received a great deal of acclaim. This led to him being named Lucasian Professor of Mathematics in 1669. Traditionally, a person who was awarded such a position had to become a priest. Newton was given an exemption from that rule.

Leonardo Pisano Bigollo

Born: c. 1170 in ItalyDied: c. 1250 (at about age 80)Nationality: ItalianFamous For: Fibonnaci Numbers

Leonardo Pisano Bigollo was an Italianmathematician. He is usually better known by his nickname, Fibonacci, and is considered to be among the foremost European mathematicians of the medieval era. He was instrumental in bringing the widespread use of Arabic numerals to the West. The Fibonacci number sequence is named after him, although he merely referenced it rather than devising it himself.

Bigollos Personal LifeThe details of Fibonaccis childhood and upbringing are almost completely unknown, and what has been deduced has been worked out largely from notes he placed in his own works. There are no contemporary drawings of him, all portraits having been produced after his death.However, he is thought to have been born in the Italian city of Pisa, the son of a prosperous merchant who may have been the Pisan consul in modern-day Algeria. For this reason, he is often said to have received an education somewhere in northern Africa.While still a youngster, Bigollo went with his father to assist his commercial and diplomatic operations in the nearby sultanate of Almohad. While he was there, he experienced the use of the system of Hindu-Arabic numerals, at that time almost unknown in the West, where Roman numerals were still the standard. He quickly realized that this new number system would make arithmetical operations far quicker and allow them to be carried out with greater efficiency than the old Roman system.

Bigollos Mathematical WorksDuring the last few years of the 12th century, Fibonacci undertook a series of travels around the Mediterranean. At this time, the worlds most prominent mathematicians were Arabs, and he spent much time studying with them. In about 1200, he returned home to Italy, and two years later he published his book,Liber Abaci.This work, whose title translates as theBook of Calculation, was extremely influential in that it popularized the use of the Arabic numerals in Europe, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly.InLiber Abaci, Fibonacci used as an example a problem regarding the growth of a rabbit population. The sequence of numbers which he used to solve the problem was that which later became known as the Fibonacci sequence. However, it had been known in India several centuries earlier; this was merely the first time that it had been seen in Western mathematics.The fact that the ratio of successive numbers in the sequence tends to the Golden Ratio of around 1.618:1 may or may not have been known to Fibonacci; in any event, he did not mention it in his book.

Born Augusta Ada Byron

Born: Dec 10, 1815 in London, EnglandDied: Nov 27, 1852 (at age 36) in Marylebone, London, EnglandNationality: BritishFamous For: Considered to be the worlds first computer programmer The only legitimate child of the famous English poet Lord Byron, Lovelace considered herself an analyst and metaphysician who took an interest in hypnosis and phrenology. She collaborated closely with Charles Babbage, whom she met in 1833 at the age of 17. Much of her career is attributed to her outstanding contribution to Babbages Analytical Engine (a mechanical general-purpose computer developed in 1837).

Ada Lovelaces Personal LifeBorn Augusta Ada Byron on December 10th, 1815, in Piccadilly Terrace, Middlesex (now in London), England, Ada Lovelace (full name Augusta Ada King, Countess of Lovelace) became an eminent and influentialmathematician, writer, and the worlds first computer programmer.Her parents, Annabella Milbanke Byron and Lord Byron, separated briefly after her birth and although her father was allowed by the English law to get full custody of Ada, he gave up his parental rights (he did ask his sister to inform him about his daughters welfare, however). Annabella moved in with one-month-old Ada to Kirkby Mallory, Leicestershire.Although her mother was the only parent she knew, the mother-daughter relationship was not very good. As a result, Ada was left in the care of her grandmother. Lord Byron died in 1824 when she was only eight years old, so she never had the chance to meet him in person. Ada Lovelace had various health problems throughout her life and in 1829 she became paralyzed after suffering from measles. She recovered gradually and in 1831, she could walk, but only with crutches.

Lovelaces Contributions to MathematicsLovelaces work opposite British mathematician Charles Babbage, who was also a professor at Cambridge and her lifelong friend, was the most significant part of her career. Between 1842 and 1843, she translated works from French and annotated a memoir written by Italian mathematician Luigi Menabrea, who supported Babbages Analytical Engine.Impressed by her analytical skills and highly-developed intellectual abilities, Babbage referred to Ada as an enchantress of numbers. In addition to being the founder of scientific computing, Lovelace aimed at creating a mathematical model that she called a calculus of the nervous system. Her detailed annotations simply entitledNotesare the main source of her achievements throughout her life and moreover, these notes are deemed the first computer program, anticipating future developments in computer science.In herNotes, she described an algorithm representing how the proposed mechanical general-purpose computer (the Analytical Engine) could be programmed to compute Bernoulli numbers and to solve complex problems. This is considered the first algorithm developed for implementation on a computer. In 1953, the Analytical Engine was recognized as an early model for a computer.On July 8th, 1835, Ada married William King, 8th Baron King, and they had three children. In 1838, she became Countess of Lovelace.

Emmy Noether

Born: March 23, 1882, in Erlangen, Bavaria, Germany

Died: April 14, 1935 (at age 53), in Bryn Mawr, Pennsylvania

Nationality: German

Famous For: Formulating Noethers theorem

Emmy Noether was born Amalie Emmy Noether in Erlangen, Bavaria, Germany on March 23, 1882. She had three other siblings, but all of them besides her brother, Fritz, passed away during their childhood. Her father was also amathematician, Max Noether, and he sparked her interest for math later on in her life. As Emmy grew up, she studied a lot of different subjects, but she did not put a lot of emphasis on math until later.

Noethers Educational YearsNoether spent a lot of time studying different languages, and she learned a lot from her mother about cooking and cleaning. Once Emmy graduated high school, she wanted to be a teacher, which led to her taking an exam to become a teacher of English and French to young women. She passed this test easily, but this led her down a difficult road ahead. She could not take classes her like her brother could because she was a woman, so she ended up auditing classes at the University of Erlangen instead.During her time auditing classes, Noether learned about mathematics in depth. After this, she took a test to become a doctoral student in mathematics. She passed this test and then went on to take five more years of classes. After those five years, Emmy Noether became the second woman to ever get her degree.

Noethers Contributions to MathematicsSoon after arriving in Gottingen in 1915, Emmy created Noethers Theorem. She also accumulated a following of students known as Noethers Boys. In 1928, she decided to accept a teaching position in Moscow at Moscow State University. During her time there, she taught classes and contributed to the Galois theory through research and studying.In 1933, Germany was taken over by the Nazis coming into power, and that is when all Jews were to be pushed out of the Universities. Her brother, Fritz, then moved to Siberia and she decided to move to the United States to become a teacher at Bryn Mawr College.

George Boole

Born: Nov 2, 1815, in Lincoln, Lincolnshire, EnglandDied: Dec 8, 1864 (at age 49) in Ballintemple, County Cork, IrelandNationality: EnglishFamous For: Boolean Logic George Boole was an Englishmathematicianand the founder of an algebraic tradition in logic. George worked as a schoolmaster and from the year 1849 to 1864, he was a professor of mathematics at Queens University in Cork, Ireland. He was not only a mathematical genius, but he was also a fine humanitarian as well.A strong minded person, George was always prepared to engage in bitter arguments with his academic colleagues. He revolutionized logic by applying methodologies from the field of symbolic algebra to logic. Today, his revolutionary advances in maths are fundamental aspects of electronics and computer science. His Boolean Algebra is utilized to design and operate computers as well as other electronic devices.

Booles Early YearsGeorge Boole was born in 1815 in Lincoln, England, into a family of modest means. His father was more of a good friend than a good breadwinner. Georges father was a struggling cobbler whose passion was being a dedicated dilettante in the field of science and technology, one who loved participating in Lincoln Mechanics Institution, a community social club promoting discussions, reading, as well as lectures regarding science and technology. In 1834, Georges father became the curator of its library.This passion of learning was inherited by his son, George Boole. With a supportive family and access to books from Sir Edward Bromhead, FRS, who lived near Lincoln, Boole taught himself advanced mathematics and foreign languages. At age 20, he opened his own school. He had to start teaching mathematics, which sparked his passion in the subject.Discontented with the textbooks, he started reading Lagrange and Laplace for ideas. Inspired by their ideas, he wrote his very first mathematical paper on calculus of variations.

Booles Career DevelopsBoole began to submit his work to theCambridge Mathematical Journal. Editor Duncan Gregory was impressed with his work and published his papers in the journal. Gregory then suggested that Boole study at Cambridge University, but he could not quit teaching as that was how he supported his family financially.As Gregory suggested, Boole began studying algebra. Soon after, his work was published and awarded. In August of 1849, he worked as a professor of mathematics at Queens College. Within two years, he was named the Dean of Science.

Booles Contributions to MathematicsBooles second work,An Investigation of The Laws of Thought on Which are Founded Mathematical Probabilities and Logic, was published in 1854. This book was an attempt to correct his 1847 book on logic. In his book, he discussed the theoretical possibility of utilizing probability theory to uncover fundamental laws that governed the society by analyzing large quantities of social data.Aside from his work on mathematical theories of logic and probability, Boole also made contributions to the development of calculus. He received numerous honorary degrees and awards.

Daniel Bernoulli

Born: Feb 8, 1700, in Groningen, Dutch RepublicDied: March 17, 1782 (at age 82), in Basel, Republic of the SwissNationality: SwissFamous For: Bernoulli Principle Daniel Bernoulli came from a famous Swiss family ofmathematiciansand eventually became a pioneer in hydrodynamics and the kinetic theory of gases. He was born on February 8, 1700, in Groningen in the Netherlands, where his father held the academic post at the university. His father, Johann Bernoulli, his uncle, Jacob Bernoulli and his older brother, Nicolous (II) were also famous mathematicians.Bernoullis Early Life and EducationWhen Daniel was five years old, his family moved back to Basel (which was their native city), where his father ended up taking over Jacobs old chair, which was left vacant after his Uncle Jacobs death. Daniel had one elder brother, Nicolaus (II), and one younger brother, Johann (II).1n 1713, when Daniel was 13 years old, he went to Basel University to study philosophy and logic, in line with his fathers wishes. He completed his bachelors degree in 1715 and went on to obtain his masters degree in 1716. Johann pushed his son in the direction of becoming a merchant, as there was no money in the career of mathematics. Daniel resisted and his father relented at his decision. Realizing his sons keen interest and inherited family talent, Johann began to tutor Daniel in the methods of calculus and his theories of kinetic energy.Bernoullis Contribution to MathematicsDaniel studied philosophy, medicine, and logic from different universities of Heidelberg, Basel, and Strasbourg. Just like his father, Daniel wanted an academic career in the university, but he did not succeed. As Daniel was unable to get an academic post, he went to the city of Venice to study practical medicine.While in Venice, his first work onMathematical Exerciseswas published in 1724. The work brought him recognition all across the Europe and in 1732, Bernoulli was offered a position in Basel to teach botany and anatomy.Bernoullis chief work was inHydrodynamique, published in 1738. This work was published in Strasbourg. It laid out the principles of fluid dynamics, which consisted of a treatise on differential equations related to the physics of flowing water (fluid dynamics).It developed the relationship between fluid velocity, pressure and density. Bernoullis theorem is the basis of aircraft design. This principle on stationary flow remains the general principle of aerodynamics and forms the basis of the modern explanation of lift.In 1734, both Daniel and his father were declared joint winners of the Grand Prize of the Paris Academy for their work on planetary orbits. This affected his relationship with his father who felt that he should have received the prize alone.Bernoullis Awards and DistinctionsDaniel Bernoulli did produce several other excellent scientific works during his job in Basel. He won several awards for his contribution to laws and theories of physics and mathematics. In 1737, he won for work on the best shape for a ships anchor. In 1740, he won for his work on essays on magnetism. Other awards include one in 1747 for a method to determine time at sea and in 1753 for the effects of forces on ships. Between 1725 and 1749, he won 10 prizes from the Paris Academy for his work in astronomy, tides, magnetism and ocean currents. David Hilbert

Born: Jan 23, 1862, in Knigsberg or Wehlau, Province of PrussiaDied: Feb 14, 1943 (at age 81), in Gottingen, GermanyNationality: GermanFamous For: Formulating Hilbert Spaces, a major theory in functional analysis David Hilbert was born in Koenigsberg, East Prussia, on January 23, 1862. He was a great leader and spokesperson of mathematics in the early 20th century. Like most great German mathematicians, Hilbert was a product of Gttingen University, at that moment the worlds mathematical center, and he spent much of his working life there. His formative years were spent at Knigsberg University where he developed fruitful scientific exchange with his fellowmathematiciansAdolf Hurwitz and Hermann Minkowski.Hilberts Academic BackgroundAt the University of Koenigsberg, Hilbert studied under Lindemann for his doctorate, which he earned in 1885. One of his friends there was Hermann Minkowski, who was also a doctoral student. In 1884, Adolf Hurwitz was appointed to Koenigsberg University and became friends with Hilbert, which was a very significant factor in Hilberts mathematical development. David Hilbert was a member of staff at Koenigsberg from 1886-1895, being the Privatdozent until 1892. He was then an Extraordinary Professor for one year before becoming a full professor in 1893.Hilberts InventionsDavid Hilbert was preeminent in numerous fields of mathematics, comprising axiomatic theory, algebraic number theory, invariant theory, class field theory as well as functional analysis. His calculus examination led him to invent Hilbert space, considered to be among the primary concepts of functional analysis as well as modern mathematical physics. He founded fields such as modern logic and met mathematics.The Foundations of GeometryIn 1899, David Hilbert published his book The Foundations of Geometry in which he described a set of axioms that eliminated the flaws from Euclidean geometry. In the same year, American mathematician Robert L. Moore also published a set of axioms for Euclidean geometry at age 19. While some axioms in both systems were similar, there was a feature about the axioms that were different. Hilberts axioms were theorems from Robert Moores and Moores axioms were proved as theorems from David Hilberts.Hilberts Contribution to MathematicsAfter the achievements with axiomatization of geometry, David Hilbert developed a program to axiomatize mathematics. With his attempt to achieve his goal, he began a formalist school of mathematics which opposed the Intuitionism of Brouwer and Kronecker. Meanwhile, Hilbert was expanding his contributions to math in various directions partial differential equations, mathematical physics, and calculus of variations. He knew that he could not achieve this by himself.In 1900, Hilbert gave a massive homework assignment to all mathematicians across the world. He did this when he presented a lecture, entitled mathematical problems before Paris International Congress of 1900. Hilbert proposed 23 mathematics problems to whose solutions he thought the 20th century mathematicians ought to devote themselves. These mathematics problems are now known as Hilberts problems and many of them remain unsolved today.

Gottfried Leibniz

Born: July 1, 1646, in Leipzig, Electorate of Saxony, Holy Roman EmpireDied: Nov 14, 1716 (at age 70), in Hanover, Electorate of Hanover, Holy Roman EmpireNationality: GermanFamous For: Refining the binary system German-born Gottfried Wilhelm Leibniz was a co-inventor of calculus, which he developed independently ofIsaac Newton.Leibnizs Early YearsLeibniz was born in Leipzig, Germany, in 1646. His father, Friedrich Leibniz, was a professor of moral philosophy at the University of Leipzig. Although his father died when Gottfried was just six years old, the elder Leibniz left behind a significant personal library of books on philosophy and theology.Gottfried began reading every book in his fathers library many of which were written in Latin. He was able to absorb and understand vast amounts of information well before he reached adulthood. Leibniz even mastered other languages in addition to his native German with little or no tutoring.Leibnizs University YearsBy the time Leibniz was old enough to attend his first year of college, he was perhaps more educated and knowledgeable than even his most advanced fellow students. He entered university study at the age of 15, and by age 17, he had earned his masters degree in philosophy. He earned his bachelors degree in law in 1666 at age 20.Leibnizs First PublicationLeibniz published his first book also in 1666, which wasOn The Art of Combinations(De Arte Combinatoria). The main theme of the book was exploring the idea for a kind of alphabet of human thought. That is, in this book Leibniz proposed that all human thought or concepts were a combination or build-up of smaller units of thought or concepts. The first part of the book was an argument for the proof of the existence of God.Leibniz Invents a CalculatorAmong Leibnizs most amazing and early achievements was the invention of one of the first mechanical calculators, or crude computers. It was called the Stepped Reckoner and could perform addition, subtraction, multiplication and division. Although the design and concept was sound, the mechanical skills of the day were not equal to manufacturing the precision metal parts needed to make the machine work properly. Two working prototypes were produced of this machine.Leibnizs first real job was that of an alchemist in Nuremberg. He soon found other employment, however, in rewriting the legal code of his electorate, putting his law and philosophy education to practical use. He dabbled considerably in international politics, formulating plans for the advancement of German policies after the disastrous Thirty Years War, which left his home country weakened, shattered, and economically backwards.Leibnizs ContributionsIn the early 1670s, Leibniz lived in Paris where he met some of the brightest luminaries of the day, including the great astronomer andmathematicianChristiaan Huygens. Here he developed his mathematical skills to a high degree, which led to his development of calculus.The contributions Leibniz made to a wide range of philosophical and scientific fields is among the most stunning achievements by any single individual in all of history. Leibniz is even credited with inventing modern library science, to name just one of many accomplishments.Gottfried Wilhelm Leibniz never married, and at the time of his death in 1716 at age 70, his reputation and influence had since declined considerably for complex reasons, both political and personal.

John Napier

Born: 1550 in Merchiston Tower, EdinburghDied: April 4, 1617 (at age 66 or 67) in EdinburghNationality: ScottishFamous For: Discovering logarithms John Napier was a Scottishmathematicianwho found lasting fame as the inventor of logarithms. He also invented at least one war weapon. His position as a member of the Scottish nobility allowed him to more spend time on scientific research than would likely have been possible for a man of a humbler background. Napier also devised a specialized form of abacus for multiplication and division, which bears the name Napiers Bones to this day.

Napiers Early YearsThe son of 16-year-old Archibald Napier, John was born in Merchiston Tower, Edinburgh in a building which now forms a part of Edinburgh Napier University, which is named in his honor. His family formed a prominent and influential part of the countrys nobility and was very wealthy.Following the pattern common at that time for members of the nobility, he did not begin formal study until the age of 13, when he attended St. Andrews University for a brief period. His uncle, who was Bishop of Orkney, advised him to continue his studies abroad, and in 1564 John sailed for the European continent.

Napiers Mathematical StudiesOnce overseas, Napier was disappointed to discover that there were few teachers of Greek available. Since he had become passionately interested in the study of religious texts, the language was vital for his continued educational development.Some historians believe that he may have traveled to Switzerland to be taught, since there were small numbers of scholars specializing in Greek in both Geneva and Basel. In any case, he was fluent in Greek and Latin by the time he returned home in 1571. Nevertheless, it was in the field of mathematics to which he was attracted.Back in Scotland, Napier married his first wife, Elizabeth, and settled at a Stirlingshire estate. He remained utterly fascinated by mathematical study, so much so that his hermit-like lifestyle led some of the local inhabitants to take him for a wizard. Meanwhile, Napier was making a further name for himself both in Scotland and abroad with his fiery denunciation of the Roman Catholic Church, to which he was vehemently opposed. In 1579, Elizabeth died and he married Agnes, to whom he remained devoted.

Napiers Invention of LogarithmsNapier turned his mind to the problem of reducing the tedium and drudgery of arithmetic, which at that time was a long-winded and boring occupation. In 1614, he published the work that was to give him lasting fame: an outline of the basic principles behind what came to be known as logarithms. Napier himself referred to them as artificial numbers.Contemporary mathematicians were impressed with Napiers work, recognizing its potential to hugely reduce the time taken for many arithmetical operations. Although he did not invent it, Napier also popularized the use of the decimal point.Pierre de Fermat

Born: 1601 in Beaumont-de-Lomagne, FranceDied: Jan 12, 1665 (at age 60 or 61), in Castres, FranceNationality: FrenchFamous For: Fermats Last Theorem Pierre de Fermat, one of the prominentmathematiciansof the 17th century, is better known for his contribution towards development of infinitesimal calculus. He was also a lawyer in terms of profession at the Parliament of Toulouse.

The Life of FermatPierre de Fermat was born in 1601 in Beaumont-de-Lomagne, France. He is believed to be of Gascogne origin. Fermats father was a wealthy merchant and his mothers family was involved in the legal profession. There is little information about the early education of Pierre, but he is believed to have attended the College de Navarre in the city of Montauban. Fermat obtained a bachelors in civil law from the University of Orleans in 1626. He was married and had five children.

Fermats Mathematical ResearchFermat was more of an amateur mathematician who explored the world of mathematics as a hobby. Post studies, Pierre moved to Bordeaux where he started working on mathematical research seriously. Despite his interest in mathematics, he always maintained it as a hobby while continuing to work as an active lawyer.Fermat was not even interested in publishing his work and used to send his work to famous mathematicians in France. It was his connection with Marin Mersenne that gave Pierre international recognition. During his lifetime, Fermat received very marginal recognition as a mathematician and it was his papers that he shared with others that kept his work alive. Otherwise, much of his work could have been lost.

Fermats Contributions to MathematicsFermat mathematician made significant contributions to number theory, probability theory, analytic geometry and the early development of infinitesimal calculus. He ventured into the areas of mathematics which included pre-evolved calculus and trigonometry.Fermats primary contribution to mathematics was in the field of number theory. C.G. Bachets translation of Diophantus of Alexandria inspired his interest in the Theory of Numbers. He introduced Fermats Last Theorem, which states that there is no solution in integers of the equation xn + yn = zn (xyz#0, n>2).Fermat contributed to the development of calculus through his work on the properties of curves.Sir Isaac Newtonsaid that his invention of calculus was based on Fermats methods of tangents. Fermats work on calculus was an aid in developing the differential calculus.

Alan Turing

Born: June 23, 1912 in Maida Vale, London, England, United KingdomDied: June 7, 1954 (at age 41) in Wilmslow, Cheshire, England, United KingdomNationality: BritishFamous For: Father of Computer ScienceAwards: Officer of the Order of the British Empire, Fellow of the Royal Society Born on June 23rd, 1912, in the Maida Vale district in London, England, Alan Turing was a prominent and influentialmathematician, cryptanalyst, logician and computer designer and scientist. He helped pave the way in the field of computer science, thanks to his Turing machine (he called it an automatic machine), a hypothetical device created in 1936 and representing a computing machine which helped make formal concepts such as mechanical computation and algorithm.

Alan Turings Early YearsTurings father, Julius, worked for the Indian Civil Service in British India. During their childhood years, Alan and his older brother stayed with a retired Army family while their parents traveled between Hastings, England, and India. He showed an interest in mathematics and science from an early age, but his headmaster was not impressed with his abilities in these fields.

Turings Educational YearsWhile studying at the Sherborne School, Turing became friends with Christopher Morcom, whose premature death turned him into an atheist who believed that all phenomena in the world must be materialistic. In 1931, he enrolled at Kings College, University of Cambridge, to study mathematics. By 1935, as a result of his thorough research in probability theory, he was elected a Fellow at Kings College. He also earned his Ph.D. in mathematical logic at Princeton University in 1938 under the direction of American mathematician Alonzo Church, who supported his work and recommended it for publication.

Turings Contribution to MathematicsIn 1936, Turing published a seminal paper entitledOn Computable Numbers, with an Application to the Decision Problem, which proposed an effective method for establishing the provability of mathematical statements. Both Turing and Church independently showed that even logical systems (weaker than arithmetic systems) are undecidable.One of their arguments consisted in the fact that lambda-definable functions are the same as all effectively calculable (computable) functions. To prove this fact, he invented the Turing machine for optimum computability. In 1948, Alan Turing was appointed Reader at the University of Manchester (Mathematics Department) while continuing his abstract work in mathematics. His main contribution at Manchester University was his design for the programming system of Ferranti Mark I, the first commercially available electronic digital computer.In 1951, he was elected for life Fellow of the Royal Society for his substantial contribution to the improvement of natural knowledge, including mathematical biology (mathematical modeling and representation of biological processes, using various applied mathematical techniques).Turing was also the recipient of the Order of the British Empire for his significant code-breaking work (with the aid of his code-breaking machine known as the Bombe) during World War II, having helped in decoding more than 84,000 intercepted messages per month.Blaise Pascal

Born: June 19, 1623, in Clermont-Ferrand, Auvergne, FranceDied: Aug 19, 1662 (at age 39) in Paris, FranceNationality: FrenchFamous For: Pascals Calculators

Born in France in 1623, Blaise Pascal was the third child and only son of tienne Pascal. His father did not believe in the French school system so he opted to homeschool his son. Ironically, the one subject that Pascal did not learn was mathematics. His father did not want his son to learn the subject until he was 15.

Pascals Early EducationStarting late did not have much of a negative effect on Pascals skills as amathematiciansince he would go on to great fame as a legendary math trailblazer. In fact, Pascal would study math on his own in secret. In particular, he would study geometry. At the age of 12, he made the discovery that two right angles are the sum of a triangle.Pascal continued to take his study of math very seriously. As a young man, the culmination of his work would lead to his innovative developments in projective geometry theorems.

Pascal Moves to ParisPascal followed his father to Paris when the elder Pascal was offered a job as a tax collector. In February of 1640, in Paris, Pascal published one of his most important works Essay on Conic Sections. To help his father out with the collection of taxes, Pascal also designed and invented a primitive calculator. Attempts at marketing the calculator were attempted, but they did not sell.In 1646, Pascal was placed under the care of two brothers from a local religious order when his father suffered a major injury. During this time, Pascal would have a religious awakening that would have a profound impact on the rest of his life.

Investing in Atmospheric PressureDuring the time of his religious experience, Pascal invested a tremendous amount of effort studying about atmospheric pressure. He undertook a series of unique experiments and which revealed a great deal of information that had not been known prior to Pascal performing his experiments.In 1653, Pascal published the groundbreaking workThe Treatise on the Equilibrium of Liquids.The Generation of Conic Sectionswas another project he was working on publishing, but it was never finished during his lifetime.

Other Contributions to MathematicsPascals most famous work from the time period would beThe Treatise on the Arithmetical Triangle, which was an innovative study into the triangle that would set the stage for a great deal of geometric revelations in the future.

John Nash Born: June 13, 1928 (age 85), in Bluefield, West Virginia

Nationality: American

Famous For: Developing the Nash equilibrium

John Forbes Nash, Jr. is amathematicianwho did his work on differential geometry and game theory.

Nashs Early Years

Since he was born in a family that loved books, John Nash became interested in the learning process. He attended Bluefield schools and his parents fondness for books provided him with an encyclopedia that he would read frequently in his childhood. His time as a student revolved around mathematics, chemistry, electrical studies and experimentation. He would read characteristic books like theMen of Mathematicsand prove integer theorems.

Nashs College Years

Form 1945 to 1948, Nash studied at the Pittsburg Carnegie Institute of Technology with the ambition of becoming an electrical engineer, much like his father. Nevertheless, his love for mathematics overpowered him with considerable interest in subjects like Diophantine equations, number theory, relativity theory and quantum mechanics.During this period, he became progressively attached to negotiation problems and came across the uncompleted works ofJohn von Neumannand Morgenstern on game theory and economic behaviors. Hence, he participated in the game theory groups. He also took an elective course on international economics that led him to the ideas and The Bargaining Problem, which was a stepping stone for Nash.

Nashs Contribution to Mathematics

John Forbes Nash, Jr. is profoundly attached to his Nash equilibrium theory that is learned and applied in making business decisions. From Pittsburgh, he joined Princeton University where he worked on the equilibrium theory and received his Ph.D. with the dissertation of non-cooperative games. This thesis contains detailed definitions and explanations of what would be known by all as Nash equilibrium.Forty-four years later, the same thesis earned him a Nobel Prize in Economics, which he shared with Reinhard Selten and John Harsanyi (game theorists). In addition, he published several articles entitledEquilibrium Points in N-person Games(1950),Econometrica about The Bargaining problem(April 1950), andTwo-person Cooperative Games(1953). He worked at RAND cooperation in Santa Monica in the summer of 1950 and also taught calculus at Princeton from 1950-1951. At the same time, he proved the Nash embedding theorem and became science assistant at MIT Massachusetts.

Archimedes

Born: c. 287 BC in Syracuse, Sicily

Died: c. 212 BC (at about age 75) in Syracuse, Sicily

Nationality: Greek

Famous For: Accurate calculation for pi

Archimedes was a great mathematician born in Syracuse, Sicily, Italy, in 287 BC. He is revered as one of the threegreatest mathematicians of all timealongside Carl Gauss andSir Isaac Newton. Archimedes focused primarily on the discipline of geometry, and he was also a renowned inventor and engineer.

Archimedes Family Life

Archimedes father, Phidias, was an astronomer of some note, and his family was well off. Therefore, Archimedes was able to become an accomplished musician and poet, and he maintained a lifelong interest in astronomy. Because of his position, Archimedes was able to travel to Alexandria, Egypt, for his formal education.

By all reports, he was thrilled with the lofty intellectual exchanges he had there. Upon completing his studies, he returned to Syracuse to help with his family and to work for King Hiero II as an engineer inventing machines of war and improving the designs of existing ones (most notably the catapult).

Archimedes Contribution to Mathematics

On his own, Archimedes continued to study geometry and science and the principles of mechanics and made such major contributions to these disciplines as an understanding of specific gravity, hydrostatics, and buoyancy along with ingenious everyday applications of the use of the lever and the pulley.

He created formulations for such mathematical accomplishments as a formula to measure the area of a circle. This was done using a system he created called using infinitesimals. This is quite similar to modern day integral calculus.

Archimedes also created a formula that enabled him to determine the volume of a solid or the volume of an item of irregular shape. Additionally, he was able to discover the precise value of pi and create a formula for determining the volume of a sphere. His formulas are still in use today.

Ren Descartes

Born: March 31, 1596, in La Haye en Touraine, Kingdom of FranceDied: Feb 11, 1650 (at age 53), in Stockholm, Swedish EmpireNationality: FrenchFamous For: Developing the Cartesian coordinate system

Ren Descartes was a Frenchmathematician, philosopher, and writer that spent nearly all of his adult life living in the Dutch Republic. He is viewed as the inventor of modern-day philosophy and hisMeditations on First Philosophyis still required text for many philosophy departments. He is very well-known for his philosophical declaration, I think; therefore I am.

Descartes Early LifeDescartes was born in La Haye, France, in March of 1596. He was educated at a boarding Jesuit school when he was eight years old. There, he studied mathematics, music, astronomy, metaphysics, natural philosophy and ethics. Later, he earned a law degree when he was 22 from the University of Poitiers.Shortly after his graduation, Descartes had three very powerful visions or dreams that he attributed for establishing the path of his life-long studies. Next, he traveled and spent time in the army. During his travels, he met Isaac Beeckman, a Dutch philosopher and scientist. Beeckman soon became a close mentor.

Descartes Middle YearsDescartes went back to France in 1622, and he spent a couple of years in Paris as well as other areas of Europe. During his stay in Paris, Descartes composed theRules for the Direction of the Mind, his first composition on method. In 1623, he went to La Haye to sell his property and invested the proceeds in bonds. This gave him a comfortable and secure income for the remainder of his life.In 1628, Descartes went to live in the Dutch Republic and stayed there until 1649. In April of 1629, he enrolled in the university in Franeker. The next year he attended the Leiden University and studied mathematics under Jacob Golius, as well as astronomy under Martin Hortensius. In Amsterdam, Descartes had a daughter with a servant in 1635 while he was teaching at the university in Utrecht.

Descartes Later YearsDescartes continued to publish works on philosophy and mathematics in the later years of his life. He published theDiscourse on the Methodin 1637. In 1641, Descartes published his metaphysics work,Meditations on First Philosophy. In 1644, thePrinciples of Philosophywas published and this was a combination of hisDiscourseandMeditationsworks.In 1647, the King of France awarded Descartes a pension. In February of 1650, he moved to Stockholm, Sweden, to be Queen Christinas philosophy tutor. There, Descartes died from pneumonia when he was 53 years old.

Contribution to MathematicsDescartes developed Cartesian (analytical) geometry, which is the use of algebra to examine geometric properties. He created an empirical comprehension of rainbows, along with proposing a naturalistic account for the solar systems formation. This led Pope Alexander VII to add his works to the List of Prohibited Books.Eratosthenes

Born: 276 BC in Cyrene (modern day Libya)Died: 194 BC (at age 82) in Alexandria, EgyptNationality: GreekFamous For: Calculating the Earths circumference

Eratosthenes was amathematicianand astronomer from Greek antiquity. His work helped lay the foundation for many of the brilliant advanced concepts in math and science in the modern era. He also served as a distinguished and innovative geographer.

Eratosthenes Early YearsRecords from nearly 2300 years ago are not complete, but there are documents that dictate the early years of Eratosthenes. He was born in a Greek colony and Libya and he pursued a formal education in the learning academies of Athens. Around the age of 35, he became the man in charge of running the Great Library at Alexandria.His primary duties were to serve as a scholar and manage the affairs of the library. He took time out to perform some writing and the end result would be among the most important works produced in world history.

Eratosthenes TreatiseDuring his tenure at the Great Library, Eratosthenes wrote a treatise centering on the topic of the world. It was entitledGeography. The word had never been used before and for good reason. It means writing about the earth and no one had ever written about it at such great depth before. In addition to writing about the very lands of the world, the treatise delved heavily into the topic of temperature and the weather.

Studying the EarthEratosthenes was very inquisitive and a man who always sought to make new discoveries. This would lead to his determination of the circumference of the earth itself.He had learned of a well in Syene where sunlight only reached the bottom of the well during the time of the summer solstice. Eratosthenes believed that he would be able to determine the circumference of the entire earth through measurements made during the solstice based on the shadows cast in relation to the distance between Syene and Alexandria. His complex work revealed the circumference of the earth being 25,000 miles. In time, the accurate number would be discovered and it was only 100 or so miles off from what Eratosthenes had determined.

Eratosthenes Methods and LegacyThe actual calculations that the great Eratosthenes would employ were quite simple. He used simple multiplication and division. In a sense, he had too since most modern mathematical languages had yet to be invented. The work of Eratosthenes would have a profound effect on the work roughly 1500 years later. Christopher Columbus would point to the work of Eratosthenes as proof it would be possible to reach far off and distance lands by sea. Obviously, Columbus would prove his point and be awarded the chance to sail the world.Aryabhata

Born: 476, probably in AshmakaDied: 550 (at age 74), location unknownNationality: IndianFamous For: Early mathematician who calculated the value of pi

Aryabhata (476-550) was an Indianmathematicianand astronomer. He is generally considered to have begun the line of great Indian astronomer-mathematicians that flourished during the countrys classical period. Several of his calculations showed remarkable accuracy for the era, with some remaining the best available for many centuries. He is sometimes referred to as Aryabhata I, since several later scientists of the same name also produced notable works.

Aryabhatas Early LifeAryabhata came from southern India, but his precise place of birth is not known. Some authorities suggest that Kerala is the most likely location, while others believe that Dhaka or Maharashtra are more probable. It is, however, generally accepted that he studied at an advanced level in Kusumapura in modern-day Patna, where he remained for some years.A contemporary poem places Aryabhata as the manager of a scientific institution; the precise nature of the body is not given, but there are grounds for suspecting that it may have been linked to the astronomical observatory that was maintained there by the University of Nalanda.

The AryabhatiyaWhile studying at the university, Aryabhata produced theAryabhatiya, his major work. Written at the age of just 23, it ranges widely across mathematics and astronomy, but is particularly notable for its calculations regarding planetary periods. The value given for the length of the Earths astronomical day differs from the true value by only a matter of minutes.Aryabhata also worked out a value for pi that equates to 3.1416, very close to the approximations still used today. Using this value, he was able to calculate that the Earth had a circumference of 24,835 miles. This is correct to within 0.2%, and remained the best figure available well into medieval times.While working on the calculation of pi, it is possible that Aryabhata may also have discovered that numbers irrationality. The relevant text is inconclusive on this point, but if he did establish the irrational nature of pi, he beat the first European mathematicians to do this by many hundreds of years.TheAryabhatiyaalso contains solid work regarding the solar system. It states correctly that the light cast by planets and the moon is caused by sunlight reflecting off their surfaces, and that all planets follow elliptical orbits. Aryabhata was also able to describe accurately the processes that lead to both solar and lunar eclipses.

Aryabhatas LegacyFor several hundred years after its authors death, theAryabhatiyawas unknown in the West, although its Arabic translation in the 9th century was of great use to the scientists of the Islamic Golden Age. The book was eventually translated into Latin shortly after 1200. The mathematical ideas contained within it were quickly adopted by Europeans, especially those dealing with areas and volumes, and with finding cube and square roots.However, Aryabhatas astronomical findings had less impact, and it was left to later men such as Copernicus and Galileo to bring about the Western astronomical revolution. The first Indian artificial was named Aryabhata in his honor, as was a new university in the state of Bihar. Pythagoras

Born: c. 570 BC in on the island of Samos

Died: c. 495 BC (at about age 75) in Metapontum

Nationality: Greek

Famous For: Pythagorean Theorem

Pythagoras was a Greekmathematicianknown for formulating the Pythagorean Theorem. He was also a philosopher who taught that numbers were the essence of all things. He associated numbers with virtues, colors, music and other qualities. He also believed that the human soul is immortal and after death it moves into another living being, sometimes an animal.The Pythagorean Theorem

Pythagoras believed the earth was round and that the sun, moon, and other planets had their own movements. His beliefs eventually led to the Copernican theory of the universe.

The principles of the Pythagorean Theorem had already been known before they were formulated by Pythagoras. The Egyptians used a form of the Pythagorean Theorem to lay out their fields and the Greeks borrowed it from the Egyptians.

The theorem says that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. A right triangle is a triangle where one angle equals 90 degrees and the hypotenuse is the side opposite the right angle. If you know the values of two sides of a right triangle, you can easily calculate the missing side.

The Pythagorean Theorem has many proofs. One of the most famous was that ofEuclid, the Greek mathematician who was born around 300 B.C. Pythagoras also developed a method of tuning instruments called the Pythagorean tuning. If Pythagoras committed any of his theorems or thoughts to paper, no one has yet found them, though there were forgeries. Pythagoras seemed to have favored oral teaching.

Euclid Born: Unknown, probably in GreeceDied: UnknownNationality: GreekFamous For: Euclidean Geometry

Euclid was a Greek mathematician, known as Euclid of Alexandria, and often referred to as the Father of Geometry. In Greek, his name means Good Glory, as Euclid is the anglicized version of the Greek name. He is famous for the treatise Elements, which is considered to catalog and place much of Greek mathematics on a firm foundation.

Considered one of the most influential works in the history of mathematics, Euclids work was the main textbook for teaching mathematics up until the 20th century. In Elements, the author deduced some geometrical principles based on a small set of axioms. Other themes approached in his work include conic sections, perspective, number theory, spherical geometry and rigor.

Euclids Life

There are few references to Euclids life. His education and even birthplace are still in dispute. Some historical references were written by Pappus of Alexandria and Proclus centuries after Euclids death (265 BC). Born in approximately 325 BC, Euclid taught mathematics and was the founder of the Alexandrian School of Mathematics.

Elements

Euclids Elements is still recognized as one of the most prominent books on mathematics in history. In it, he pulls together materials from others who studied and researched mathematics before him. He compiled much of that information along with his own original thoughts and research in Elements. It includes information about topics like number theory, algebra, and geometry.

Praise for Elements

Some say that Abraham Lincoln admitted he felt greatly influenced by three works: William Shakespeares works, the King James Bible, and Euclids Elements. It is considered an authoritative masterpiece, laying out carefully and systematically propositions (what can be proven) and axioms and postulates (what can be assumed).The book includes the basic rules of logic, everyday geometric objects precise definitions, and the rules of arithmetic. Although being an amazing work in the history of mathematics, it still has its critics. For example, Bertrand Russell, a British philosopher, calls one of Euclids propositions a tissue of nonsense. However, Euclids defenders state that the only issue he had is that he did not study Russell.

Euclids Other Works

Euclid had a few works that survived throughout the years. For instance, On Divisions of Figures was a work that focused on geometrical figures. His work Catoptrics was about mathematical theories of mirrors. There are some other works that have been lost, but there is some record of them, including Conics, Porisms, and Surface Loci, among several others.

Euclids Legacy

As one of the most well-known mathematicians of all time, there are many forms of math named after him, including Euclidean geometry, the Euclidean number, and the Euclidean algorithm.

ProjectInMath

Submitted to:Mary Grace Catapang

Submitted by:Roelyn Mae Villanueva