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Al-Khayyami (1048-1131 CE) Middle Eastern: Specialty: Algebra Born in Iran just prior to the occupation of the area by the Seljuk Turks, he was able to garner the support of many rulers over the years. He wrote not only Astronomical and mathematical works, but works of poetry and philosophy. His major text was Treatise on Demonstrations of Problems of al-Jabr and Al-Muqabala, which was primarily geared towards solutions of cubic equations. However, it was algebraically based, not geometric. He used an approach of reviewing equations of up to degree 3 and then showing solutions of those solvable using only positive solutions. Muhammud Ibn Musa Al-Khwarizmi (c. 780-850 CE) Islam/Russian: Specialty: Algebra Born south of the Aral Sea, he was one of the first scholars of the House of Wisdom. Both the Greeks and the Babylonians influenced his math. He wrote ‘The condensed Book on the Calculation of al-Jabr and al-Muqabala’. He was interested in writing a practical mathematics manual. He used geometric proofs to demonstrate his algebraic calculations, like the Babylonians. Also, the influence of oriental mathematicians showed in his numerous examples and problems. In addition, he drew a map of the Islamic world, which was reportedly the best of its time. He is given credit for the term algebra, which was a weak Greek translation of al-Jabr. Al-Samaw’al (c.1125-1174 CE) Jewish/Iraqi: Specialty: Algebra Since the House of Wisdom had been closed in Baghdad, he
studied independently with others and traveled throughout the Middle East. He
was born to well-educated Jewish parents, which allowed him to study religion,
math and medicine. He is famous for his introduction of negative coefficients,
which made adding and subtracting polynomials a much easier task. He used a
chart-based format, ultimately coming up with the law of exponents. The
remarkable thing is his major math works were completed by age19. He then turned
to medicine and wrote medical texts. He converted to Islam and wrote an
autobiography against Judaism, which became a famous work. Kenneth Appel (1932-) American: Specialty: Programming, Graph Theory This mathematician, while at the University of Chicago
solved a famous problem involving four colors not having adjacent sides in a two
dimensional surface. The solution involves substantial computer modeling and has
been described as not being elegant. His work pioneered a shift in attitudes
among some mathematicians in using computers as tools to solve some complex
problems. Archimedes (287-212 BCE) Greek: Specialty: Physical Applications of Mathematics Son of an Astronomer, many rulers relied upon him to use
his knowledge to solve engineering problems facing society. Many of his letters
survived and they were directed at the most learned people of his city of
Syracuse. He came up with the Archimedean screw for transporting water, the
first logical explanation of how a lever works and held the Roman invaders at
bay for months. In fact, the Roman leader called for his life to be spared but
an angry soldier killed him. Aristotle (384-322 BCE) Greek: Specialty: Logic He studied at Plato’s Academy from age 18 until he was
37, when Plato passed on. After a short time educating a Macedonian prince, he
started his own school in Athens. He wrote on many subjects, and made terms such
as postulates, axioms and syllogisms part of our every day math terminology. He
also contributed by providing a distinction between number and magnitude. Benjamin Banneker (1731-1806 CE) American: Specialty: Surveying, Astronomy An African- American, his grandmother taught him to read
and write. His abilities were
recognized early in his life, although he faced a societal bias of being a free
black farmer in the Northern United States.
He was fortunate he was able to borrow technical books and scientific
instruments from his neighbors, a family of surveyors.
He taught himself the principles of mathematics, surveying, and
astronomy. He helped survey the
District of Columbia and wrote an almanac. Jakob (1654-1705 CE) and Johann (1667-1748 CE) Bernoulli Swiss: Specialty: Physics Jakob taught himself mathematics, while traveling through several
European countries. Upon his return home, he became a professor of physics, and
then mathematics. His brother, Johann, studied business and medicine, but became
enamored with math. Together they mastered the works of Leibniz and wrote about
them as well as their discoveries along his line of thought. Johann replaced his
brother as a professor upon the elder’s death. Bhaskara (1114-1185 CE) Indian: Specialty: Astronomy, Mechanical Arts Born into a family of long scholarship, he served as the
head of an astronomical observatory much of his life. His father was also an
astronomer. He wrote one major astronomical works and two major mathematical
works. His grandson founded a college to study his work. Janos Bolyai (1802-1860 CE) Hungarian: Specialty: Geometry His father a professor, Bolyai entered the military until
retiring due to physical considerations. His father had studied parallels and
had conversed with Gauss for years without any resolution. He warned his son not
to pursue this area of study, but his son did not listen. Janos wrote Gauss
about his discoveries but Gauss told him that he had already made these
discoveries although they had not been published. These ideas were later found
to be central to the idea of non-Euclidean geometry. Brahmagupta (598-??? CE) Indian: Specialty: Astronomy He was also known as Bhillamalacarya. Little is known
except he wrote the Correct Astronomical System of Brahma when he was 30. It was
a great mathematical work, but much of the math is buried inside calculations
for astronomical work, a common thing for Indian mathematicians of the era.
Translations and bad copying have weakened our knowledge of this work, but the
drawings show clear, full descriptions of how to calculate the answers. Gerolamo Cardano (1501-1576 CE) Italian: Specialty: General Mathematics Trained as a physician, but he was denied admission to the
Milan professional physicians group due to his illegitimate birth. He practiced
in a small city, lectured in mathematics and wrote a textbook on math. He later
convinced the Milan physicians to accept him and became in demand throughout
Europe. He was brought before the Inquisition in 1570 and found guilty. He was
released from prison, lived in Rome and wrote an autobiography. Augustin-Louis Cauchy (1789-1857 CE) French: Specialty: Engineering, Pure Mathematics One of the world’s prolific mathematicians of the 19th
century, he was a difficult person to get along with. He trained in engineering and worked in military projects
until he was encouraged to pursue mathematics by Laplace and Lagrange.
After he wrote several texts in analysis, the French mathematical
community recognized his skills. His
political views prevented him from staying in France until the revolution of
1848. Nicolaus Copernicus (1473-1543 CE) Prussian: Specialty: Astronomy Born into a family of means, he was sent to study at the
University of Krakow. When he left, he was appointed to a position in the church
through family influence. He traveled, studying in Italy and came home to a
rather undemanding church position that allowed him to study astronomy. He wrote
an in depth manuscript of his theory (De Revolutionibus) but its publication was
delayed until he received the encouragement of a Mathematical Professor. John Dee (1527-1608 CE) English: Specialty: Logic, Astronomy, Symbolism Graduating from Cambridge, he studied under various
mathematicians on the European Continent. He served as the court astrologer to
the Queen of England. In his later years he became interested in the mystical
elements of math, writing about them and how symbols could be combined to
produce the secrets of the physical world. In the end, his mysticism and
accusations of the practice of black magic caused him to be exiled from the
court. He ultimately died in poverty. Abraham De Moivre (1667-1754 CE) French: Specialty: Physics Educated classically, his secondary school closed. He
transferred and was introduced to probability and physics. He studied Newton’s
theory on fluxions and worked further in that area. He was never a university
professor, but tutored and worked with games of chance on behalf of gamblers. Rene Descartes (1596-1650 CE) French: Specialty: Logic, Philosophy From Nobility, he was of poor health while growing up. He
concluded that much of the information learning in school was of questionable
reliability. He traveled extensively, participated in the thirty years war and
ultimately settled in Holland. He wrote a major treatise on physics, but did not
publish it immediately in fear of the church and the inquisition. He published
it after persuasion, as well as several other essays on the physical world. He
found acclaim, was hired by the queen of Sweden and tutored her. His health soon
failed and he died. Euclid (approximately 300 BCE) Greek: Specialty: unknown but generalist He wrote the most important mathematical text of the time
and possibly of all time. The text itself has 13 books, which are broken up into
many areas of ‘modern’ mathematics. Little is known about his life, but
references from future mathematicians give us an idea he was alive around 300
BCE. There are no copies of the book, but since it has been the most translated
work of its time (except the bible) we know something about his work. It is
generally agreed this work was a compendium, and has served as a catalyst for
some mathematicians, but it is somewhat dull by modern standards. Leonhard Euler (1707-1783 CE) Swiss: Specialty: Calculus Euler was recognized very early for his skills in
mathematics, but his father did not support his choice until a discussion with
Johann Bernoulli. He was turned down for a position in Switzerland due to his
age, but found a home with two of Bernoulli’s sons in Russia. Russia at the
time had just created an Academy of Sciences in order to modernize itself. He
lived with his wife and their 13 children, but politics convinced him to move to
Berlin. After confrontations with the King, he went back to Russia. He
ultimately went blind, but was still able to contribute because of his ability
to perform the calculations in his head. Galileo Galilei (1564-1642 CE) Italian: Specialty: Astronomy He started his upper education by pursuing the training of
a physician, but found he was more interested in mathematics. He left without a
degree, but had a good background of the older mathematics, missing learning
about modern algebra. He was brought before the Inquisition as a result of his
identification that the earth revolved around the sun. He was sentenced to home
imprisonment and no more publishing of his works. He wrote and was published
outside the reach of the Inquisition. Most knowledgeable persons had come to the
conclusion that the earth was not the center of the universe by this time. The
Church eventually had to back down and admit its prior conclusions were
incorrect. Karl Frederic Gauss (1777-1855 CE) German: Specialty: Astronomy, number theory Coming from a poor family, Gauss showed his prowess in
mathematics at a very young age. He
was granted a scholarship to a science-oriented academy and ultimately received
a Doctorate. He wrote many papers
discussing his methods of calculating orbits of heavenly bodies.
When war came to the region, he was fortunate that the French general
gave specific orders to look out for his welfare. Approximately a year later,
Gauss left the occupied area and moved to Gottingen as a professor of astronomy.
Gauss was never happy teaching but he was a prolific writer.
Many of his papers still have an impact on subjects to this day. David Hilbert (1862-1943 CE) Prussian: Specialty: Generalist Hilbert was one of the major forces behind the rise of the
University of Gottingen as one of the premier center of mathematical progress in
the early 20th century. His claim to fame is his list of 23 problems
that he felt would be of primary importance to the mathematicians of the 20th
century. After the Nazi’s assumed power, Hilbert saw Gottingen lose its
prominence. He died during the second world war. Qin Jiushao (1202-1261 CE) Chinese: Specialty: Generalist, Astronomy He grew up in the midst of the war under which Genghis Khan
conquered much of Northern China. He learned his skills in mathematics from a
recluse. In his spare time dodging arrows, he thought about math. He is most
famous for his Mathematical treatise in Nine Sections, which took 81 problems
and showed how to solve them. Much of Chinese Math at the time was taught
through example. He also became rich, built a large house where he housed many
female musicians who were reportedly his consorts. Johannes Kepler (1571-1630 CE) German: Specialty: Astronomy He studied the theories of Copernicus. Originally he
planned to be a minister, but became a math teacher. His work furthered the
studies of the universe along with those of Tycho Brahe. Joseph-Louis LaGrange (1736-1813 CE) Italian: Specialty: Calculus Born in Turin to a family of French descent, LaGrange was
attracted to mathematics and became a professor at 19. He and Euler were friends
and he replaced Euler when he left Berlin. After some time, he moved to Paris
and wrote his most important work, Analytical Mechanics. This text extended the
work of many contemporary mathematicians. He worked on furthering the French
educational system and was honored by Napolean. Pierre Simon De Laplace (1749-1827 CE) French: Specialty: Celestial Mechanics While he started school to train for a career in the
church, he found his true calling in mathematics. He worked training military
students while pursuing his studies, writing a number of papers, which allowed
him to be recognized for his prowess in math. He wrote on Celestial Mechanics,
showing how Newton’s law of gravitation implied long term stability of our
solar system. He also wrote on probability and received honors for his
contributions to France by being named a marquis by Louis XVIII. He was
eulogized as the ‘Newton of France’. Gottfried Wilhelm Leibniz (1646-1716 CE) German: Specialty: Calculus Born into an academic family, he learned quickly that he
liked to study. His father died when he was six. He taught himself Latin. He
studied philosophy in college, but was not awarded a doctorate due to politics.
He was awarded his doctorate at a different university, and then turned to
studies in philosophy. He invented many of the symbols we use in calculus today.
He turned to politics later in life but never quit studying mathematics in the
little spare time he had. Leonardo of Pisa (c. 1170-1240 CE) aka Fibonacci Italian: Specialty: Geometry, Algebra His father a merchant in North Africa, growing up he
traveled with him and learned the mathematics of many Moslem teachers. He later
traveled on business in the region, learning the math of Islamic scholars.
Ultimately he returned home, spending 25 years writing about his math learning
in Italian. Both the City of Pisa and the Court of Frederick II recognized him
for his contributions. Isaac Newton (1642-1727 CE) English: Specialty: Calculus, Mathematical Theory Newton started his life by being raised by his grandmother.
He was sent to a grammar school, but found an unusual schoolmaster who taught
him plane geometry and geometric constructions. When he went to Cambridge, he
was far advanced in math compared to his peers. Through self-study, helped by
grants, he learned the majority of 17th century math. He was a man
who could exclude all stimuli around him to work on a problem. He was not a
great teacher, although he was a professor, as he spoke above his audience. He
wrote his studies up for publication, but failed to follow through for the most
part so his works ended up being circulated only in the English mathematical
community. Blaise Pascal (1623-1662 CE) French: Specialty: Number theory Showing his math abilities early, he was exposed to the
modern math of France at a very young age, He started his own research before he
was 20. He developed a calculating machine and worked on the actions of fluid
under air pressure. In his 30’s he became more interested in religious matters
and he died prior to his 40th birthday. Henri Poincare (1854-1912 CE) French: Specialty: Generalist Born into an upper middle class family, Poincare displayed
an aptitude for mathematics early in life, winning several countrywide
competitions. He received his doctorate and taught in Caen and Paris. He was a
generalist in approach, but wrote extensively about the importance of science
and mathematics. He is famous for his observations on the psychology of
discovery in mathematics. Pedro Nunes (1502-1578 CE) Portuguese: Specialty: Algebra, Navigation, Astronomy A professor of Mathematics and Cartographer for the King of
Portugal, he was fortunate to have many of the future leaders of the country as
his students. He was of Jewish birth, but never persecuted in the Inquisition as
one of his former students was the Inquisitor General. Nunes’s Algebra text
was originally written in Portuguese, but he translated it to Spanish to
increase its impact on Mathematics. Pythagoras (572-497 BCE) Greek: Specialty: Number Theory, Geometry He was considered less of a thinker than a mystic and led
his followers in a school of mathematical doctrines. Many of the theories coming
from his followers have been credited to Pythagoras and these include research
in ratios that led to P. Triples and the P. Theorem. Robert Record (1510-1558 CE) English: Specialty: Pedagogy Primarily a writer of Mathematical and Astronomical Texts,
he was also a Physician. His texts were written in the form of master and pupil
and showed step-by-step technique. Claude Shannon (1916-2001 CE) American: Specialty: Information Theory His theories, although written in the 1940’s, about the
physical limits of communication circuits in wired and wireless communication
are still as solid as when they were written. His work in digital circuitry,
before the engineers had addressed the problems, has helped make modern
technology what it is today. He designed and worked with artificial intelligence
machines while at Bell Labs and MIT. Simon Stevin (1548-1620 CE) Belgian: Specialty: Engineering, Navigation Born in Belgium, he moved from there to Holland as the area
was under Spanish rule. Much of his life was spent in civil service, serving the
ruler as engineer, tutor in math and ballistics and advisor in other
mathematically based activities. He also served as the quartermaster of the army
and dean of a university school of engineering where the curriculum was taught
in Dutch. This school provided training for engineers, navigators and merchants.
He wrote the texts for the subjects taught at the university where he was dean. Michael Stifel (1487-1567 CE) German: Specialty: Algebra Ordained as a Catholic Priest, after disagreeing with
several clerical abuses he became an early follower of Martin Luther. He became
interested in calculus. After studying the Bible he prophesized the end of the
world and in front of his congregation nothing happened. He was discharged from
his parish and later studied math at the university level. He became an expert
on algebra, writing several texts, and later in life studied more on word
calculus and wrote several more texts. James Joseph Sylvester (1814-1897 CE) English: Specialty: Mathematics Pedagogy Born into a Jewish family, he studied for several years at
Cambridge, but was not allowed to obtain a degree for religious reasons.
He received a degree from Trinity College, Dublin.
He moved to the United States but left because of his hatred of slavery.
Back in England, he spent ten years as an attorney, and then fifteen
years as a professor of mathematics. He
moved to the United States after the Civil War and founded the American Journal
of Mathematics. Seki Takakazu (1642-1708 CE) Japanese: Specialty: Algebra Born into the family of a samurai, he trained as an
accountant. Although he published
very few works, those that survived show he understood the theory of equations,
including polynomials. He
introduced determinants with setting up and solving equations. Karl Weierstrass (1815-1897 CE) German: Specialty: Pedagogy Headed for a career as a civil servant, Weierstrass found he loved mathematics and taverns. He left the University without a degree and became a high school teacher. After a series of papers, he received a doctorate and a professorship at the University of Berlin. His clear lecturing style won him wide acclaim throughout Europe. Stephen Wolfram (1959-) British: Specialty: Scientific Computing Publishing his first scientific paper at 15, receiving his doctorate at 20, Wolfram’s early works were primarily related to physics. He designed the first computer algebra system, and was one of the fathers of complex systems research. His work has led to a wide range of applications including the foundations for complexity theory and artificial life. Following his scientific work on complex systems research, he turned to academics at Caltech, then Princeton, and finally as Professor of Physics, Mathematics, and Computer Science at the University of Illinois. He is responsible for the Mathematica software and continues his research in the areas of physics, biology, computer science and mathematics. |
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