1.
Carl Friedrich Gauss
Carl Friedrich Gauss (1777-1855) is considered to be the
greatest German mathematician of the nineteenth century. His discoveries and
writings influenced and left a lasting mark in the areas of number theory,
astronomy, geodesy, and physics, particularly the study of electromagnetism.
Gauss was born in Brunswick, Germany, on April 30, 1777, to
poor, working-class parents. His father labored as a gardener and brick-layer
and was regarded as an upright, honest man. However, he was a harsh parent who
discouraged his young son from attending school, with expectations that he
would follow one of the family trades. Luckily, Gauss' mother and uncle,
Friedrich, recognized Carl's genius early on and knew that he must develop this
gifted intelligence with education.
At the age of fourteen, Gauss was able to continue his
education with the help of Carl Wilhelm Ferdinand, Duke of Brunswick. After
meeting Gauss, the Duke was so impressed by the gifted student with the
photographic memory that he pledged his financial support to help him continue
his studies at Caroline College. At the end of his college years, Gauss made a
tremendous discovery that, up to this time, mathematicians had believed was
impossible. He found that a regular polygon with 17 sides could be drawn using
just a compass and straight edge. Gauss was so happy about and proud of his
discovery that he gave up his intention to study languages and turned to
mathematics.
Gauss' next discovery was in a totally different area of
mathematics. In 1801, astronomers had discovered what they thought was a
planet, which they named Ceres. They eventually lost sight of Ceres but their
observations were communicated to Gauss. He then calculated its exact position,
so that it was easily rediscovered. He also worked on a new method for
determining the orbits of new asteroids. Eventually these discoveries led to
Gauss' appointment as professor of mathematics and director of the observatory
at Gottingen, where he remained in his official position until his death on
February 23, 1855.
Carl Friedrich Gauss, though he devoted his life to
mathematics, kept his ideas, problems, and solutions in private diaries. He
refused to publish theories that were not finished and perfect. Still, he is
considered, along with Archimedes and Newton, to be one of the three greatest
mathematicians who ever lived.
2. Janos Bolyai
János Bolyai, (born December 15,
1802, Kolozsvár, Hungary [now Cluj, Romania]—died January 27,
1860, Marosvásárhely, Hungary [now Târgu Mureş, Romania]), Hungarian
mathematician and one of the founders of non-Euclidean geometry— a geometry that differs from geometry in its definition of parallel
lines. The discovery of a consistent alternative geometry that might correspond
to the structure of the universe helped to free mathematicians to study
abstract concepts irrespective of any possible connection with the physical
world.
By the age of
13, Bolyai had mastered calculus and analytic mechanics under the tutelage of
his father, the mathematician Farkas Bolyai. He also became an accomplished
violinist at an early age and later was renowned as a superb swordsman. He
studied at the Royal Engineering College in Vienna (1818–22) and served in the
army engineering corps (1822–33).
The elder
Bolyai’s preoccupation with proving Euclid’s parallel axiom infected his son, and, despite
his father’s warnings, János persisted in his own search for a solution. In the
early 1820s he concluded that a proof was probably impossible and began
developing a geometry that did not depend on Euclid’s axiom.
Although Bolyai
continued his mathematical studies, the importance of his work was unrecognized
in his lifetime. In addition to work on his non-Euclidean geometry, he
developed a geometric concept pairs of
real numbers.
3. Lobachevsky
Nikolay
Ivanovich Lobachevsky is born in Nizhniy Novgorod on November 20, 1792, in the
family of a poor petty officer.
When Nikolay
gets 9, his mother brings him to Kazan and arranges Nikolay together with his
two brothers to attend a grammar school for free. Since that time life and work
of future star of mathematics takes place in the city of Kazan.
Seven years of
nearly prison regime in the university do not crush recalcitrant spirits of
Lobachevsky, now a professor. He reads courses in mathematics and physics,
heads department of physics, teaches geodesy and astronomy, being responsible
for observatory. Later he becomes the dean of the faculty of physics and
mathematics. Nikolay Ivanovich’s creativity results in writing two school-books
for grammar schools – “Geometry” comes off the press in 1823 and “Algebra” in
1825. Both school-books are not approved due to some revolutionary changes
Nikolay Ivanovich has suggested to make in traditional science. He starts
experiencing problems with the university’s curator.
However,
Lobachevsky keeps working on formulating geometry’s bases and finally makes a
brilliant discovery, which results in absolutely new geometry. The
mathematician makes a report about his discovery – he calls it “Imaginary
Geometry” – at his faculty. He wants to know what his colleagues think about
his discovery and asks to publish his work in “Scientific Notes” of the
faculty. However, no comments followed, and later the manuscript of his
discovery is lost.
In 1827 Nikolay
Ivanovich Lobachevsky becomes a rector of Kazan University and dedicates
following 19 years to the university, making it flourish. He manages to
introduce new educational standards, his reign results in library, astronomical
and magnetic observatories,
dissecting room, physical and chemical laboratories. His ideas are so revolutionary
and future-oriented that brilliant scientists of his time fail to foresee their
significance. However, misunderstanding and, sometimes, open humiliation,
cannot force Nikolay Ivanovich to stop his studies. Several years of hard work
result in “Geometrical studies of theory of parallels”, summarizing his ideas
and published in German language in 1840. Lobachevsky doesn’t receive a single
positive report, except a prediction of one professor that sooner or later
Lobachevsky’s theory would find its admirers.
4. Bernhard
Riemann
Bernhard Riemann (1826-1866) was the
son of a poor country minister in northern Germany. He studied the works of
Euler and Legendre while he was still in secondary school. It is said that he
mastered Legendre's treatise on Theory of Numbers in less than a week! Riemann
was shy and modest and was probably unaware of his own extraordinary abilities.
In fact he went to the University of Gottingen (when he was nineteen) to study
theology and (hence) become a minister himself. Fortunately before it was too
late he realized his mistake and with the permission of his father switched to
MATHEMATICS. The presence of the legendary C.F.Gauss made Gottingen the center
of the mathematical world. But Gauss was remote and unapproachable, so after a
while Riemann switched to University of Berlin. Once there he learned a great
deal from Dirichlet and Jacobi. Two years later he returned to Gottingen, where
he obtained his doctor's degree in 1851.
Riemann had a short life and
published comparatively little, but his works permanently altered the course of
mathematics in analysis, geometry and number theory. His first published paper was his celebrated dissertation of 1851 on the
general theory of functions of a complex variable. Riemann's fundamental aim
here was to free the concept of an analytic function from any dependence on
explicit expressions such as power series, and to concentrate instead on
general principles and geometric ideas. In doing so he used/created concepts
such as Cauchy-Riemann equations, Riemann surfaces etc. Gauss was rarely
enthusiastic about achievements of his contemporaries, but in his official
report to the faculty he warmly praised Riemann's work: "The dissertation
submitted by Herr Riemann offers convincing evidence of the author's thorough
and penetrating investigations in those parts of the subject treated in the
dissertation, of a creative, active, truly mathematical mind, and of a
gloriously fertile originality."
