Euler may be the most influential mathematician who ever lived (though some would make him second to Euclid); he ranks #77 on Michael Hart's famous list of the Most Influential Persons in History. His colleagues called him "Analysis Incarnate." Laplace, famous for denying credit to fellow mathematicians, once said "Read Euler: he is our master in everything." His notations and methods in many areas are in use to this day. Euler was the most prolific mathematician in history and is often judged to be the best algorist of all time. (The ranking #4 may seem too low for this supreme mathematician, but Gauss succeeded at proving several theorems which had stumped Euler.)

Just as Archimedes extended Euclid's geometry to marvelous heights, so Euler took marvelous advantage of the analysis of Newton and Leibniz: He gave the world modern trigonometry, pioneered (along with Lagrange) the calculus of variations, generalized and proved the Newton-Giraud formulae, etc. He was also supreme at discrete mathematics, inventing graph theory. He also invented the concept of generating functions; for example, letting p(n) denote the number of partitions of n, Euler found the lovely equation: Sn p(n) xn = 1 / ?k (1 - xk)

Euler was also a major figure in number theory: He proved that the sum of the reciprocals of primes less than x is approx. (ln ln x), invented the totient function and used it to generalize Fermat's Little Theorem, found both the largest then-known prime and the largest then-known perfect number, proved e to be irrational, proved that all even perfect numbers must have the Mersenne number form that Euclid had discovered 2000 years earlier, and much more. Euler was also first to prove several interesting theorems of geometry, including facts about the 9-point Feuerbach circle; relationships among a triangle's altitudes, medians, and circumscribing and inscribing circles; and an expression for a...

...LeonhardEulerEuler, Leonhard (1707-83), Swiss mathematician, whose major work was done in the
field of pure mathematics, a field that he helped to found. Euler was born in
Basel and studied at the University of Basel under the Swiss mathematician
Johann Bernoulli, obtaining his master's degree at the age of 16. In 1727, at
the invitation of Catherine I, empress of Russia, Euler became a member of the
faculty of the Academy of Sciences in Saint Petersburg. He was appointed
professor of physics in 1730 and professor of mathematics in 1733. In 1741 he
became professor of mathematics at the Berlin Academy of Sciences at the urging
of the Prussian king Frederick the Great. Euler returned to St. Petersburg in
1766, remaining there until his death. Although hampered from his late 20s by
partial loss of vision and in later life by almost total blindness, Euler
produced a number of important mathematical works and hundreds of mathematical
and scientific memoirs.
In his Introduction to the Analysis of Infinities (1748; trans. 1748), Euler
gave the first full analytical treatment of algebra, the theory of equations,
trigonometry, and analytical geometry. In this work he treated the series
expansion of functions and formulated the rule that only convergent infinite
series can properly be evaluated. He also discussed three-dimensional surfaces
and proved...

...LeonhardEulerLeonhardEuler, (born April 15, 1707, died Sept. 18, 1783), was the most
prolific mathematician in history. His 866 books and articles represent about
one third of the entire body of research on mathematics, theoretical physics,
and engineering mechanics published between 1726 and 1800. In pure mathematics,
he integrated Leibniz's differential calculus and Newton's method of fluxions
into mathematical analysis; refined the notion of a function; made common many
mathematical notations, including e, i, the pi symbol, and the sigma symbol; and
laid the foundation for the theory of special functions, introducing the beta
and gamma transcendal functions. He also worked on the origins of the calculus
of variations, but withheld his work in deference to J. L. Lagrange. He was a
pioneer in the field of topology and made number theory into a science, stating
the prime number theorem and the law of biquadratic reciprocity. In physics he
articulated Newtonian dynamics and laid the foundation of analytical mechanics,
especially in his Theory of the Motions of Rigid Bodies (1765). Like his teacher
Johann Bernoulli, he elaborated continuum mechanics, but he also set forth the
kinetic theory of gases with the molecular model. With Alexis Clairaut he
studied lunar theory. He also did fundamental research on elasticity, acoustics,
the wave theory of light, and the hydromechanics of ships.
Euler was...

...LeonhardEulerLeonhardEuler was born on the fifteenth day of April in the year seventeen hundred and seven, in Basel, Switzerland. He was considered one of the best scientists, and mathematicians to ever walk on the planet earth. He created over nine hundred publications, and was a member of the prestigious Petersburg Academy of Sciences. His studies include topics on shipbuilding, acoustics, optics, astronomy, mechanics, and magnetism. His life was filled with irony and success.
The definition of mathematician irony is when Euler went to apply at Basel University as a professor and was turned down. Here is one of the smartest scientists ever and he was rejected as a college professor. What a bunch of morons. He went to Basel University when he was thirteen, then graduated with a masters degree at age sixteen. After that he wrote two articles on reverse trajectory, which was approved by Bernoulli, another famous mathematician. That could have been a little detail they over looked, when it should have been a huge hint that this kid was smart So after being denied at his alma mater, Leonhard goes into tutoring, after a couple years at science academies. The kids he tutored were none other than King Frederich II of Prussia’s nieces. How did he go from being turned down as a math professor to a tutor for Prussian royalty? Talk about a math burn.
Before he was tutoring the royal...

...Euler and Hamiltonian Circuits
As I type this sentence millions of students all over the country are in their math class either a) struggling to open their eyelids or b) tapping their fingers due to boredom and impatience. They have all failed to understand how the topic would later come of use. Although mathematics may seem to be “unnecessary” it teaches our brains to strategize, and think differently through the use of trial and error and problem solving. Most individuals consider mathematics to be a dreadful topic, and can never really comprehend how it can be beneficial in our lives on a daily basis. Most of the time, they may seem to be correct. However, they are not. Most of the time, we are using its strategies without even acknowledging it. We use it for almost anything we do: currency, measurement, time, etc. Two examples of math we use on a regular basis are Euler and Hamiltonian Circuits.
An Euler Circuit is a circuit that reaches each edge of a graph exactly once. (Malkevitch, 8) This theory is named after LeonhardEuler, an outstanding mathematician during the 18th century. Euler had been the first person to study this category of circuits. In addition, he was the creator of the theory of graphs, or graph theory. One of the many things he had found was that most graphs do not have an Euler circuit at all. Euler had also contributed to the field of...

...LeonhardEuler (/ˈɔɪlər/ oil-er;[2] German pronunciation: [ˈɔʏlɐ] ( listen), local pronunciation: [ˈɔɪlr̩] ( listen); 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of amathematical function.[3] He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the pre-eminent mathematician of the 18th century, and one of the greatest mathematicians ever to have lived. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes.[4] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."[5]
Contents [hide] * 1 Life * 1.1 Early years * 1.2 St. Petersburg * 1.3 Berlin * 1.4 Eyesight deterioration * 1.5 Return to Russia * 2 Contributions to mathematics and physics * 2.1 Mathematical notation * 2.2 Analysis * 2.3 Number theory * 2.4 Graph theory * 2.5 Applied mathematics * 2.6 Physics and astronomy *...

...LeonhardEulerLeonhardEuler (1707-1783) was born in Basel [Switzerland]. His father ... gave him his first instruction in mathematics. ... In his nineteenth year he composed a dissertation on the masting of ships, which received the second prize from the French Academy of Sciences. ... In 1735 the solving of an astronomical problem, proposed by the Academy, for which several eminent mathematicians had demanded some months' time, was achieved in three days by Euler with aid of improved methods of his own. But the effort threw him into a fever and deprived him of the use of his right eye.
[Later] he became blind [in both eyes], but this did not stop his wonderful literary productiveness. ... Euler wrote an immense number of works. ... [He] introduced (simultaneously with Thomas Simpson in England) the now current abbreviations for trigonometric functions, and simplified formulas by ... designating the angles of a triangle by A,B,C, and the opposite sides by a, b, c. ...
He pointed out the relation between trigonometric and exponential functions. ... Euler laid down the rules for the transformation of co-ordinates in space. ... [He] proved a well-known theorem, giving the relation between the number of vertices, faces, and edges of certain polyhedra, which, however, appears to have been known to Descartes. The powers of Euler were directed also towards...

...I. Greek Mathematicians
Thales of Miletus
Birthdate: 624 B.C.
Died: 547-546 B. C.
Nationality: Greek
Title: Regarded as “Father of Science”
Contributions:
* He is credited with the first use of deductive reasoning applied to geometry.
* Discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal.
* Accredited with foundation of the Ionian school of Mathematics that was a centre of learning and research.
* Thales theorems used in Geometry:
1. The pairs of opposite angles formed by two intersecting lines are equal.
2. The base angles of an isosceles triangle are equal.
3. The sum of the angles in a triangle is 180°.
4. An angle inscribed in a semicircle is a right angle.
Pythagoras
Birthdate: 569 B.C.
Died: 475 B.C.
Nationality: Greek
Contributions:
* Pythagorean Theorem. In a right angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides.
Note: A right triangle is a triangle that contains one right (90°) angle. The longest side of a right triangle, called the hypotenuse, is the side opposite the right angle. The Pythagorean Theorem is important in mathematics, physics, and astronomy and has practical applications in surveying.
* Developed a sophisticated numerology in which odd numbers denoted male and even female:
1 is the generator of numbers and...

...LeonhardEuler, a Swiss mathematics and physics genius, was born on April 15, 1707 in Basel Switzerland, and died on September 18, 1783 in Saint Petersburg. Before he died he has done many great things. He introduced mathematical notations, shorthand trigonometric functions, and the idea of function and how it is written(f(x)). He also invented the symbol pi (π) for the ratio of a circle's circumference to its diameter, the ‘e’ for the base of the natural logarithm (The Euler Constant), the Greek letter Sigma for summation and the letter ‘/i’ for imaginary units. He also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories. He was known for being the greatest mathmetical of his time. He was the king of mathematics.
Along with Leonhard Euler's great inventions he also had a very interesting childhood. Leonhard was born in a family of pastors. His father, Paul Euler, was the pastor of a Reformed Church and his mother Margueritte Brucker, was a pastor's daughter. When he was 7 years old he started school, he had a private mathematics tutor to tutor him. At 13, he attended lectures at the local university. In 1723, he got his masters degree with a dissertation comparing the natural philosophy systems of Newton and Descartes....