18th Century Mathematics

• initially sealed Euler’s reputation was announced in 1735 and concerned the calculation of infinite sums. It was called the Basel problem after the Bernoulli’s had tried and failed to solve it
• solved an intransigent mathematical and logical problem, known as the Seven Bridges of Königsberg Problem,
• published 900 books
• unbelievable mental calculation skills and photographic memory
• long life and thirteen children
• was blind in his later years
• a fire in 1771 which cost him his home (and almost his life), and the loss in 1773 of his dear wife of 40 years, Katharina. He later married Katharina's half-sister, Salome Abigail, and this marriage would last until his death from a brain hemorrhage in 1783.

18th Century Mathematics

• the demonstration of geometrical properties such as Euler’s Line and Euler’s Circle;
• the definition of the Euler Characteristic χ (chi) for the surfaces of polyhedra,
• a new method for solving quartic equations;
• the Prime Number Theorem,
• proofs (and in some cases disproofs) of some of Fermat’s theorems and conjectures;
• the discovery of over 60 amicable numbers
• a method of calculating integrals with complex limits (foreshadowing the development of modern complex analysis);
• the calculus of variations, including its best-known result, the Euler-Lagrange equation;
• a proof of the infinitude of primes, using the divergence of the harmonic series;
• the integration of Leibniz's differential calculus with Newton's Method of Fluxions into a form of calculus we would recognize today,

EULER

PHILLIP MUGUHU

• born in Basel, Switzerland
• spent most of his academic life in Russia and Germany because he could not find a good position in switzerland due to the poularity of the Bernoullis
• geometry, calculus, trigonometry , algebra, number theory, optics, astronomy, cartography, mechanics, weights and measures and even the theory of music.
• came up with many notations f(x), e, i, use of a, b, c as constants and x, y, z as unknowns
• combined several symols together in an amazing feat of mathematical alchemy to produce one of the most beautiful of all mathematical equations, e^(iπ ) = -1, aka Euler’s Identity.

THE BERNOULLIS

• the Bernoulli’s, produced half a dozen outstanding mathematicians over a couple of generations at the end of the 17th and start of the 18th Century
• family was a prosperous family of traders and scholars from the free city of Basel in Switzerland

BERNOULLI BROTHERS

• Jacob and Johann Bernoulli,flouted their father's wishes for them and began studying mathematics together.
• jealous and competitive relationship
• Jacob's - professor at Basel University and died from TB,
• Johann took over Jacobs position
• was very jealous of big bro
• Eulers teacher
• began being jealous of Daniel(his son) - stole ideas and changed dates
• Guillaume de l'Hôpital (0/0)

• first mathematicians to not only study and understand infinitesimal calculus but to apply it to various problems
• designing a sloping ramp which would allow a ball to roll from the top to the bottom in the fastest possible time.
• Jacob Bernoulli’s book “The Art of Conjecture”
• Jacob Bernoulli also discovered the appropximate value of the irrational number e while exploring the compound interest on loans.
• Johann’s sons and even his grandchildren were all accomplished mathematicians and teachers. Daniel Bernoulli, in particular, is well known for his work on fluid mechanics especially Bernoulli’s Principle

Adrien-Marie Legendre

• statistics, number theory, abstract algebra and mathematical analysis in the late 18th and early 19th Centuries
• Elements of Geometry”, a re-working of Euclid’s book, became the leading geometry textbook for almost 100 years
• inspired the creation, and almost universal adoption, of the metric system of measures and weights

Pierre-Simon Laplace

Johann Lambert

• referred to as “the French Newton”
• mathematician and astronomer
• mainly on differential equations and finite differences, mathematical and philosophical concepts of probability and statistics
• developed his own version of the so-called Bayesian interpretation of probability independently of Thomas Bayes
• maintained that there should be a set of scientific laws that would allow us to predict everything about the universe and how it works.(complete science determinism)

• Swiss mathematician and prominent astronomer,
• provided a rigorous proof in 1761 that π is irrational,
• first to introduce hyperbolic functions into trigonometry

Joseph Louis Lagrange

• contributed to differential equations and number theory,
• credited with originating the theory of groups
• 4-square theorem, that any natural number can be represented as the sum of four squares
• Lagrange’s Mean Value Theorem - given a section of a smooth differentiable curve, there is at least one point on that section at which the derivative of the curve is equal to the mean derivative of the section.

18th Century Mathematics

• Mostly overtaken by the works of Newton and Leibniz
• dominated by mathematicians from France despite the popularity of Euler and Bernoulli
• most developments were attributed to"the three L's" Joesph Lagrange, Pierre-Simon Laplace and Adrien-Marie Legendre

VIOLET TIEMA