He studied the geometric properies of complex numbers, formalised mathematical induction, suggested quaternions, and came up with new mathematical notation. Fibonacci is also responsible for popularising the Arabic numerals (0, 1, 2, 3, 4, …) in Europe, which was still using Roman numerals (I, V, X, D, …) in the 12th century CE. Gödel also found an example of these “impossible theorems”: the continuum hypothesis. Thābit studied algebra, geometry, mechanics and statics. Hasan Ibn al-Haytham (أبو علي، الحسن بن الحسن بن الهيثم, c. 965 – 1050) lived in Cairo during the Islamic Golden Age, and studied mathematics, physics, astronomy, philosophy, and medicine. In his spare times, he built machines that could juggle or solve the Rubik’s Cube puzzle. According to legend, he corrected a mistake in his father‘s accounting at the age of 3, and found a way to quickly add up all integers from 1 to 100 at the age of 8. He was a great advocate of rationalism, and also made contributions to physics, medicine, linguistics, law, history, and many other subjects. It would take other mathematicians many years to fully understand these letters, and realise the impact of his work. When solving problems, Mirzakhani would draw doodles and diagrams on large sheets of paper, to see the underlying patterns and beauty. De Moivre’s Annuities on Lives, published in 1724, was the most significant work on life contingencies since Halley’s seminal Breslau paper. 1895:  Poincaré’s paper “Analysis Situs” starts modern topology. This had been an open problem for over 350 years! He investigated hypercycloids, published Tartaglia’s and Ferrari’s solution for cubic and quartic equations, was the first European to systematically use negative numbers, and even acknowledged the existence of imaginary numbers (based on −1). He was an early pioneer of calculus, as well as working in number theory, probability, geometry and optics. David Hilbert famously declared that “No one shall expel us from the paradise that Cantor has created”. He was one of the many famous scientists from the Bernoulli family – including his father Johann, his uncle Jacob, and his brother Nicholas. He studied at Yale University, and later returned there as a professor. Charles Babbage (1791 – 1871) was a British mathematician, philosopher and engineer. Leonardo da Vinci (1452 – 1519) was an Italian artist and polymath. He explains how to eliminate variables and how to find the side length of two and three-dimensional shapes given their volume or area. In fact, he had a deep academic rivalry with several of his brothers and sons. Updates? Others think it may be a very early trigonometry table. The goal of the Bourbaki group was to unify all of mathematics with a formal, axiomatic foundation. De Moivre’s (Uniform), Exponential, Weibull, Makeham, Gompertz Generalization of De Moivre’s Curtate future lifetime Chapter 2 (Dickson, Hardy and Waters = DHW) Lecture: Weeks 2-3 (STT 455)Survival ModelsFall 2014 - Valdez 2 / 28. The position of a knot indicates the place value (ones, tens, hundreds, …). This was the foundation for formal mathematical logic, and has many applications in computer science. 1858:  August Ferdinand Möbius invents the Möbius strip. While taking a bath, Archimedes discovered a way to determine the volume of irregular objects using the amount of water they displaced when submerged. His inventions include windmills, pantograph, as well as a radial steam turbine called aeolipile or Hero’s engine. Apollonius of Perga (c. 200 BCE) was a Greek mathematician and astronomer best known for his work on the four conic sections. Al-Khwārizmī is often called the father of algebra. He studied under Plato in Athens, Greece and under Egyptian priests in Heliopolis, Egypt. He invented many mechanical devices, including combination locks, gyroscopes with three degrees of freedom, and drive shafts (or Cardan shafts) that are still used in vehicles today. He might be the first mathematician to understand and use negative numbers, while writing a commentary with solutions for The Nine Chapters on the Mathematical Art, a famous Chinese book about mathematics. 1066:  William the Conqueror wins the battle of Hastings and is crowned King Every digit from 1 to 19 consists of circles (representing 1) and horizontal lines (representing 5). Each of the symbols represents a date, and consists of a small image combined with several small circles. Abraham de Moivre, (born May 26, 1667, Vitry, Fr.—died Nov. 27, 1754, London), French mathematician who was a pioneer in the development of analytic trigonometry and in the theory of probability.

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