Mathematics

Page last modified 21/11/2019

 

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Prime Numbers up to 1,000,000,  https://www.mathsisfun.com/numbers/prime-number-lists.html

Scientific calculator, https://www.mathway.com/Precalculus

Maths problems explained and worked through, https://www.mathsisfun.com/

 

2018, The largest prime number so far known was calculated by Patrick Laroche. It had 24,862,048 digits.

2010, Japanese systems engineer Shigeru Kondo computed the value of e to 1,000,000,000,000 decimal places.

14/10/2010, French-American mathematician who developed fractal geometry, Benoit Mandelbrot, died aged 85.

5/1995, Fermat’s Last Theorem was finally proved in generality, for all values of n. It was proposed by Pierre de Fermat (ca. 1607 – 1665) in 1637, that an + bn = cn had no solution for any value of n greater than 2.

1988, Japanese computer scientist Yasumasa Kanada calculated Pi to 201,326,000 decimal places.

1985, The number composed of 1,031 ones in a row was found to be prime.

2/8/1957, John von Neumann, Hungarian-US mathematician, died in Washington DC.

27/4/1936, English mathematician Karl Pearson died in Coldharbour, Surrey.

6/1/1922, Jakob Rosanes, Ukrainian-German mathematician, died.

26/4/1920, Mathematician Srinivasa Ramanujan died.

12/2/1916, Julius Wilhelm Richard Dedekind, German mathematician, died in Braunschweig.

28/4/1906, Austrian-US mathematician Kurt Godel was born in Brno, Czechoslovakia.

24/1/1902, Oskar Morgenstern, German-US mathematician, was born in Silesia (Poland).

1896, Jacques Hadamard proved that, for large values of a, the number of primes less than a approximates to a / log a.

1985, The largest-then-known prime number,(2 to the power 216,065) minus 1, with 66,050 digits,was discovered.

26/1/1895, Arthur Cayley, British mathematician, died in Cambridge.

1894, The New York Mathematical Society was formed, later to become the American Mathematical Society.

5/11/1879, James Clerk Maxwell, Scottish mathematician and physicist, died in Cambridge, England.

22/5/1868, Julius Plucker, German mathematician, died in Bonn, Germany.

1865, The London Mathematical Society was founded and began to issue its journal, Proceedings.

1865, German mathematician August Ferdinand Mobius (born Schulpforte 17/11/1790) presented his discovery of a figure that had only one side and one edge, now known as the Mobius Strip.

8/11/1858, George Peacock, mathematician, died in Ely, England.

23/2/1855, Johann Karl Friedrich Gauss, mathematician, died in Gottingen, Germany.

29/4/1854, Jules Henri Poincare, French mathematician, was born in Nantes. In 1895 he effectively founded the science of topology, although some of its principles were already known.

12/4/1852, Ferdinand Lindemann was born in Hannover, Germany. In 1882 he proved that Pi is a transcendental number.

6/4/1829, Neils Abel, Norwegian mathematician (born 1802) died inArendal.

23/2/1826, Nikolai Ivanovich Lobachevski (born near Nizhni Novgorod, Russia) gave a paper at Kazan University outlining the principles of non-Euclidean geometry.

2/11/1815, Mathematician George Boole was born in Lincoln, England. In 1847 he published his paper on symbolic logic.

25/1/1812. Mathematician William Shanks was born in Corsenside, England. He attempted a calculation of Pi to 707 places in 1853. However in 1944 it was discovered he had made an error at place 528, causing all digits thereafter to be erroneous.

25/8/1802, Neils Abel, Norwegian mathematician (died 1829) was born in Findoe.

29/10/1783, Jean Alembert, French mathematician, died in Paris.

18/9/1783, Leonhard Euler, Swiss mathematician, died in St Petersburg, Russia.

1782, Latin Squares were developed by Euler. These are n x n matrices with n different symbols,where each symbol occurs once in each row and once in each column. Sudoku puzzles are a type of Latin Square. These squares can be used in randomised drug experiments where n groups can be given different non-duplicated schedules of the drug.

1777, Euler first used i to denote the square root of minus 1. He did not publish this until 1794, and it was Gauss who gained widespread acceptance for this notation with his work Disquisitiones arithmeticae in 1801.

1761, Mathematician Thomas Bayes died (born 1701). He developed Bayes Theorem, an ‘intuitive’method of calculating probabilities based on prior observations; for example if the Sun roose yesterday morning, and the day before, it will likely rise this morning too. If every time the Sun rises (A) a cock is heard to crow (B), the probability that in the future the two events will occur together is Pr(A[B)  = Pr(B[A) x PrPr(A) / Pr(B). In other words, the RHS terms are trhe numerical values for how often A occurs, B occurs and A and B occur together.

15/4/1754, Jacopo Riccati, mathematician, died in Treviso, Italy.

1736, The symbol e for natural logarithms, devised by Leonhard Euler  in 1727, first appeared in print.

1736, Graph Theory was originated by Leonhard Euler. It had topological origins, dealing woth networks of points connected by lines (the Konigsberg Bridge problem), and does not deal with graphs sich as bar charts or pie charts.

1734, Swiss mathematician Leonhardt Euler introduced the term f(x) to denote a mathematical function.

1733, The Bell Curve, showing that valuers for random processes couldcluster around a mean with values further off becoming less likely,was invented by Abraham de Moivre (1667 - `1754). This was developed in 1833 by German mathematician Friedrich Gauss (1777 – 1855).

16/5/1718, Maria Agnesi, Italian mathematician, was born (died 9/1/1799).

1717, Abtaham Sharp calculated the value of Pi to 72 places.

1691, Leibniz first used the mathematical terms coordinate, ordinate and abscissa. He also introduced the term ‘function’ to describe a mathematical equation where every unique input produces one unique output, for example if the function is x2, then input 4 produces output 16.

21/11/1675, Leibniz became the first mathematician to use the modern notation of f[x] dx for integration/differentiation.

1665, Isaac Newton worked out a system of ‘fluxions’ – precursor of modern calculus. He also began work on a theory of gravity.

12/1/1665, French mathematician Pierre de Fermat (born 1601) died.

1659, First publication of the (division) sign, in Teutsche Algebra, written by Johann Heinrich and published long after his death in 1588.

1653, Mathematician Blaise Pascal (1623-1662) wrote his treatise, On the Arithmetical Traingle (published posthumously in 1665). His Triangle consisted of rows of numbers where each term is the sum of the two above, e.g. 1 – 1,1 – 1,2,1 – 1,3,3,1, ….This triangle is important in Probability Theory and for polynomial equations and fractals..

1648, Death of French monk Marin Mersenne (born 1588), who first identified what are now know as Mersenne Prime Numbers; those whose formula is 2n – 1.

30/9/1632, Thomas Allen, English mathematician, died at Gloucester Hall (born 21/12/1542 at Gloucester Hall).

1631, First recorded used of the multiplication sign, by William Oughtred. First use of the signs < and > to mean ‘less than’ and ‘more than’.

1629, Brackets were first used in mathematics by the Dutch mathematician, Albert Gerard.

1614, Logarithms were invented by the Scottish mathematician, John Napier (1550-1617), who in that year published a 97-page work entitled ‘Mirifici Logarithmorum Canonia Descriptio’. He coined the word ‘logarithm from two Greek words meaning ‘ratio’ and ‘number’.

1603, Pietro A Cataldi discovered the 6th and 7th Perfect Numbers, which are 8,859,869,056 and 137,438,691,328.

1588, Italian mathematician Pietro Cataldi discovedred the largest known prime number, 524,287. It remained the largest-known prime for almost two centuries.

5/3/1574, William Oughtred was born in Eton. Around 1621 he invented the slide rule.

1572, Complex / imaginary numbers were applied to solve equations in Rafael Bombelli’s work, Algebra. Imaginary numbers are those with a negative square root,and complex numbers are those with a real and imaginary element, such as 3 + 4i, which are expressed on a 2-d grid.

1556, The = sign was created by Robert Recorde, on the basis that nothing can be more equal than a pair of parallel lines.

21/12/1542, Thomas Allen, English mathematician, was born in Uttoxeter, Staffordshire (died 30/9/1632 at Gloucester Hall).

1525, The first manual of geometry was compiled by the German engraver, Albrecht Durer.

1524, First recorded usage of the modern square root symbol, in Die Coss, by Christoff Rudolff.

1513, The fifth Perfect Number was discovered, 33,350,336. A Perfect Number is one whose factors add up to the number itself, like 6 is the sum of 1, 2 and 3.

1489, The first recorded use of the mathematical symbols + and -, in the book Mental Arithmetic by Johann Wildmann, published in Leipzig. They were used for ‘excess’ and ‘deficiency’, and by the 1500s came to mean ‘add’ and ‘subtract’.

1434, Leone Battista, born in Genoa, Italy, 14/2/1404, published a nook on the geometrical laws of perspective in drawing.

1299, In Florence, Italy, the use of Arabic numerals was banned.

1240, Death of Italian mathematician Leonardo Pisano Bigollo (or, Fibonacci) (born ca. 1170). He developed the Fibonacci Series, 1,1,2,3,5,8,13,21,34….where each term is the sum of the two previous ones. This series governs how biological systems reproduce.

1055, The Arabs introduced decimal notation to Spain.

15/5/1048, The Persian mathematician and poet Omar Khayyam was born at Nisipar. He was the first to solve cubic equations (those containing terms to the power of three).

830, The Arabic text Hisab al jabr w’al muqabalah (The Science of Reunion and Opposition) became the basis of algebra in the West. Renaissance scholars sometimes preferred the Latin term ‘analysis’.

665, Death of Indian mathematician Brahmagupta (ca. 598-665). He drew up formal rules for the use of zero in mathematics, as a number not just as a placeholder.

605, Use of decimal notation in India. In China, Pi was calculated to be between 3.1415926 and 3.1415927.

462, Birth of Aryabhata, Indian mathematician who wrote on the powers and roots of numbers.

17/4/485, Proclus, Greek mathematician, died in Athens.

250, Diophantes of Alexandria wrote the first known book on algebra.

200, In China, a polygon of 3072 sides was used to calculate the value of Pi as 3.14159. Chinese mathematicians used powers of 10 to express numbers.

120, Death of Nichomachus,mathematician who first formulated the concept of Perfect Numbers. These are numbers whose factors, including 1, add to the number itself; 6 = 3+2+1, and 28 = 14+7+4+2+1. 496 and 98,128 are the next two Perfect Numbers. By 2007, just 44 such numbers were known.

95 BCE, First use of negative numbers, in China.

323 BCE, Euclid published his work ‘Elements’, the standard text on geometry. He proved that there must be infinitely many prime numbers.

395 BCE, Theodorus of Cyrene demonstrated that the square roots of 3,5,6,7,8,10, 12,13,14, 15 and 17 were irrational.

445 BCE, The earliest concept of irrational numbers (numbers like the square root of 2, or Pi, that have infinite decimal places). Hippacos of Metapontium discovered that some magnitudes are ‘not commensurable’, such as the diagonal and sode of a square; they have no common unit. Also at this time Zeno of Elea formulated paradoxes contrasting continuity with discreteness, such as the notion that a faster runner cannot ever catch a tortoise that has a headstart. These questions are still not fully answered today.

465 BCE, The dodecahedron, a solid with 12 faces, was described by Hippasus of Greece.

545 BCE, Death of Thales of Miletus. He derived the ‘Thales Proposition’; that triangles over the diameter of a circle are always right-angled.

628 CE, The Indian astronomer amd mathematician Brahmagupta first described the concept of ‘zero’ as a true number. By 300 BCE use of the number zero was common in Babylonian mathematical texts. The name’zero’cpomes from the Sanskrit ‘sunya’, meaning ‘nothing’; it became ‘sifr’ in Arabic, and was latinised by Leonardo Fibonacci into ‘zephirum’

876 BCE, First known use of a symbol for zero, in India. The actual concept of zero may have been known earlier than this.

1300 BCE, Decimal numerals in use in China.

1725 BCE, Egyptian geometrical uinderstanding was advanced, with formulae for the volume of a truncated pyramid.

1875 BCE, The Pythagorean Theorem was known in Mesopotamia.

1975 BCE, Quadratic equations, where symbols up to the power of two are used, were known and could be solved in Mesopotamia.

3000 BCE, Numerology was being practised in Egypt. The art of numerology helped develop the science of mathematics, along with the need to keep accounts of trading and payments.

3400 BCE, In Sumeria, clay counting tokens and written mathematical symbols first used.

 

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