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Around 30 000BC to 5000BC. We have the findings of some kind of mathematical pursuit, from recording the number on bones, to early geometrical designs. Around 4000BC to 2000BC. Babylonians and Egyptians developed calendars and began using them. Around 1900BC one of the two mathematical papyri is written  the Moscow Papyrus (also called the Golenishev papyrus) giving details of Egyptian geometry. Between 1850 and 1750BC Babylonians know of and use what we now call Pythagoras' theorem. They also compiled tables of square and cube roots. About 1700BC the Ahmes (or Rhind) papyrus is written. It shows number work of Egyptian scribe, in particular dealing with fractions. Around 600BC Thales of Miletus develops an abstract geometry, elevating it from the measurement of surfaces and solids to the first use of logical proof. If at all, Pythagoras of Samos lived sometimes between 50th and the 52nd Olympiads, or between 580 and 568 BC. He founded a school at Crotona, teaching that numbers are the cause of the various qualities of everything that surrounds us. About 450BC Greeks begin to use written numerals and Zeno presented his paradoxes. 387BC Plato founds his Academy in Athens. Plato thought that there was an ideal world in which ideas of everything that exist in our world are created. We try to recreate these ideas in our everyday world by creating things, but they can never be as perfect as the 'ideals' of these things. He identified five regular polyhedra, which are now called Platonic bodies. About 360BC Eudoxus of Cnidus develops the theory of proportion, and the method of exhaustion. About 300BC Euclid writes The Elements  the most popular book on the planet after Bible and the Kuran, until the middle of the 19 th century when the certainty of Euclidean geometry was replaced by the possibilities of nonEuclidean ones. About 250BC Archimedes gave the formulae for calculating the volume of a sphere and a cylinder. Between 235 and 230BC Eratosthenes of Cyrene (a librarian of the famous Alexandrian Library) estimated the Earth's circumference with remarkable accuracy finding a value which is about 15% too big and develops his sieve for finding prime numbers. Between 200 and 180BC two Chinese classics in mathematical history are written  Jiuzhang suanshu (Nine Chapters) , which mainly deals with geometry and Suanshu shu (A Book on Arithmetic). About 250AD Mayan civilisation flourished in Central America, who used very similar to our, placevalue number system, but to a base 20. At the same time in Greece Diophantus of Alexandria wrote Arithmetica, which is sometimes considered to be the first book on algebra, a study of number theory problems in which only rational numbers are allowable solutions. 301AD Iambilichus wrote Life of Pythagoras which is more or less all we know with certainty about Pythagoras. 400AD is the time of Hypatia, the first recorded woman mathematician. She became head of the school at Alexandria and wrote commentaries on Diophantus and Apollonius. 628 Brahmagupta wrote Brahmasphutasiddanta (The Opening of the Universe) which is an astronomical/mathematical work. Zero and negative numbers were used. 810 House of Wisdom was founded in Baghdad. Greek and Indian mathematical and astronomical texts were translated into Arabic. About the same time AlKhwarizmi wrote one of the most celebrated books of all time in mathematics  Hisab aljabr w'almuqabala (Calculation by Completion and Balancing) which gave origin to the word 'algebra'. Around 850 Thabit ibn Qurra made a number of important discoveries in number theory and wrote Book on the determination of amicable numbers which contained general methods to construct them. Ibn Qurra knew the pair of amicable numbers 17296 and 18416. Around 990 alKaraji gave a version of Pascal's triangle in his book on algebra AlFakhri . 1142 sees the translation of Euclid's Elements from Arabic into Latin by Adelard of Bath. Two years later Gherard of Cremona began translating other Arabic works (and Arabic translations of Greek works) into Latin. He introduced Arabic numerals in his translation of Ptolemy's Almagest. The name of 'sine' also comes from this translation. 1200 Chinese use the symbol for zero. 1202 Fibonacci wrote Liber abaci (The Book of the Abacus) . In it he set out arithmetic and algebra known at the time and introduced his famous sequence of numbers. In 1336 Mathematics became a compulsory subject for a degree at the University of Paris. In 1434 Alberti wrote the first general treatise on the laws of perspective, Della Pictura. This will, among others, be an important work for the development of modern geometry centuries later. In and around 1450 Nicholas of Cusa studied geometry and logic. His work is important for the study of infinity  both the infinitely small and the infinitely large. He also described circle as the limit of regular polygons. In 1482 the first mathematical book was printed  it is Campanus of Novara's edition of Euclid's Elements. First English translation of Euclid was published by Recorde in 1551 as The Pathewaie to Knowledge. Six years later he introduced '=' sign (equal sign). In 1591 Viete published his In artem analyticam isagoge (Introduction to the analytical art) , in which he used, for the first time, the consonants for known quantities. Descartes will later use the consonants at the end of the alphabet for the unknowns (such as x, y, and z). Napier published his work on logarithms in Mirifici logarithmorum canonis descriptio (Description of the Marvellous Rule of Logarithms) in 1614, and in 1617 Briggs published his under Logarithmorum chilias prima (Logarithms of Numbers from 1 to 1000) , introducing the logarithms to the base of 10. In the same year (1617) Napier invented Napier's bones as a mechanical calculator. In 1634 Descartes discovered Euler's theorem for polyhedra, V  E + F =2 In 1636 Fermat discovered the pair of amicable numbers 17296 and 18416, which were known to Thabit ibn Qurra some 800 years earlier. In 1637 Descartes published his La Geometrie which set the basis of Analytical Geometry. Between 1640 and 1642 Pascal published his Essay pour les conique and built the first calculating machine (which could only deal with additions) to help his father with tax calculations. In 1653 he published Treatise on the Arithemtical Triangle but although it became known as Pascal's triangle, it was known to mathematicians for centuries before. Fermat claimed to have proved, what is now known as Fermat's Last Theorem. Unfortunately, he did not have enough space in his margin to explain the proof, thereby annoyingly teasing mathematicians and giving them innumerable headaches for centuries to come. Correspondence of some five letters between Pascal and Fermat in 1654 is considered as one of the beginnings of the definition of the laws that govern chance and probability. 1662 The Royal Society is founded in London. Barrow, Newton's teacher, becomes the first Lucasian professor of Mathematics at the University of Cambridge in 1663. Newton discovered binomial theorem in 1665 and began his work on the differential calculus. He published his crowning work The Principia or Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy) in 1687. The Academie of Sciences is founded in Paris. In 1673 Leibniz demonstrated his calculating machine to the Royal Society  this one could multiply, divide and extract roots. In 1675 he is the first to use the modern notation for an integral. Leibniz was also the first to use the word "coordinate" in 1692. In 1724 Academy of Sciences was founded in St. Petersburg. Three years later, in 1727 Euler was appointed at St. Petersburg, where he introduced the symbol e for the base of natural logarithms in Meditation upon Experiments made recently on firing of Cannon. The manuscript was published only in 1862. A first serious attempt to break the supremacy of Euclid appeared in 1733 in Saccheri's Euclides ab omni Naevo Vindicatus , although, in his words, he vindicated Euclid rather than trying to attack him. See the story about Euclidean and nonEuclidean geometrie. 1735 Euler introduced notation for f(x). In 1742 Goldbachs conjectures, in a letter to Euler, that every even number 4 can be written as the sum of two primes. It has not yet been proved either way. In 1746 D'Alembert made the first serious attempt to prove the fundamental theorem of algebra. In 1752 Euler stated his theorem for polyhedra, VE+F= 2. 1763 Monge began his study of descriptive geometry, which he did not publish after the French Revolution in 1799, as it was decreed a military secret at the school where he worked at the time when he first formulated it. In 1796 Gauss gave the first correct proof of the law of quadratic reciprocity. Only a year later, in Geometria del compasso Mascheroni proved that all Euclidean constructions can be made with compasses alone and so a ruler is not required. In 1799 Gauss proved the fundamental theorem of algebra , showing that earlier proofs, such as that of d'Alembert from 1746, could be corrected. In 1801 he proved Fermat's conjecture that every number can be written as the sum of three triangular numbers. Janos Bolyai completed his work on nonEuclidean geometry in 1823, but published it only in an appendix to the work of his father, Farkas Bolyai in 1832. At the same time, across Europe, Babbage began constructing difference engine which should be able to calculate logarithms and trigonometric functions. In 1824 Steiner developed the concept of synthetic geometry, which he published in 1832. In 1829 Lobachevsky developed his version of nonEuclidean geometry independently from Bolyai. The paper was rejected by the St. Petersburg Academy of Sciences. In 1837 Wantzel proved that the two classical problems of duplicating the cube, and trisecting an angle could not be solved with the ruler and compass. In 1839 Lame proved Fermat's Last Theorem for n=7. In 1852 Francis Guthrie posed the Four Colour conjecture to De Morgan. Möbius described a strip of paper that only has one side and one edge in 1858. London Mathematical Society was founded in 1864. 1900 Hilbert posed 23 problems at the Second International Congress of Mathematicians in Paris as a challenge for the 20 th century. 1905 Einstein published his Theory of Relativity. 1966 Lander and Parkin used computer to find a counterexample to Euler's Conjecture. They found 275+845+1105+1335=1445. 1975 Mandelbrot published his Les objects fractals, forme, hazard et dimension , which introduced the theory of fractals. Wiles proved Fermat's Last Theorem in 1994. The 38th Mersenne prime was found in 1999  it is .


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