History Of Math

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1. What is the Rhind Papyrus?

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The Rhind Mathematical Papyrus is a text that contains problems and solutions of Egyptian mathematics. It's named after the British archeologist A. Henry Rhind who purchased it in 1858. Originally it came in two parts of a single scroll and the missing middle part was discovered in 1922 among a private papyri collection in New York. The Rhind Papyrus is dated circa 1650 B.C. and contains problems that deal with proportional reasoning and multiplication by doubling. We know most of Egypt’s mathematics from this document

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2. What is the Nine Chapters of Mathematical Art?

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The Nine Chapters of Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE. It consists of 246 problems that provide methods to solve everyday problems of engineering, surveying, trade, and taxation. This book is one of the earliest surviving mathematical texts from China. It has played a fundamental role in the development of mathematics in China. Entries in the book usually take the form of a statement of a problem followed by the statement of the solution and an explanation of the procedure that led to the solution.

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3. Who Liu Hui and what were his contributions to mathematics?

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Liu Hui was a chinese commentor of the Nine Chapters and derived the figure 3.14 (Pi) to the approximation of 3.14159 with the use of a regular polygon of 96 sides and by considering a polygon of 3,072 sides.

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4. Demostrate how ancient Egyptians multiplied numbers such as 23 x 47.

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Egyptians would multiply and divide by simply using addition. For example, if they wanted to multiply 23x47, they would first make a list of numbers starting with one then doubling them (i.e. 1, 2, 4, 8, 16, 32), then they would find the numbers that add up to the first number which in this case its 23 and the numbers from the list that add up to 23 are 1,2,4 and 16. Then, with the second number, in this case 47, they would make a list starting with the number itself then doubling it (i.e. 47, 94, 188, 376, 752). Next, they would simply match the numbers that they added to get the first number in the first list to the ones from the second list in the same place. In this case, 1 and 47 are across from each other being that they are the first numbers on each list, 2 and 94 are second in the lists, 4 and 188 are third in the lists, 16 and 752 are fifth in the lists. So in this case, the Egyptians would take the numbers 47, 94, 188 and 752 and add them together to get 1081.

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5. Briefly explain the Babylonian numeral system.

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The Babylonian numeral system consisted of only two symbols one for the units and one to count the tens. Babylonians used a place value system with a base of 60. For numbers bigger than 59, they would leave a space to mark the nonexistence of a digit in a certain place value, similar to the modern day zero. They understood the idea of nothingness, it was not seen as a number but the the lack of a number.
47*16=752 23=16+4+2+1 1081=752+188+94+47 47+47=94+94=188+188=376+376+752+188+94+47=1081

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6. Write the Babylonian form of the decimal number 456,259.5 using modern bract notation, e.g. [2.3;20].

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[2,6,44,19;30]

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7. Convert the Babylonian numeral: [3,6,7;30,10] into a modern decimal numeral.

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3 x 60^2 + 5 x 60^1 + 7 x 60^0 + 30 x 60^-1 +10 x 60^-2
= 3 x 3600 + 5 x 60 + 7 + 30 x .01666666667 + 10 X 2.777777778
= 10800 + 300 + 7 + .5 x + .002777
= 11,107.500277

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8. Who was Thales of Miletus and what were his contributions to mathematics?

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Thales of Miletus was an ancient Greek philosopher born in Miletus in Greek. He was interested in investigating almost all areas of knowledge, philosophy, history, science, mathematics, engineering, geography, and politics. He founded the Milesian school of natural philosophy and developed the scientific method. He is recognized for five basic propositions with proofs of plane geometry which are; a circle is bisected by any diameter, the base angles of an isosceles triangle are equal, the angles between two intersecting straight lines are equal, two triangles are congruent if they have two angles and the included side equal, and an angle in a semicircle is a right angle.

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9. Who was Pythagoras of Samos and what were his contributions to mathematics?

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Pythagoras (c. 580–500 B.C.) was an ancient Greek philosopher who was interested in numbers and their meanings. He proposed that the Earth is a sphere, and that the Earth, Moon, and stars revolve around the Sun, and that astronomy could be written as mathematical sentences called equations. Pythagoras used lines, triangles, and squares made out of pebbles to represent numbers. Today Pythagoras is best remembered for the Pythagorean theorem, which is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the triangle's other two sides.

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10. Who Archytas of Tarentum and what were his contributions to mathematics?

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Archytas of Tarentum was a Greek mathematician, political leader and philosopher. He was also a military leader and was elected general seven consecutive times and had his own school. He was associated with Plato. Archytas was the first to solve the duplication of the cube. He knew rational calculation and had an understanding of proportion and there is also proof showing his proof that ratios cannot be divided by a mean proportional.

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11. Who was Eudoxus of Cnidus and what were his accomplishments in mathematics?

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was a Greek astronomer, mathematician, scholar and student of Plato. Eudoxus' main contributions to mathematics were his theory of proportions and his method of exhaustion. He came up with a solution on how to deal with irrationals. Eudoxus' theory of proportions is concerned with the ratio of magnitudes, which were represented by lengths of line segments. He provided a definition for the meaning of the equality between two ratios in the use of proportionalities. Eudoxus' method of exhaustion was a way of calculating areas and volumes such as the volume of a pyramid is one-third the volume of a prism with the same base and height and the volume of a cone is one-third the volume of a cylinder with the same base and height.

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12. Who was Herodotus?

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Herodotus was a 4th century Greek historian who was called the father of history because he was the first person to write a comprehensive account of what he knew about the present and learned about the past. He wrote about Thales and noted that Thales predicted the solar eclipse of 585 BC. He is most known for the book he wrote The Histories.

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13. Who was Democritus and what were his accomplishments in math?

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Democritus was a Greek mathematician born about 460 BC. He was the first mathematician to give the formula for the volume of a pyramid. This formula was for not just a square-based pyramid but one whose base is a regular polygon with any number of sides, including the cone.

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14. Who was Euclid of Alexandria and what were his contributions to mathematics?

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Euclid, the Greek mathematician, lived for about 60 years. Later known as the Alexandrian Mathematician and the Father of Geometry, he compiled his famous 13 volume treatise called Elements that made references to the geometry and other mathematics known in his day.

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15. Who was Eratosthenes and what were his accomplishments in math?

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Eratosthenes was a 4th century Greek mathematician, poet, athlete, geographer, astronomer, and music theorist. He was the first person to calculate the circumference of the earth by using the length of stadiums during that time period and calculated the tilt of the Earth's axis with remarkable accuracy. He was said to have accurately calculated the distance from the earth to the sun and Earth to the moon and invented the leap day. Eratosthenes also proposed a simple algorithm for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes.

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16. Who was Apollonius of Perga and what were his accomplishments in math?

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He was known as 'The Great Geometer'. He had a very great influence on the development of mathematics, and best known for his book Conics which introduced terms such as the four types of curves that result when a solid cone is cut into sections by a plane: the circle, the ellipse, the hyperbola, and the parabola. Apollonius discovered and named the latter two curves. In Conics, he gives a thorough treatment of the theory of these curves and related matters, developing a total of 387 propositions. His work led to the separation of geometry into the two divisions of solid geometry and plane geometry.

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17. Who was Aristarchus of Samos and what were his contributions to mathematics?

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Aristarchus was a mathematician and astronomer who lived about 310 BC to about 230 BC. He is most known for the first to propose a sun centered universe and for his attempt to determine the sizes and distances of the sun and moon. He determined that the Sun was about 20 times as distant from the Earth as the Moon, and 20 times the Moon's size, which was wrong but had the correct method of reasoning.

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18. Who was Autolycus of Pitane and what were his contributions to mathematics?

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Autolycus of Pitane (c. 360 BC – c. 290 BC) was a Greek astronomer, mathematician, and geographer. He studied the movements of a sphere. He wrote a book on spheres called On the Moving Sphere and another on the rising and setting of celestial bodies. His book On the Moving Sphere is believed to be the oldest mathematical treatise from ancient Greece that is completely preserved. It is believed they were the earliest written mathematics related books which have survived.

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19. Who was Theon of Alexandria and what were his contributions to mathematics?

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Theon (ca. 335 – ca. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt and worked as a teacher of mathematics and astronomy. He edited and arranged Euclid's Elements and Ptolemy's Handy Tables, as well as writing various commentaries. He removed difficulties that might have been felt by learners when studying the book.

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20. Who was Hypatia and what were her contributions to mathematics?

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was an Egyptian Neoplatonist philosopher who was the first notable woman in mathematics. She taught philosophy and astronomy and was also head of the Platonist school at Alexandria. As a Neoplatonist philosopher, she belonged to the mathematic tradition of the Academy of Athens, as represented by Eudoxus of Cnidusshe was of the intellectual school of the 3rd century thinker Plotinus, which encouraged logic and mathematical study in place of empirical enquiry and strongly encouraged law in place of nature Hypatia wrote on the Conics of Apollonius. She was the author of treatises on mathematics.

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21. Who was Heron of Alexandria and what were his contributions to mathematics?

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Heron, (also known as Hero) was a Greek mathematician. Hero’s major contributions to mathematics were his formula of square root, also his primary contribution to geometry was his writings and his findings. Hero also wrote many books.Hero also designed instruments used in daily life. Hero is credited as one of the earliest and most comprehensive and detailed recorders in the ancient technology.

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22. Who was Socrates and what were his contributions to mathematics?

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Socrates was an ancient Greek philosopher who taught Plato, who taught Aristotle, who, in turn, taught Alexander the Great.Socrates himself never wrote anything. All we know about Socrates is what other people wrote about him, of whom Plato is considered to be the most reliable source.

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23. Who was Plato and what were his contributions to mathematics?

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Plato (427-347 B.C.) was a classical Greek philosopher, mathematician, student of Socrates, and founder of the Academy in Athens. Over the door of the Academy was written: "Let no one unversed in geometry enter here". Plato concentrated on the idea of "proof" and insisted on accurate definitions and clear hypotheses. He laid the foundations for Euclid's systematic approach to mathematics and the most important mathematical work of the 4th century was done by friends or pupils of Plato. In the Timaeus there is a mathematical construction of the elements earth and the fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.

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24. Who was Aristotle and what were his contributions to mathematics?

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Aristotle (Aristoteles) was a Greek philosopher, a student of Plato (another famous philosopher) and also teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, politics, government, ethics, biology and zoology. He made a first european clasification of science.

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25. Who was Archimedes and describe some important contributions he made to
Mathematics?

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Archimedes was a great mathematician of ancient times and his greatest contributions were in geometry on the areas of plane figures and on the areas of area and volumes of curved surfaces. His methods started the idea for calculus which was invented 2,000 years. His most famous work is Measurement of the Circle, where he determined the exact value of pi between the two fractions, 3 10/71 and 3 1/7 by inscribing and circumscribing a circle with a 96-sided regular polygon and he also proved that the volume of an inscribed sphere is two-thirds the volume of a circumscribed cylinder.

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26. Who was Pappus of Alexandria and what were his accomplishments in math?

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Pappus of Alexandria (c. 290 – c. 350) was a Greek mathematicians. He was a teacher in Alexandria. He is known for his Synagoge or Collection, and for Pappus's Theorem in projective geometry. Collection, his best-known work, is a compendium of mathematics in eight volumes, which covers a wide range of topics, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra.

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27. Claudius Ptlomely and what were his contributions to mathematics?

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was a Greco-Roman writer of Alexandria, known as a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology Ptolemy was the author of several scientific treatises, at least three of which were of continuing importance to later Islamic and European science.

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28. Who was Nicomachus of Geresa and what were his contributions to
mathematics?

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Nicomachus (c. 60 – c. 120) was an important mathematician in the ancient world and is best known for his contributions to arithmetic. He wrote Introduction to Arithmetic, where he writes especially on the significance of prime numbers and perfect numbers and argues that arithmetic is ontologically prior to the other mathematical sciences like geometry, music, and astronomy and that is their cause.

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29. Who was Theaetetus and what were his contributions to mathematics?

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Theaetetus, (ca. 417 BC – 369 BC) was a classical Greek mathematician. His principal contributions were on irrational lengths, which was included in Book X of Euclid's Elements and he also shows that there are five regular convex polyhedra. The aim of Book X of Euclid's treatise on the "Elements" is to investigate the commensurable and the incommensurable, the rational and irrational continuous quantities.

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30. Who was Dinostratus and what were his contributions to mathematics?

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Dinostratus (c. 390 BC – c. 320 BC) was a Greek mathematician and geometer. His contribution to mathematics was his solution to the problem of squaring the circle. He is known for using the quadratrix to solve the problem of squaring the circle.

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31. Who was Proclus and what were his contributions to mathematics?

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Proclus Lycaeus (8 February 412 – 17 April 485 AD), was a Greek philosopher called "The Successor" or "Diadochos". He wrote an commentary on the first book of Euclid's Elements of Geometry. This commentary is one of the most valuable sources we have for the history of ancient mathematics and its Platonic account of the status of mathematical objects was influential. Proclus also listed the first mathematicians associated with Plato and commentaries on dialogues of Plato.

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32. Who was Hipparchus of Nicaea and what were his contributions to mathematics?

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He was a Greek astronomer, geographer, and mathematician of the Hellenistic period. He is considered the founder of trigonometry, but is most famous for his incidental discovery of precession of the equinoxes

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33. Who was Brahmagupta and what were his contributions to mathematics?

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Brahmagupta (598–668 CE) was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brahmasphutasiddhanta, Correctly Established Doctrine of Brahma, where modern rules of negative to be positive first appear. Brahmagupta was the first to use zero as a number and gave rules to compute with zero. He used negative numbers and zero for computing. He also gave the solution of the general linear equation.

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34. Who was Bhaskara and what were his contributions to mathematics?

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Bhaskara was a 12th century Indian astronomer and mathematician. He applied the concept of zero, decimal notation, the use of letters to represent unknown quantities in equations, and he developed rules for equations for trigonometry. The three most important books he published were Lilavati (The Beautiful), which is about mathematics; Bijaganita (Seed Counting), which is about algebra Karanakutuhala (The Calculation of Astronomical Wonders) about astronomy. Lilavati is the first known published work that uses the decimal position system.

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35. Who was Ramanujan and what were his contributions to mathematics?

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He was an Indian mathematician andautodidact who, with almost no formal training inpure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Living in India with no access to the larger mathematical community, which was centred in Europe at the time, Ramanujan developed his own mathematical research in isolation. As a result, he sometimes rediscovered known theorems in addition to producing new work.

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36. Who was Aryabhata and and what were his contributions to mathematics?

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Was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. The works of Aryabhata dealt with mainly mathematics and astronomy. He also worked on the approximation for pi.

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37. Who was al-Khowarizmi and what were his contributions to mathematics?

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Al-Khowarizmi (c. 780– c. 850) was a Persian mathematician, astronomer, geographer, and a scholar in the House of Wisdom in Baghdad. His work on the Indian numerals, introduced the decimal positional number system to the Western world. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic which led to algebra and trigonometry.

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38. Who was Omar Khayyam and what were his contributions to mathematics?

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Omar Khayyám (1048–1131) was a Persian polymath: philosopher, mathematician, astronomer and poet. He had notable works in geometry, specifically on the theory of proportions. He is the author of one of the most important treatises on algebra, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle and he wrote on the triangular array of binomial coefficients known as Pascal's triangle.

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39. Who was Gerbert and what were his contributions to mathematics?

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Gerbert was a Pope and a mathematician who wrote on division and computation by the abacus. He collected trifles on polygonal numbers and compiled an alleged geometry from Boethius. He was also said to have had a part in popularizing the Hindu numerals. Gerbert was also reputed to have been a man of vast learning and acute intellect.

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40. Who was Leonardo da Pisa and what were his contributions to mathematics?

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Leonardo of Pisa, or most commonly Fibonacci, was an Italian mathematician (c. 1170 – c. 1250), considered by some "the most talented western mathematician of the Middle Ages." He is best known for the spreading of the Hindu-Arabic numeral system in Europe and for a number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci. In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc.

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41. Who was Galileo Galilei and what were his contributions to mathematics?

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Galileo Galilei (15 February 1564 – 8 January 1642), was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. He has been called the "father of science. His achievements in science include improvements to the telescope and astronomical observation. In mathematics he produced Galileo's paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares.

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42. Who was Rene Descartes and what were his contributions to mathematics?

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Rene Descartes (31 March 1596 – 11 February 1650) was a French philosopher and writer. Descartes' influence in mathematics is Cartesian coordinate system allowing algebraic equations to be expressed as geometric shapes, in a 2D coordinate system which uses algebra to describe geometry. He is credited as the father of analytical geometry, the bridge between algebra and geometry.

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43. Who was Fermat and what were his contributions to mathematics?

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Fermat invented the factorization method. In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers. It was while researching perfect numbers that he discovered the little theorem. Fermat's factorization method—as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4.

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44. Who was Leonard Euler and what were his contributions to mathematics?

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Leonard Euler (15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. Euler worked in almost all areas of mathematics such as geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He made important discoveries in 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 a mathematical function.

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45. Who was Maria Agnesi and what were her contributions to mathematics?

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Maria Agnesi (May 16, 1718 – January 9, 1799) was an Italian linguist, mathematician, and philosopher. She studied the curve that was studied by Pierre de Fermat which they later called the "witch of Agnesi." The curve is also known as cubique d'Agnesi or agnésienne The curve is obtained by drawing a line from the origin through the circle of radius and center , then picking the point with the coordinate of the intersection with the circle and the coordinate of the intersection of the extension of line with the line.

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46. Who was Sophie Germain and what were her contributions to mathematics?

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Sophie Germain (April 1, 1776 – June 27, 1831) was a French mathematician, physicist, and philosopher. She is known for her work on Fermat's Last Theorem which provided a foundation for mathematicians exploring the subject for hundreds of years after. She claimed to have proved the theorem for n = p – 1, where p is a prime number of the form p = 8k + 7 however, her proof contained a weak assumption.

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47. Who was Sir Isaac Newton and what were his contributions to mathematics?

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was an English physicist and mathematician who is widely regarded as one of the most influential scientists of all time and as a key figure in the scientific revolution. His book ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations for most of classical mechanics. Newton's Principia formulated the laws of motion and universal gravitation that dominated scientists' view of the physical universe for the next three centuries.

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48. Who was Leibnitz and what were his contributions to mathematics?

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Was a German mathematician and philosopher. He occupies a prominent place in the history of mathematics and the history of philosophy.
Leibniz developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation.

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49. Who was Johann Kepler and what were his contributions to mathematics?

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Johann Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer and astrologer. He is best known for his eponymous laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation. His efforts to complete Brahe's planetary led to his discovery of the usefulness of logarithms in making computations.

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50. Who was Nicolaus Copernicus and what were his contributions to mathematics?

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was a Renaissance mathematician and astronomer who formulated a heliocentric model of the universe which placed the Sun, rather than the Earth, at the center. The publication of Copernicus' book, De revolutionibus orbium coelestium just before his death in 1543, is considered a major event in the history of science. It began the Copernican Revolution and contributed importantly to the scientific revolution.

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51. Who was Carl Gauss and what were his contributions to mathematics?

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Carl Friedrich Gauss, was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. He referred to mathematics as "the queen of sciences". He came up with the notion of Gaussian curvature which led to an important theorem, the Theorema Egregium establishing an important property of the notion of curvature. He also claimed to have discovered the possibility of non-Euclidean geometries but never published it.

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52. Who was George Cantor and what were his contributions to mathematics?

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George Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. His method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic.

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53. Who was Giovanni Girolamo Saccheriand what were his contributions to mathematics?

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Giovanni Girolamo Saccheri was an Italian Jesuit priest, scholastic philosopher, and mathematician. He taught philosophy, theology, and mathematics at Pavia from 1697 until his death. He came extremely close to discovering non-Eucliean geometry He intended to proof an alternative to Euclid's parallel postulate. He assumed that the parallel postulate was false, and attempted to derive a contradiction. This principle is accepted as the basis of elliptic geometry. Today, his results are theorems of hyperbolic geometry.

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54. Who was Nikolai Ivanovich Lobachevsky?

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was a Russian mathematician and geometer. He was known primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry. The non-Euclidean geometry that Lobachevsky developed is referred to as hyperbolic geometry. He replaced Euclid's parallel postulate with the one stating that there is more than one line that can be extended through any given point parallel to another line of which that point is not part.

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55. Who was Amalie Emmy Noether and what were her contributions to mathematics?

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was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. She revolutionized the theories of rings, fields, and algebras. In physics, Noether's theorem explains the fundamental connection between symmetry and conservation laws.

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56. Who was Jerome Cardan and what were his contributions to mathematics?

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was an Italian Renaissance mathematician, physician, astrologer and gambler. He is best known for his achievements in algebra. His gambling led him to formulate elementary rules in probability, making him one of the founders of the field. His book "Book on Games of Chance" contains the first systematic treatment of probability, as well as a section on effective cheating methods. He also acknowledged the existence of what are now called imaginary numbers, although he did not understand their properties and he introduced the binomial coefficients and the binomial theorem.

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58. Who was Francois Viete and what were his contributions to mathematics?

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Francois Viete (1540 – 23 February 1603), was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. His work Vieta gave algebra a foundation as strong as in geometry. He then ended the algebra of procedures creating the first symbolic algebra. He was also a lawyer by trade and served both Henry III and Henry IV.

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58. Who was Laplace and what were his contributions to mathematics?

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was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace.

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59. Who was Janos Bolyai and what were his contributions to mathematics?

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Was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.

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60.Who was Georg Friedrich Bernhard Riemann and what were his contributions to mathematics?

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was an influential German mathematician who made lasting contributions to analysis, number theory, and differential geometry, some of them enabling the later development of general relativity. Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory.

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61. Who was Jacob Bernoulli and what were his contributions to mathematics?

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was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and had sided with Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders the calculus of variations. However, he is most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.

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62. Who was Nina Karlovna Bari and what were her contributions to mathematics?

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was a Soviet mathematician known for her work on trigonometric series. She was killed by a train in the Moscow Metro. She went to college at Moscow State University.

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63. Who was Mary Cartwright and what were her contributions to mathematics?

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was a British mathematician. With J. E. Littlewood she was the first to analyze a dynamical system with chaos. She was born in Aynho, Northamptonshire where her father was the vicar and died in Cambridge, England. Through her grandmother Jane Holbech she was descended from the poet John Donne and William Mompesson, the Vicar of Eyam.

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64. Who was Nicolaus Copernicus and what were his contributions to mathematics?

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was a Renaissance mathematician and astronomer who formulated a heliocentric model of the universe which placed the Sun, rather than the Earth, at the center. The publication of Copernicus' book, De revolutionibus orbium coelestium just before his death in 1543, is considered a major event in the history of science. It began the Copernican Revolution and contributed importantly to the scientific revolution.

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65. Who was Hendrik Antoon Lorentz and what were his contributions to mathematics?

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was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the transformation equations subsequently used by Albert Einstein to describe space and time.

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66. Who was Niels Henrik David Bohr and what were his contributions to mathematics?

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Bohr developed the Bohr model of the atom with the atomic nucleus at the centre and electrons in orbit around it, which he compared to the planets orbiting the Sun. He helped develop quantum mechanics, in which electrons move from one energy level to another in discrete steps, instead of continuously. was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922.

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67. Who was Zeno of Elea and what were his contributions to mathematics?

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Zeno of Elea was a Greek philosopher and mathematician. He is famous for his paradoxes which deal with the continuity of motion were the existence of “the one” (indivisible reality) he wanted to contradict the commonsense belief in the existence of “the many” (distinguishable qualities and things capable of motion). They were insoluble until the development of precise concepts of continuity and infinity. He made a series of arguments in which he proved by logical means that motion and plurality are impossible.

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68. Who was Brook Taylor and what were his contributions to mathematics?

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Taylor was elected a fellow of the Royal Society early in 1712, Taylor's theorem is named after the mathematician Brook Taylor, who stated a version of it in 1712. In calculus, Taylor's theorem gives an approximation of a k times differentiable function around a given point by a k-th order Taylor polynomial. For analytic functions the Taylor polynomials at a given point are finite order truncations of its Taylor series, which completely determines the function in some neighborhood of the point.

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69. Who was Sir William Rowan Hamilton and what were his contributions to Mathematics?

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Was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In mathematics, he is perhaps best known as the inventor of quaternions.

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70. Who was Bernhard Placidus Johann Nepomuk Bolzano and what were his contributions to Mathematics?

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was a Bohemian mathematician, logician, philosopher, theologian, Catholic priest and antimilitarist of German mother tongue. Bolzano made several original contributions to mathematics. To the foundations of mathematical analysis he contributed the introduction of a fully rigorous ε-δ definition of a mathematical limit. Today he is mostly remembered for the Bolzano–Weierstrass theorem