Man Who Loves Only Numbers - Last Part

Last Week i and my wife Sneha started reading The Man Who Loved Only Numbers by Paul Hoffman.

Actually my manager Hugh Barney gave me this book and he was so kind to give it to me seeing my enthu of maths.

Great book written by Great Author about Great Person Paul Erdos.

Today i want to share few important quotations about some great persons mentioned in this book from the remaining chapters.

1) Monty Halparin, OC is a Canadian-born emcee, producer, actor, singer and sportscaster, best known as host of the long-running television game show Let's Make a Deal.

Hall was the host of the long-running game show Let's Make a Deal, which he developed and produced with partner Stefan Hatos. Let's Make a Deal aired on NBC daytime from December 30, 1963 to December 27, 1968 and on ABC daytime from December 30, 1968 to July 9, 1976, along with two primetime runs. It also aired in syndication from 1971 to 1977, from 1980 to 1981, from 1984 to 1986, and again on NBC briefly from 1990 to 1991. He was producer or executive producer of the show through most of its runs. During the show's initial run, Hall became well known alongside model Carol Merrill and announcer Jay Stewart.

Because of his work on Let's Make a Deal, Hall's name is used in a popular probability puzzle known as the Monty Hall problem. In the mathematical sciences, the problem examines the counter-intuitive effects of switching one's choice of doors if "Monty" reveals a goat behind one of doors the player didn't choose. Hall himself gave an explanation of the solution to that problem, and why the solution did not apply to the case of the actual show, in an interview with The New York Times reporter John Tierney in 1991. Because Hall had control over the way the game progressed, he played on the psychology of the contestant. The puzzle was mentioned on the CBS drama Numb3rs in an episode during its first season, and also in the newly-released movie 21.

2) Marilyn vos Savant (born August 11, 1946) is an American magazine columnist, author, lecturer and playwright who rose to fame through her listing in the Guinness Book of World Records under "Highest IQ". Since 1986 she has written Ask Marilyn, a Sunday column in Parade magazine in which she solves puzzles and answers questions from readers on a variety of subjects.

Born Marilyn Mach in St. Louis, Missouri, to Mary vos Savant and Joseph Mach, vos Savant believes that both men and women should keep their premarital surnames for life, with sons taking their father's surname and daughters their mother's.The word "savant", meaning a person of learning, appears twice in her family: her maternal grandmother's maiden name was Savant, while her maternal grandfather's surname was vos Savant. She is of German and Italian ancestry, and is a descendant of physicist and philosopher Ernst Mach.She attended Washington University in St. Louis, but dropped out to help with a family investment business, seeking financial freedom to pursue a career in writing.

Marilyn's listing in the 1986 Guinness Book of World Records brought her widespread media attention. A profile in Parade accompanied by a selection of questions and her answers to them proved so popular that the magazine gave her a weekly column, "Ask Marilyn". In it, she solves puzzles of logic and mathematics and answers questions about philosophy, physics, politics, education, and human nature, as well as responding to more traditional requests for personal advice. "Ask Marilyn" has provided the basis for several of her books.

3) Michael F. Jacobson, who holds a Ph.D. in microbiology, co-founded the Center for Science in the Public Interest in 1971, along with two fellow scientists he met while working at the Center for the Study of Responsive Law. When his colleagues left CSPI in 1977, Jacobson served as executive director. Today, Jacobson sits as secretary on the board of directors of the organization.

He has been a national leader in the movement to require nutrition labels on all foods and most beverages to help consumers make informed decisions about what to consume. He coined the phrases "junk food" and "empty calorie".

Jacobson is a vegetarian and sits on the national board of the "Great American Meatout." He has said that “CSPI is proud of finding something wrong with practically everything.” Jacobson and his organization have criticized a wide variety of foods and beverages as unhealthful. He and CSPI frequently use colorful terms to emphasize their oppositionn to certain foods. What has been called the "food cop glossary" includes Fettuccine alfredo- "heart attack on a plate," salt - "the forgotten killer," sugary soft drinks - "liquid candy," movie theater popcorn -"Godzilla of snacks," fondue - "fondon't," ice cream - "coronaries in cones," double cheeseburger - "a coronary bypass special," appetizers - "the most treacherous territory on a restaurant menu," Starbucks' Venti Caffe Mocha with whipped cream - "a Quarter Pounder with Cheese in a cup," Ruby Tuesday's Fresh Chicken & Broccoli Pasta - "angioplasta," Chipotle Chicken Burrito - "tortilla terror," and Cheesecake Factory's Chris' Outrageous Chocolate Cake - "factory reject." (Kathryn Masterson, "Food Cop: Love Him or Hate Him, Chicago Trib, 14 Oct 07)

4) Béla Bollobás (born August 3, 1943 in Budapest, Hungary) is a Hungarian mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics and graph theory. His first doctorate was for work in discrete geometry in 1967, after which he spent a year in Moscow with Gelfand. After spending a year in Oxford he went to Cambridge, where in 1972 he received a Ph.D. in functional analysis.

He is an external member of the Hungarian Academy of Sciences. He has been a Fellow of Trinity College, Cambridge since 1970, and is currently the Jabie Hardin Chair Professor at the University of Memphis.


He is known as an important expositor of combinatorial mathematics, on which he has written a number of books, and for spreading the combinatorial approach. His students include Tim Gowers, Fields Medal winner, and current Rouse Ball Professor of Mathematics at the University of Cambridge; Imre Leader, also professor of mathematics at Cambridge; Charles Read and Jonathan Partington, both Professors of Mathematics at the University of Leeds. He co-wrote 18 papers with Paul Erdos, giving him an Erdos number of 1.He proved that the chromatic number of the random graph on n vertices is asymptotically n / 2logn.

5) Carl Pomerance (born in 1944 in Joplin, Missouri) is a well known number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number N has at least 7 distinct prime factors. He immediately joined the faculty at the University of Georgia, becoming full professor in 1982. He subsequently worked at Lucent Technologies for a number of years, and then became a Distinguished Professor at Dartmouth College.

He has won many teaching and research awards, including the Chauvenet Prize in 1985, MAA's distinguished university teaching award in 1997, and the Conant Prize in 2001. He has over 120 publications to his credit, including co-authorship with Richard Crandall of Prime numbers: a computational perspective, Springer-Verlag, 2001, 2005. He is the inventor of one of the most important factorisation methods, the quadratic sieve algorithm, which was used in 1994 for the factorisation of RSA-129. He is also one of the discoverers of the Adleman-Pomerance-Rumely primality test.

His Erdos number is 1.

6) In mathematics, a Ruth-Aaron pair consists of two consecutive integers (e.g. 714 and 715) for which the sums of the prime factors of each integer are equal:

714 = 2 × 3 × 7 × 17
715 = 5 × 11 × 13
and 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29
If only distinct prime factors are counted, the first few Ruth-Aaron pairs are:

(5, 6), (24, 25), (49, 50), (77, 78), (104, 105), (153, 154), (369, 370), (492, 493), (714, 715), (1682, 1683), (2107, 2108)

7) Fermat's little theorem is the basis for the Fermat primality test.

8) Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus, as well as his research into the theory of numbers. He also made notable contributions to analytic geometry, probability, and optics.

9) Ernst Eduard Kummer (29 January 1810 - 14 May 1893) was a German mathematician. Highly skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a Gymnasium, where he inspired the mathematical career of Leopold Kronecker.

Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series (contiguity relations). The Kummer surface results from taking the quotient of a two-dimensional abelian variety by the cyclic group {1,-1}

Kummer also proved Fermat's last theorem for a considerable class of prime exponents (see regular prime, ideal class group). His methods were closer, perhaps, to p-adic ones than to ideal theory as understood later, though the term 'ideal' arose here. He studied what were later called Kummer extensions of fields: that is, extensions generated by adjoining an nth root to a field already containing a primitive nth root of unity. This is a significant extension of the theory of quadratic extensions, and the genus theory of quadratic forms (linked to the 2-torsion of the class group). As such, it is still foundational for class field theory.

10) A Smith number is a composite number for which, in a given base, the sum of its digits is equal to the sum of the digits in its prime factorization. (In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed). For example, 378 = 2 × 3 × 3 × 3 × 7 is a base 10 Smith number, since 3 + 7 + 8 = 2 + 3 + 3 + 3 + 7. It's important to remember that, by definition, the factors are treated as digits. For example, 22 in base 10 factors to 2 × 11 and yields three digits: 2, 1, 1. Therefore 22 is a Smith number because 2 + 2 = 2 + 1 + 1.

In base 10, the first few Smith numbers are

4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086

11) Blaise Pascal was a French mathematician, physicist, and religious philosopher. He was a child prodigy who was educated by his father. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the construction of mechanical calculators, the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. Pascal also wrote in defense of the scientific method.

Pascal was a mathematician of the first order. He helped create two major new areas of research. He wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

12) Gottfried Wilhelm Leibniz was a German polymath who wrote primarily in Latin and French.

He occupies an equally grand place in both the history of philosophy and the history of mathematics. He invented calculus independently of Newton, and his notation is the one in general use since then. He also discovered the binary system, foundation of virtually all modern computer architectures. In philosophy, he is mostly remembered for optimism, i.e. his conclusion that our universe is, in a restricted sense, the best possible one God could have made. He was, along with René Descartes and Baruch Spinoza, one of the three greatest 17th-century rationalists, but his philosophy also looks back to the scholastic tradition and anticipates modern logic and analysis. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, linguistics, and information science. He also wrote on politics, law, ethics, theology, history, and philology, even occasional verse. His contributions to this vast array of subjects are scattered in journals and in tens of thousands of letters and unpublished manuscripts. As of 2008, there is no complete edition of Leibniz's writings.

13) Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, born in Russia. He is best known as the creator of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers, and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.

14) Derrick Henry "Dick" Lehmer was an American mathematician who refined Edouard Lucas' work in the 1930s and devised the Lucas-Lehmer test for Mersenne primes. Lehmer's peripatetic career as a number theorist, with he and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing.

Lehmer was born in Berkeley, California, to Derrick Norman Lehmer, a professor of mathematics at the University of California, Berkeley, and Clara Eunice Mitchell.

He studied physics and earned a Bachelor degree from UC Berkeley, and continued with graduate studies at the University of Chicago.

He and his father worked together on Lehmer sieves.

Lehmer received a Master's degree and a Ph.D., both from Brown University, in 1929 and 1930, respectively; his wife obtained a Master's degree in 1930 as well, coaching mathematics to supplement the family income, while also helping her husband type his Ph.D. thesis, An Extended Theory of Lucas' Functions, which he wrote under Jacob Tamarkin.

15) Kenneth Alan "Ken" Ribet is an American mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include algebraic number theory and algebraic geometry.

He is credited with paving the way towards Andrew Wiles's proof of Fermat's last theorem. Ribet proved that the epsilon conjecture which was established by Jean-Pierre Serre was indeed true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama-Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curves, sufficed. An earlier theorem, the converse to Herbrand's theorem on the divisibility properties of Bernoulli numbers, is also related to Fermat's Last Theorem.

As a student at Far Rockaway High School, he was on a competitive mathematics team, but his first field of study was chemistry. He earned his bachelor's degree and master's degree from Brown University in 1969, and his Ph.D. from Harvard University in 1973. In 1998, he received an honorary doctorate from Brown University. He was elected to the American Academy of Arts and Sciences in 1997 and the National Academy of Sciences in 2000.

16) Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. Sometimes known as the princeps mathematicorum and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.

Gauss was a child prodigy. There are many anecdotes pertaining to his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at the age of 21, though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

17) Georges-Louis Leclerc, was a French naturalist, mathematician, biologist, cosmologist and author. Buffon's views influenced the next two generations of naturalists, including Jean-Baptiste Lamarck and Charles Darwin. Darwin himself, in his foreword to the 6th edition of the Origin of Species, credited Aristotle with foreshadowing the concept of natural selection but also stated that "the first author who in modern times has treated it in a scientific spirit was Buffon". The Lycée Buffon in Paris is named after him.

18) Niels Henrik Abel (August 5, 1802 – April 6, 1829) was a noted Norwegian mathematician who proved the impossibility of solving the quintic equation in radicals.

Abel's life started in poverty and ended in poverty. Abel was born in Nedstrand, near Finnøy. Abel was strikingly handsome. His father, Søren Georg Abel, had a degree in theology and philosophy and his grandfather was an active Protestant minister at Gjerstad near Risør. After Abel's grandfather's death, his father was appointed as minister at Gjerstad. When Abel was 13 years old, the long economic crisis in Norway affected Abel's family. In 1815 he entered the Cathedral School in Christiania. At first, he was uninspired because the school disappointed Abel, but everything changed when a new mathematics teacher, Bernt Michael Holmboe, was appointed in 1817. Holmboe saw Abel's talent in mathematics and encouraged him to learn university level mathematics. When his father died in 1820, the family was left in strained circumstances. Holmboe supported Abel with a scholarship to remain at school and raised money from his friends to enable Abel to study at the Royal Frederick University. Abel entered the university in 1821 and graduated in 1822.

19) Leopold Kronecker was a German mathematician and logician who argued that arithmetic and analysis must be founded on "whole numbers", saying, "God made the integers; all else is the work of man" (Bell 1986, p. 477). This put Kronecker in bitter opposition to some of the mathematical extensions of Georg Cantor, Kronecker's student (cf. Davis (2000), pp. 59ff). Kronecker was a student and lifelong friend of Ernst Kummer.

Leopold Kronecker was born in Liegnitz, Prussia into a Jewish family . In 1845, Kronecker wrote his dissertation at the University of Berlin on number theory, giving special formulation to units in certain algebraic number fields. Peter Gustav Dirichlet was his teacher.

After obtaining his degree, Kronecker managed the estate and business of his uncle, producing nothing mathematical for eight years. In his 1853 memoir on the algebraic solvability of equations, Kronecker extended the work of Évariste Galois on the theory of equations. He accepted a professorship at Friedrich-Wilhelms University of Berlin in 1883.

Kronecker also contributed to the concept of continuity, reconstructing the form of irrational numbers in real numbers. In analysis, Kronecker rejected the formulation of a continuous, nowhere differentiable function by his colleague, Karl Weierstrass. In an 1850 paper, On the Solution of the General Equation of the Fifth Degree, Kronecker solved the quintic equation by applying group theory.

Kronecker's finitism made him a forerunner of intuitionism in foundations of mathematics.

20) Jules Henri Poincaré was a French mathematician and theoretical physicist, and a philosopher of science. Poincaré is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.

As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is considered to be one of the founders of the field of topology.