**Eric Temple Bell** (February 7, 1883 – December 21, 1960) was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction as **John Taine**.

Eric Temple Bell | |
---|---|

Bell as pictured in Wonder Stories in 1931 | |

Born | February 7, 1883 Peterhead, Scotland, UK |

Died | December 21, 1960 (aged 77) |

Residence | United States |

Nationality | British |

Alma mater | Stanford University Columbia University (Ph.D.) |

Known for | Number theory Bell series Bell polynomials Bell numbers Bell triangle Ordered Bell numbers |

Awards | Bôcher Memorial Prize (1924) |

Scientific career | |

Fields | Mathematics |

Institutions | University of Washington California Institute of Technology |

Doctoral advisor | Frank Nelson Cole Cassius Keyser |

Doctoral students | Howard Percy Robertson Morgan Ward Zhou Peiyuan |

Bell was born in Peterhead, Aberdeen, Scotland, but his father, a factor, relocated to San Jose, California in 1884, when he was fifteen months old. The family returned to Bedford, England after his father's death, on January 4, 1896. Bell returned to the United States by way of Montreal in 1902.

Bell was educated at Bedford Modern School, where his teacher Edward Mann Langley inspired him to continue the study of mathematics, Stanford University, the University of Washington, and Columbia University^{[1]} (where he was a student of Cassius Jackson Keyser). He was part of the faculty first at the University of Washington and later at the California Institute of Technology.

He researched number theory; see in particular Bell series. He attempted—not altogether successfully—to make the traditional umbral calculus (understood at that time to be the same thing as the "symbolic method" of Blissard) logically rigorous. He also did much work using generating functions, treated as formal power series, without concern for convergence. He is the eponym of the Bell polynomials and the Bell numbers of combinatorics. In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. He died in 1960 in Watsonville, California.

During the early 1920s, Bell wrote several long poems. He also wrote several science fiction novels, which independently invented some of the earliest devices and ideas of science fiction.^{[2]} Only the novel *The Purple Sapphire* was published at the time, using the pseudonym John Taine; this was before Hugo Gernsback and the *genre* publication of science fiction. His novels were published later, both in book form and serialized in magazines. Basil Davenport, writing in *The New York Times*, described Taine as "one of the first real scientists to write science-fiction [who] did much to bring it out of the interplanetary cops-and-robbers stage." But he concluded that "[Taine] is sadly lacking as a novelist, in style and especially in characterization."^{[3]}

Bell wrote a book of biographical essays titled *Men of Mathematics*, (one chapter of which was the first popular account of the 19th century woman mathematician Sofia Kovalevskaya) and which is still in print. The book inspired notable mathematicians including Julia Robinson,^{[4]} John Forbes Nash, Jr.,^{[5]} and Andrew Wiles^{[6]} to begin a career as a mathematician. However, historians of mathematics have disputed the accuracy of much of Bell's history. In fact, Bell does not distinguish carefully between anecdote and history. He has been much criticized for romanticizing Évariste Galois. For example: "[E. T.] Bell's account [of Galois's life], by far the most famous, is also the most fictitious."^{[7]}

His treatment of Georg Cantor, which reduced Cantor's relationships with his father and with Leopold Kronecker to stereotypes, has been criticized even more severely.^{[8]}

Bell's later book *Development of Mathematics* has been less famous, but Constance Reid finds it has fewer weaknesses. *The Last Problem* is a hybrid, between a social history and a history of mathematics.

*An Arithmetical Theory of Certain Numerical Functions*, Seattle Washington, The University, 1915, 50p. PDF/DjVu copy from Internet Archive.*The Cyclotomic Quinary Quintic*, Lancaster, Pennsylvania, The New Era Printing Company, 1912, 97p.*Algebraic Arithmetic*, New York, American Mathematical Society, 1927, 180p.*Debunking Science*, Seattle, University of Washington book store, 1930, 40p.*The Queen of the Sciences*, Stechert, 1931, 138p.*Numerology*, Baltimore: The Williams & Wilkins Co., 1933, 187p. LCCN 33-6808- Reprint: Westport, CT: Hyperion Press, 1979, ISBN 0-88355-774-6, 187p. – "Reprint of the ed. published by Century Co., New York" LCCN 78-13855

*The Search for Truth*, Baltimore, Reynal and Hitchcock, 1934, 279p.- Reprint: Williams and Wilkins Co, 1935

*The Handmaiden of the Sciences*, Williams & Wilkins, 1937, 216p.*Man and His Lifebelts*, New York, Reynal & Hitchcock, 1938, 340p.- Reprint: George Allen & Unwin Ltd., 1935, 2nd printing 1946
- Reprint: Kessinger Publishing, 2005

*Men of Mathematics*, New York, Simon & Schuster, 1937, 592p.*The Development of Mathematics*, New York, McGraw–Hill, 1940, 637p.- Second Edition: New York, McGraw–Hill, 1945, 637p.
- Reprint: Dover Publications, 1992

*The Magic of Numbers*, Whittlesey House, 1946, 418p.- Reprint: New York, Dover Publications, 1991, ISBN 0-486-26788-1, 418p.
- Reprint: Sacred Science Institute, 2006

*Mathematics: Queen and Servant of Science*, McGraw-Hill, 1951, 437p.*The Last Problem*, New York, Simon & Schuster, 1961, 308p.- Reprint: Mathematical Association of America, 1990, ISBN 0-88385-451-1, 326p.

- "Arithmetical paraphrases". In:
*Transactions of the American Mathematical Society***22**, 1921, pp. 1–30 and 198–219 - "Arithmetical equivalents for a remarkable identity between theta functions". In:
*Mathematische Zeitschrift***13**, 1922, pp. 146–152 - "Existence theorems on the numbers of representations of odd integers as sums of 4
*t*+ 2 squares". In:*Crelles Journal***163**, 1930, pp. 65–70 - "Exponential numbers". In:
*The American Mathematical Monthly***41**, 1934, pp. 411–419

*The Purple Sapphire*(1924)*The Gold Tooth*(1927)*Quayle's Invention*(1927)*Green Fire*(1928)*The Greatest Adventure*(1929)*The Iron Star*(1930)*The White Lily*(1930)*The Time Stream*(1931)*Seeds of Life*(1931)*Before the Dawn*(1934)*Tomorrow*(1939)*The Forbidden Garden*(1947)*The Cosmic Geoids and One Other*(1949)*The Crystal Horde*(1952)*G.O.G. 666*(1954)

*The Singer*(1916)

- "Obvious is the most dangerous word in mathematics."
^{[9]}

**^**Goodstein, Judith R.; Babbitt, Donald (June–July 2013), "E.T. Bell and Mathematics at Caltech between the Wars" (PDF),*Notices of the American Mathematical Society*,**60**(6): 688, doi:10.1090/noti1009, retrieved 30 June 2013**^**Reid (1993), p. 253, "Most fiction writers are, after all, primarily fiction writers", he [Glenn Hughes, professor of English literature] wrote of Bell. "Some of them may show a trifle more finesse in plot handling or characterization, but none of them surpasses Bell in grandness of conception or accuracy of detail. One has always the uncanny feeling that [he] is dealing in probabilities, and that many of his most extravagant dreams are but pre-visions of nightmares in store for the human race.**^**Davenport, Basil (October 19, 1952), "Spacemen's Realm",*The New York Times*.**^**Reid, Constance (1996),*Julia, a Life in Mathematics*, MAA spectrum, Cambridge University Press, p. 25, ISBN 9780883855201,The only idea of real mathematics that I had came from

*Men of Mathematics*. In it I got my first glimpse of a mathematician per se. I cannot overemphasize the importance of such books about mathematics in the intellectual life of a student like myself completely out of contact with research mathematicians.**^**Kuhn, Harold W.; Nasar, Sylvia (2002),*The Essential John Nash*, Princeton University Press, p. 6, ISBN 9780691095271,By the time I was a student in high school I was reading the classic "Men of Mathematics" by E. T. Bell and I remember succeeding in proving the classic Fermat theorem about an integer multiplied by itself

*p*times where*p*is a prime.**^**Hodgkin, Luke (2005),*A History of Mathematics: From Mesopotamia to Modernity*, Oxford University Press, p. 254, ISBN 9780191664366,The fact that Wiles was stimulated in childhood by E. T. Bell's romantic personalized anecdotal book

*Men of Mathematics*to nurse an ambition to solve the problem Fermat's Last Theorem is in itself an index of the power which a certain view of the history of mathematics can exercise.**^**Rothman (1982), 103.**^**See chiefly Grattan-Guinness, Ivor (1971), "Towards a Biography of Georg Cantor",*Annals of Science*27: 345–91.**^**Beck, Matthias; Marchesi, Gerald; Pixton, Dennis; Sabalka, Lucas (2002–2012),*A First Course in Complex Analysis*(PDF), p. 26.

- Sources

- Reid, Constance (1993).
*The Search for E. T. Bell, Also Known as John Taine*. Washington, DC: Mathematical Association of America. x + 372 pp. ISBN 0-88385-508-9. OCLC 29190602. - Rothman, T. (1982). "Genius and biographers: the fictionalization of Evariste Galois".
*American Mathematics Monthly*89, no. 2, 84–106.

- Further reading

- Tuck, Donald H. (1974).
*The Encyclopedia of Science Fiction and Fantasy*. Chicago: Advent. p. 36. ISBN 0-911682-20-1.

- Biographical sketch by Constance Reid
- O'Connor, John J.; Robertson, Edmund F., "Eric Temple Bell",
*MacTutor History of Mathematics archive*, University of St Andrews. - Eric Temple Bell at the Mathematics Genealogy Project
- Works by John Taine at Faded Page (Canada)
- MAA presidents: Eric Temple
- John Taine at the Internet Speculative Fiction Database
- John Taine at Library of Congress Authorities, with 26 catalog records (distinct from Bell)
- Eric Temple Bell at Library of Congress Authorities, with 26 catalog records (distinct from Taine)
- Author profile in the database zbMATH

In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan, but they are named after Eric Temple Bell, who wrote about them in the 1930s.

Starting with B0 = B1 = 1, the first few Bell numbers are:

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, ... (sequence A000110 in the OEIS).The nth of these numbers, Bn, counts the number of different ways to partition a set that has exactly n elements, or equivalently, the number of equivalence relations on it.

Outside of mathematics, the same number also counts the number of different rhyme schemes for n-line poems.As well as appearing in counting problems, these numbers have a different interpretation, as moments of probability distributions. In particular, Bn is the nth moment of a Poisson distribution with mean 1.

Bell seriesIn mathematics, the **Bell series** is a formal power series used to study properties of arithmetical functions. Bell series were introduced and developed by Eric Temple Bell.

Given an arithmetic function and a prime , define the formal power series , called the Bell series of modulo as:

Two multiplicative functions can be shown to be identical if all of their Bell series are equal; this is sometimes called the *uniqueness theorem*: given multiplicative functions and , one has if and only if:

- for all primes .

Two series may be multiplied (sometimes called the *multiplication theorem*): For any two arithmetic functions and , let be their Dirichlet convolution. Then for every prime , one has:

In particular, this makes it trivial to find the Bell series of a Dirichlet inverse.

If is completely multiplicative, then formally:

In mathematics, the Bell triangle is a triangle of numbers analogous to Pascal's triangle, whose values count partitions of a set in which a given element is the largest singleton. It is named for its close connection to the Bell numbers, which may be found on both sides of the triangle, and which are in turn named after Eric Temple Bell. The Bell triangle has been discovered independently by multiple authors, beginning with Charles Sanders Peirce (1880) and including also Alexander Aitken (1933) and Cohn et al. (1962), and for that reason has also been called Aitken's array or the Peirce triangle.

Bôcher Memorial PrizeThe Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five years) for a notable research memoir in analysis that has appeared during the past six years in a recognized North American journal or was authored by a member of the Society. This provision, introduced in 1971 and modified in 1993, is a liberalization of the terms of the award. The current award is $5,000.

Edward Mann LangleyEdward Mann Langley (22 January 1851 – 9 June 1933) was a British mathematician, author of mathematical textbooks and founder of the Mathematical Gazette. He created the mathematical problem known as Langley’s Adventitious Angles.

G.O.G. 666G.O.G. 666 is a science fiction novel by author John Taine (pseudonym of Eric Temple Bell). It was first published in 1954 by Fantasy Press in an edition of 1,815 copies.

Green Fire (novel)Green Fire is a science fiction novel by American writer John Taine (pseudonym of Eric Temple Bell). It was first published in 1928 by E. P. Dutton. The novel was adapted and produced as a play.

List of Scottish science fiction writersThis is an alphabetical list of science fiction writers connected to Scotland by birth, death or long-term residence.

Men of MathematicsMen of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré is a book on the history of mathematics published in 1937 by Scottish-born American mathematician and science fiction writer E. T. Bell (1883–1960). After a brief chapter on three ancient mathematicians, it covers the lives of about forty mathematicians who flourished in the seventeenth through nineteenth centuries. The book is illustrated by mathematical discussions, with emphasis on mainstream mathematics.

To keep the interest of readers, the book typically focuses on unusual or dramatic aspects of its subjects' lives. Men of Mathematics has inspired many young people, including the young John Forbes Nash Jr. and Freeman Dyson, to become mathematicians. It is not intended as a rigorous history, includes many anecdotal accounts, and presents a somewhat idealised picture of mathematicians, their personalities, research and controversies.

Morgan WardMorgan Ward (1901–1963) was an American mathematician, a professor of mathematics at the California Institute of Technology.Ward received his Ph.D. from Caltech in 1928, with a dissertation entitled The Foundations of General Arithmetic; his advisor was Eric Temple Bell. He became a research fellow at Caltech, and then in 1929 a member of the faculty; he remained at Caltech until his death in 1963. Among his doctoral students was Robert P. Dilworth, who also became a Caltech professor. Ward is the academic ancestor of over 500 mathematicians and computer scientists through Dilworth and another of his students, Donald A. Darling.Ward's research interests included the study of recurrence relations and the divisibility properties of their solutions, diophantine equations including Euler's sum of powers conjecture and equations between monomials, abstract algebra, lattice theory and residuated lattices, functional equations and functional iteration, and numerical analysis. He also worked with the National Science Foundation on the reform of the elementary school mathematics curriculum, and with Clarence Ethel Hardgrove he wrote the textbook Modern Elementary Mathematics (Addison-Wesley, 1962).

Ward's works are collected in the Caltech library. A symposium in his memory was held at Caltech on November 21-22, 1963.

Robert P. DilworthRobert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician. His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right". He is best known for Dilworth's theorem (Dilworth 1950) relating chains and antichains in partial orders; he was also the first to study antimatroids (Dilworth 1940).

Dilworth was born in 1914 in Hemet, California, at that time a remote desert ranching town. He went to college at the California Institute of Technology, receiving his baccalaureate in 1936 and continuing there for his graduate studies. Dilworth's graduate advisor was Morgan Ward, a student of Eric Temple Bell, who was also on the Caltech faculty at the time. On receiving his Ph.D. in 1939, Dilworth took an instructorship at Yale University. While at Yale, he met and married his wife, Miriam White, with whom he eventually had two sons. He returned to Caltech as a faculty member in 1943, and spent the remainder of his academic career there.

Dilworth advised 17 Ph.D. students and as of 2010 has 373 academic descendants listed at the Mathematics Genealogy Project, many through his student Juris Hartmanis, a noted complexity theorist. Other notable mathematicians advised by Dilworth include Curtis Greene and Alfred W. Hales.

Seeds of LifeSeeds of Life is a science fiction novel by American writer John Taine (pseudonym of Eric Temple Bell). It was first published in 1951 by Fantasy Press in an edition of 2,991 copies. The novel originally appeared in the magazine Amazing Stories Quarterly in October 1931.

The Cosmic Geoids and One OtherThe Cosmic Geoids and One Other is a collection of two science fiction novellas by author John Taine (pseudonym of American writer Eric Temple Bell). It was first published in 1949 by Fantasy Publishing Company, Inc. in an edition of 1,200 copies. The title novella is a loose sequel to Taine's novel, The Time Stream, and was later serialized in the magazine Spaceway, in three parts beginning in December 1954. The other novella, "Black Goldfish", was first serialized in the magazine Fantasy Book, in two parts beginning in 1948.

The Crystal HordeThe Crystal Horde is a science fiction novel by American writer John Taine (pseudonym of Eric Temple Bell). It was first published in book form in 1952 by Fantasy Press in an edition of 2,328 copies. The novel is substantially rewritten from a version that originally appeared in the magazine Amazing Stories Quarterly in 1930 under the title White Lily.

The Forbidden Garden (novel)The Forbidden Garden is a science fiction novel by author John Taine (pseudonym of Eric Temple Bell). It was first published in 1947 by Fantasy Press in an edition of 3,029 copies.

The Iron StarThe Iron Star is a science fiction novel by American writer John Taine (pseudonym of Eric Temple Bell). It was first published in 1930 by E. P. Dutton.

The Time StreamThe Time Stream is a science fiction novel by American writer John Taine (pseudonym of Eric Temple Bell). The novel was originally serialized in four parts in the magazine Wonder Stories beginning in December 1931. It was first published in book form in 1946 by The Buffalo Book Company in an edition of 2,000 copies of which only 500 were ever bound. It is the first novel to see time as a flowing stream.

Umbral calculusIn mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to 'prove' them. These techniques were introduced by John Blissard (1861) and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas (or James Joseph Sylvester), who used the technique extensively.

Zhou PeiyuanZhou Peiyuan (Chinese: 周培源; Wade–Giles: Chou P'ei-yüan; August 28, 1902 – November 24, 1993) was a Chinese theoretical physicist and politician. He served as president of Peking University, and was an academician of the Chinese Academy of Sciences (CAS).Born in Yixing, Jiangsu, China, Zhou graduated from Tsinghua University in 1924. Then he went to the United States and obtained a bachelor's degree from University of Chicago in Spring of 1926, and a master's degree at the end of the same year. In 1928, he obtained his doctorate degree from California Institute of Technology under Eric Temple Bell with thesis The Gravitational Field of a Body with Rotational Symmetry in Einstein's Theory of Gravitation. In 1936, he studied general relativity under Albert Einstein in the Institute for Advanced Study at Princeton. He did his post-doc researches in quantum mechanics at University of Leipzig in Germany and Swiss Federal Institute of Technology Zurich. He was a professor of physics at Peking University, and later served as the president of the University. He was elected as a founding member of CAS in 1955.

Tsinghua University's Zhou Pei-Yuan Center for Applied Mathematics is named in his honor. In 2003, a bronze statue of Zhou was unveiled on the campus of Peking University.

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