Ralph P. Boas, Jr
Encyclopedia
Ralph Philip Boas, Jr was a mathematician, teacher, and journal editor. He wrote over 200 papers, mainly in the fields of real
and complex analysis
.
He was born in Walla Walla, Washington
and got his A.B. degree
and Ph.D.
at Harvard University
(Ph.D., 1937; advisor, David Widder
). In 1950 he became Professor of Mathematics at Northwestern University
, where he stayed until his retirement in 1980. He continued mathematical work after retiring, for instance as co-editor (with George Leitmann
) of the Journal of Mathematical Analysis and Applications from 1985 to 1991.
, and colleagues were behind the 1938 paper A Contribution to the Mathematical Theory of Big Game Hunting published in the American Mathematical Monthly
under the pseudonym H. Pétard (referring to Hamlet
's "hoist by his own petard") . The paper offers short spoof
s of theorems and proofs from mathematics
and physics
, in the form of applications to the hunting
of lion
s in the Sahara desert. One "proof" parodies
the Bolzano–Weierstrass theorem
,
The paper became a classic of mathematical humor
and spawned various follow-ons over the years with theories or methods from other scientific areas adapted to hunting lions.
The paper and later work is published in Lion Hunting and Other Mathematical Pursuits : A Collection of Mathematics, Verse, and Stories by the Late Ralph P. Boas, Jr, ISBN 0-88385-323-X. Various online collections of the lion hunting methods exist too.
, Power problems in abstract spaces, Duke Mathematical Journal
, 11 (1944), 835–837. This paper and the name became part of the Hewitt-Marczewski-Pondiczery theorem.
The name, revealed in Lion Hunting and Other Mathematical Pursuits cited above, came from Pondicherry (a place in India
disputed by the Dutch
, English
and French
) and a slavic
twist. The initials "E.S." were a plan to write a spoof on extra-sensory perception
(ESP).
on a paper (The set on which an entire function is small, American Journal of Mathematics
, 70, 400–402), giving him an Erdős number
of 1.
His best-known books are the lion-hunting book previously mentioned and the monograph A Primer of Real Functions. The current edition of the primer has been revised and edited by his son, mathematician Harold P. Boas
.
The best-known of his 13 doctoral students is Philip J. Davis
, who is also his only advisee who did not graduate from Northwestern. Boas advised Davis, who was at Harvard University
, while Boas was visiting at Brown University
.
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
and complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
.
He was born in Walla Walla, Washington
Walla Walla, Washington
Walla Walla is the largest city in and the county seat of Walla Walla County, Washington, United States. The population was 31,731 at the 2010 census...
and got his A.B. degree
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
and Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
(Ph.D., 1937; advisor, David Widder
David Widder
David Vernon Widder was an American mathematician. He earned his Ph.D. at Harvard University in 1924 under George Birkhoff and went on to join the faculty there....
). In 1950 he became Professor of Mathematics at Northwestern University
Northwestern University
Northwestern University is a private research university in Evanston and Chicago, Illinois, USA. Northwestern has eleven undergraduate, graduate, and professional schools offering 124 undergraduate degrees and 145 graduate and professional degrees....
, where he stayed until his retirement in 1980. He continued mathematical work after retiring, for instance as co-editor (with George Leitmann
George Leitmann
George Leitmann is an American control theorist and an emeritus Professor in the Department of Mechanical Engineering at the University of California, Berkeley. He is considered to be one of the leading authorities in optimal control theory and its applications.He received his Ph.D...
) of the Journal of Mathematical Analysis and Applications from 1985 to 1991.
The hunting of big game
Boas, Frank SmithiesFrank Smithies
Frank Smithies FRSE was a British mathematician who worked on integral equations, functional analysis, and the history of mathematics....
, and colleagues were behind the 1938 paper A Contribution to the Mathematical Theory of Big Game Hunting published in the American Mathematical Monthly
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
under the pseudonym H. Pétard (referring to Hamlet
Hamlet
The Tragical History of Hamlet, Prince of Denmark, or more simply Hamlet, is a tragedy by William Shakespeare, believed to have been written between 1599 and 1601...
's "hoist by his own petard") . The paper offers short spoof
Spoof
-General uses:* Parody by imitation* Satire, a literary technique of writing or art which principally ridicules its subject* Forgery of goods or documents* Spoof , a guessing game...
s of theorems and proofs from mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, in the form of applications to the hunting
Hunting
Hunting is the practice of pursuing any living thing, usually wildlife, for food, recreation, or trade. In present-day use, the term refers to lawful hunting, as distinguished from poaching, which is the killing, trapping or capture of the hunted species contrary to applicable law...
of lion
Lion
The lion is one of the four big cats in the genus Panthera, and a member of the family Felidae. With some males exceeding 250 kg in weight, it is the second-largest living cat after the tiger...
s in the Sahara desert. One "proof" parodies
Parody
A parody , in current usage, is an imitative work created to mock, comment on, or trivialise an original work, its subject, author, style, or some other target, by means of humorous, satiric or ironic imitation...
the Bolzano–Weierstrass theorem
Bolzano–Weierstrass theorem
In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite-dimensional Euclidean space Rn. The theorem states thateach bounded sequence in Rn has a convergent subsequence...
,
- The Bolzano-Weierstrass Method. Bisect the desert by a line running N-S. The lion is either in the E portion or in the W portion; let us suppose him to be in the W portion. Bisect this portion by a line running E-W. The lion is either in the N portion or in the S portion; let us suppose him to be in the N portion. We continue this process indefinitely, constructing a sufficiently strong fence about the chosen portion at each step. The diameter of the chosen portions approaches zero, so that the lion is ultimately surrounded by a fence of arbitrarily small perimeter.
The paper became a classic of mathematical humor
Mathematical joke
A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor. The humor may come from a pun, or from a double meaning of a mathematical term. It may also come from a lay person's misunderstanding of a mathematical concept...
and spawned various follow-ons over the years with theories or methods from other scientific areas adapted to hunting lions.
The paper and later work is published in Lion Hunting and Other Mathematical Pursuits : A Collection of Mathematics, Verse, and Stories by the Late Ralph P. Boas, Jr, ISBN 0-88385-323-X. Various online collections of the lion hunting methods exist too.
Pondiczery
E. S. Pondiczery was another pseudonym used by Boas (maybe with collaborators), this time for a serious paper on topologyTopology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, Power problems in abstract spaces, Duke Mathematical Journal
Duke Mathematical Journal
Duke Mathematical Journal is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz...
, 11 (1944), 835–837. This paper and the name became part of the Hewitt-Marczewski-Pondiczery theorem.
The name, revealed in Lion Hunting and Other Mathematical Pursuits cited above, came from Pondicherry (a place in India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
disputed by the Dutch
Dutch people
The Dutch people are an ethnic group native to the Netherlands. They share a common culture and speak the Dutch language. Dutch people and their descendants are found in migrant communities worldwide, notably in Suriname, Chile, Brazil, Canada, Australia, South Africa, New Zealand, and the United...
, English
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...
and French
French people
The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...
) and a slavic
Slavic languages
The Slavic languages , a group of closely related languages of the Slavic peoples and a subgroup of Indo-European languages, have speakers in most of Eastern Europe, in much of the Balkans, in parts of Central Europe, and in the northern part of Asia.-Branches:Scholars traditionally divide Slavic...
twist. The initials "E.S." were a plan to write a spoof on extra-sensory perception
Extra-sensory perception
Extrasensory perception involves reception of information not gained through the recognized physical senses but sensed with the mind. The term was coined by Frederic Myers, and adopted by Duke University psychologist J. B. Rhine to denote psychic abilities such as telepathy, clairaudience, and...
(ESP).
Other
Boas collaborated with Paul ErdősPaul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
on a paper (The set on which an entire function is small, American Journal of Mathematics
American Journal of Mathematics
The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.- History :The American Journal of Mathematics is the oldest continuously-published mathematical journal in the United States, established in 1878 at the Johns Hopkins University...
, 70, 400–402), giving him an Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
of 1.
His best-known books are the lion-hunting book previously mentioned and the monograph A Primer of Real Functions. The current edition of the primer has been revised and edited by his son, mathematician Harold P. Boas
Harold P. Boas
Harold P. Boas is an American mathematician.He received his A.B. and S.M. degrees in applied mathematics from Harvard University in 1976 and his Ph.D. in mathematics from the Massachusetts Institute of Technology in 1980 under the direction of Norberto Kerzman. He was a J. F...
.
The best-known of his 13 doctoral students is Philip J. Davis
Philip J. Davis
Philip J. Davis is an American applied mathematician.Davis was born in Lawrence, Massachusetts. He is known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics...
, who is also his only advisee who did not graduate from Northwestern. Boas advised Davis, who was at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, while Boas was visiting at Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
.
Further reading
- Some Modern Mathematical Methods in the Theory of Lion Hunting, O. Morphy, American Mathematical MonthlyAmerican Mathematical MonthlyThe American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
, volume 75 (1968), pages 185–187. - Linguistic Contributions To The Formal Theory Of Big-Game Hunting, R. Mathiesen, Lingua Pranca, 1978.