View source for Helen Popova Alderson

{{short description|Mathematician and translator}}
{{redirect|Helen Alderson|the fictionalized veterinarian's wife|James Herriot|the footballer|Helen Alderson (footballer)}}
{{Use dmy dates|cs1-dates=ly|date=April 2022}}
'''Helen Popova Alderson''' (1924–1972) was a Soviet and British mathematician and mathematics translator known for her research on [[quasigroup]]s and on higher [[reciprocity law]]s.

==Life==
Alderson was born on 14 May 1924 in [[Baku]], then part of the [[Soviet Union]], to a family of two academics from [[Moscow]]. Her father, a [[neurophysiologist]], had been a student of [[Ivan Pavlov]]. She began studying mathematics at [[Moscow University]] in 1937, when she was only 13. She had to break off her studies because of [[World War II]], moving to Paris as a refugee with her family.{{r|obit}}

After the war, she returned to study at the [[University of Edinburgh]]. She completed a Ph.D. there in 1951; her dissertation was ''Logarithmetics of Non-Associative Algebras''.{{r|obit|mgp}}

After leaving mathematical research to raise two children in Cambridge, she was funded by the [[Calouste Gulbenkian Foundation]] with a Fellowship at [[Lucy Cavendish College, Cambridge]], beginning in the late 1960s. At Cambridge, she worked with [[J. W. S. Cassels]].{{r|obit}}

She died on 5 November 1972, from complications of kidney disease.{{r|obit}}

==Research==
In the theory of higher [[reciprocity law]]s, Alderson published necessary and sufficient conditions for 2 and 3 to be [[seventh power]]s, in [[modular arithmetic]] modulo a given [[prime number]] <math>p</math>.{{r|septic}}{{ran|7X}}

According to {{harvtxt|Smith|1976}}, "plain quasigroups were first studied by Helen Popova-Alderson, in a series of papers dating back to the early fifties".
Smith cites in particular a posthumous paper {{harv|Alderson|1974}}{{ran|FPQ}} and its references. In this context, a [[quasigroup]] is a mathematical structure consisting of a set of elements and a [[binary operation]] that does not necessarily obey the [[associative law]], but where (like a [[group (mathematics)|group]]) this operation can be inverted. Being plain involves having only a finite number of elements and no non-trivial subalgebras.{{r|smith}}

==Translation==
As well as Russian, English, and French, Alderson spoke Polish, Czech, and some German.{{r|obit}} She became the English translator of ''Elementary Number Theory'', a textbook originally published in Russian in 1937 by B. A. Venkov. Her translation was published by Wolters-Noordhoff of Groningen in 1970. As well as the original text, it includes footnotes by Alderson updating the material with new developments in number theory.{{r|ent}}{{ran|ENT}}

==Selected publications==
{{rma|ENT|tw=3em|{{citation
 | last = Venkov | first = B. A.
 | location = Groningen
 | mr = 0265267
 | publisher = Wolters-Noordhoff Publishing
 | others = Translated from the Russian and edited by Helen Alderson
 | title = Elementary number theory
 | year = 1970}}}}

{{rma|7X|tw=3em|{{citation
 | last = Alderson | first = Helen Popova
 | journal = [[Mathematical Proceedings of the Cambridge Philosophical Society]]
 | mr = 0323763
 | pages = 421–433
 | title = On the septimic character of 2 and 3
 | volume = 74
 | issue = 3
 | year = 1973| doi = 10.1017/S030500410007715X
 | bibcode = 1973PCPS...74..421A
 }}}}

{{rma|FPQ|tw=3em|{{citation
 | last = Alderson | first = Helen Popova
 | doi = 10.1016/0021-8693(74)90002-7
 | journal = [[Journal of Algebra]]
 | mr = 0352298
 | pages = 1–9
 | title = The structure of the logarithmetics of finite plain quasigroups
 | volume = 31
 | issue = 1
 | year = 1974| doi-access = free
 }}}}

==References==
{{reflist|refs=

<ref name=ent>{{citation
 | last = Goodstein | first = R. L. | authorlink = Reuben Goodstein
 | date = February 1972
 | doi = 10.2307/3613726
 | issue = 395
 | journal = [[The Mathematical Gazette]]
 | page = 62
 | title = Review of ''Elementary Number Theory''
 | volume = 56| jstor = 3613726 }}</ref>

<ref name=mgp>{{mathgenealogy|id=42206}}</ref>

<ref name=obit>{{citation|url=http://www.numbertheory.org/obituaries/OTHERS/alderson.html|title=Helen Popova Alderson|work=Some biographies of past contributors to number theory|first=Keith|last=Matthews|publisher=Number Theory Web|accessdate=2018-10-22}}</ref>

<ref name=septic>{{citation
 | last1 = Leonard | first1 = Philip A.
 | last2 = Williams | first2 = Kenneth S.
 | journal = [[Pacific Journal of Mathematics]]
 | mr = 0364064
 | pages = 143–147
 | title = The septic character of 2, 3, 5 and 7
 | url = https://projecteuclid.org/euclid.pjm/1102912220
 | volume = 52
 | year = 1974| doi = 10.2140/pjm.1974.52.143
 | doi-access = free
 }}</ref>

<ref name=smith>{{citation
 | last = Smith | first = Jonathan D. H.
 | contribution = Chapter 5: Plain algebras and equational completeness
 | doi = 10.1007/BFb0095452
 | mr = 0432511
 | pages = 93–112
 | publisher = Springer-Verlag
 | series = Lecture Notes in Mathematics
 | title = Mal'cev varieties
 | volume = 554
 | year = 1976}}</ref>

}}

{{Authority control}}

{{DEFAULTSORT:Alderson, Helen Popova}}
[[Category:1924 births]]
[[Category:1972 deaths]]
[[Category:Scientists from Baku]]
[[Category:Soviet mathematicians]]
[[Category:Soviet women mathematicians]]
[[Category:British mathematicians]]
[[Category:Women mathematicians]]
[[Category:Technical translators]]
[[Category:Russian–English translators]]
[[Category:Alumni of the University of Edinburgh College of Science and Engineering]]
[[Category:Fellows of Lucy Cavendish College, Cambridge]]
[[Category:20th-century translators]]
[[Category:Soviet emigrants to the United Kingdom]]
[[Category:Soviet expatriates in France]]