Stanisław Świerczkowski
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Stanisław (Stash) Świerczkowski (16 July 1932 – 30 September 2015) was a
Polish Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles, people from Poland or of Polish descent * Polish chicken *Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwr ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
famous for his solutions to two iconic problems posed by
Hugo Steinhaus Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz Un ...
: the
three-gap theorem In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places points on a circle, at angles of , , , ... from the starting point, then there will be at most three distinct distances between pairs ...
and the Non-Tetratorus Theorem.


Early life and education

Stanisław (Stash) Świerczkowski was born in
Toruń )'' , image_skyline = , image_caption = , image_flag = POL Toruń flag.svg , image_shield = POL Toruń COA.svg , nickname = City of Angels, Gingerbread city, Copernicus Town , pushpin_map = Kuyavian-Pom ...
, Poland. His parents were divorced during his infancy. When war broke out his father was captured in Soviet-controlled Poland and murdered in the 1940
Katyń Massacre The Katyn massacre, "Katyń crime"; russian: link=yes, Катынская резня ''Katynskaya reznya'', "Katyn massacre", or russian: link=no, Катынский расстрел, ''Katynsky rasstrel'', "Katyn execution" was a series of m ...
. He belonged to the Polish nobility; Świerczkowski's mother belonged to the upper middle class and would have probably suffered deportation and murder by the Nazis. However she had German connections and was able to gain relatively privileged class 2
Volksliste The Deutsche Volksliste (German People's List), a Nazi Party institution, aimed to classify inhabitants of Nazi-occupied territories (1939-1945) into categories of desirability according to criteria systematised by ''Reichsführer-SS'' Heinrich Hi ...
citizenship. At the end of the war Świerczkowski's mother was forced into hiding near Toruń until she was confident that she could win exoneration from the Soviet-controlled government for her Volksliste status and be rehabilitated as a Polish citizen. Meanwhile, Świerczkowski lived in a rented room in Toruń and attended school there. Świerczkowski won a university place to study
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
at the
University of Wrocław , ''Schlesische Friedrich-Wilhelms-Universität zu Breslau'' (before 1945) , free_label = Specialty programs , free = , colors = Blue , website uni.wroc.pl The University of Wrocław ( pl, Uniwersytet Wrocławski, U ...
but switched to mathematics to avoid the drudgery of astronomical calculations. He discovered a natural ability through his friendship with
Jan Mycielski Jan Mycielski (born February 7, 1932 in Wiśniowa, Podkarpackie Voivodeship, Poland)Curriculum vitae
from ...
and was able to remain at Wrocław to complete his masters under
Jan Mikusiński Jan Mikusiński (April 3, 1913 Stanisławów – July 27, 1987 Katowice) was a Polish mathematician based at the University of Wrocław known for his pioneering work in mathematical analysis. Mikusiński developed an operational calculus – know ...
. He graduated with a PhD in 1960, his dissertation including the now-famous Three-Distance Theorem, which he proved in 1956 in answer to a question of Hugo Steinhaus.


Noted mathematical results

The
three-gap theorem In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places points on a circle, at angles of , , , ... from the starting point, then there will be at most three distinct distances between pairs ...
says: take arbitrarily finitely many integer multiples of an irrational number between zero and one and plot them as points around a circle of unit circumference; then at most three different distances will occur between consecutive points. This answered a question of Hugo Steinhaus. The theorem belongs to the field of
Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by ...
since the smallest of the three distances observed may be used to give a rational approximation to the chosen irrational number. It has been extended and generalised in many ways. The Non-Tetratorus Theorem, published by Świerczkowski in 1958, states that it is impossible to construct a closed chain (torus) of regular
tetrahedra In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...
, placed face to face. Again this answered a question of Hugo Steinhaus. The result is attractive and counter-intuitive, since the tetrahedron is unique among the
Platonic solids In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all e ...
in having this property. Recent work by Michael Elgersma and
Stan Wagon Stanley Wagon is a Canadian- American mathematician, a professor of mathematics at Macalester College in Minnesota. He is the author of multiple books on number theory, geometry, and computational mathematics, and is also known for his snow sculp ...
has sparked new interest in this result by showing that one can create chains of tetrahedra that are arbitrarily close to being closed. In 1964, in a joint work with
Jan Mycielski Jan Mycielski (born February 7, 1932 in Wiśniowa, Podkarpackie Voivodeship, Poland)Curriculum vitae
from ...
, he established one of the early results on the
axiom of determinacy In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person topological games of length ω. AD states that every game o ...
(AD), namely that AD implies that all sets of
real number In mathematics, a real number is a number that can be used to measurement, measure a ''continuous'' one-dimensional quantity such as a distance, time, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small var ...
s are
Lebesgue measurable In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of ''n''-dimensional Euclidean space. For ''n'' = 1, 2, or 3, it coincides ...
. Świerczkowski's last mathematical work was on proving
Gödel's incompleteness theorems Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the phil ...
using
hereditarily finite set In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite, and all of its elements are finite sets, recursively all the way down to ...
s instead of encoding of finite sequences of natural numbers. It is these proofs that were the basis for the production, in 2015, of mechanised proofs of Gödel's two famous theorems.


Career

Świerczkowski had a very migratory career. He was allowed abroad from Poland to study at
Dundee University , mottoeng = "My soul doth magnify the Lord" , established = 1967 – gained independent university status by Royal Charter1897 – Constituent college of the University of St Andrews1881 – University College , ...
where his work with
Alexander Murray MacBeath Alexander Murray Macbeath (30 June 1923 Glasgow – 14 May 2014 Warwick) was a mathematician who worked on Riemann surfaces. Macbeath surfaces and Macbeath regions are named after him. Early life and education Macbeath was the son of Alexan ...
would later attract the attention of
André Weil André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the ''de facto'' early leader of the mathematical Bourbaki group. ...
. He then took up a research fellowship at
Glasgow University , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...
before being obliged to return to Poland. When the
Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of ...
granted him a passport to attend a conference in Stuttgart he used this as an opportunity to leave Poland for good in 1961, first resuming his fellowship in Glasgow before taking a job in the recently created
University of Sussex , mottoeng = Be Still and Know , established = , type = Public research university , endowment = £14.4 million (2020) , budget = £319.6 million (2019–20) , chancellor = Sanjeev Bhaskar , vice_chancellor = Sasha Roseneil , ...
. In 1963 he visited André Weil at the
Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
and thereafter, between 1964 and 1973, held posts at the
University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seat ...
, the
Australian National University The Australian National University (ANU) is a public research university located in Canberra, the capital of Australia. Its main campus in Acton encompasses seven teaching and research colleges, in addition to several national academies and ...
and
Queen's University Queen's or Queens University may refer to: * Queen's University at Kingston, Ontario, Canada *Queen's University Belfast, Northern Ireland, UK ** Queen's University of Belfast (UK Parliament constituency) (1918–1950) **Queen's University of Belfa ...
in Canada. In 1973 he left mathematics, moved to the Netherlands and built a yacht in which he sailed around the world for ten years. The period 1986 to 1997 was again spent teaching mathematics, at
Sultan Qaboos University Sultan Qaboos University, located in Al Seeb in the Muscat Governorate, is one of the two public universities in the Sultanate of Oman. Most students entering the university are selected based on their performance in high school final examina ...
. His last post was at the
University of Colorado at Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado s ...
(1998–2001). Thereafter he retired to
Tasmania ) , nickname = , image_map = Tasmania in Australia.svg , map_caption = Location of Tasmania in AustraliaCoordinates: , subdivision_type = Country , subdi ...
.


References


External links

* * {{DEFAULTSORT:Swierczkowski, Stanislaw 1932 births 2015 deaths People from Toruń Polish mathematicians Alumni of the University of Glasgow University of Washington faculty Australian National University faculty Queen's University at Kingston faculty Sultan Qaboos University faculty University of Colorado Boulder faculty