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{{Short description|Polish mathematician (1932–2015)}}
{{AFC submission|t||ts=20160423134019|u=Charleswallingford|ns=118|demo=}} <!--- Important, do not remove this line before article has been created. --->
{{EngvarB|date=March 2018}}
{{Use dmy dates|date=March 2018}}
{{Infobox scientist
{{Infobox scientist
| name = Stanisław Świerczkowski
| name = Stanisław Świerczkowski
| image =
| image =
| image_size =
| image_size =
| caption =
| caption =
| birth_date = {{birth date|1932|7|16|mf=y}}
| birth_date = {{birth date|df=y|1932|7|16}}
| birth_place = [[Toruń, Poland]]
| birth_place = [[Toruń]], Poland
| death_date = {{death date and age|2015|9|30|1932|7|16}}
| death_date = {{death date and age|df=y|2015|9|30|1932|7|16}}
| death_place = [[Australia]]
| death_place = [[Australia]]
| residence = [[Australia]]
| nationality = [[Poland|Polish]]
| nationality = Polish
| field = Mathematics
⚫
| work_institution = [[Glasgow University]], [[University of Sussex]], [[University of Washington]], [[Australian National University]], [[Sultan Qaboos University]], [[Queen's University at Kingston|Queen's University]], [[University of Colorado at Boulder]]
| field = Mathematics
⚫
| alma_mater = [[University of Wroclaw]],
⚫
| work_institution = [[Glasgow University]], [[University of Sussex]], [[University of Washington]], [[Australian National University]], [[Sultan Qaboos University]], [[Queen’s University]], [[University of Colorado at Boulder]]
⚫
| doctoral_advisor = [[Hugo Steinhaus]]
⚫
| alma_mater = [[University of Wroclaw]],
| doctoral_students =
⚫
| doctoral_advisor = [[Hugo Steinhaus]]
| doctoral_students = [[Robert Walters]]
| known_for = [[Three-gap theorem]], [[Non-tetratorus theorem]]
⚫
| prizes = [[Foundation of Alfred Jurzykowski]] (1996)<ref>{{cite journal|author=Jerzy Krzywicki|title=Nagrody Fundacji Jurzykowskiego w matematyce|journal=Roczniki Polskiego Towarzystwa Matematycznego Seria II: Wiadomo Sci Matematyczne XXXVI|volume=73|year=2000|pages=115–138|url=http://www.wmi.uni.wroc.pl/sites/default/files/upload_attach/163-168_jk_wm36.pdf}}</ref>
| known_for = [[Three-Distance Theorem, Non-Tetratorus Theorem]]
| religion =
⚫
| prizes = [[Foundation of Alfred Jurzykowski]] (1996)<ref>{{cite journal|author=Jerzy Krzywicki|title=Nagrody Fundacji Jurzykowskiego w matematyce|journal=Roczniki Polskiego Towarzystwa Matematycznego Seria II: Wiadomo Sci Matematyczne XXXVI|volume=73|year=2000|pages=115–138|url=http://www.wmi.uni.wroc.pl/sites/default/files/upload_attach/163-168_jk_wm36.pdf}}</ref>
| religion =
| footnotes =
| footnotes =
| spouse =
| spouse =
| children = 2
| children = 1 son, 1 daughter
}}
}}


'''Stanisław (Stash) Świerczkowski''' (July 16, 1932 – September 30, 2015) was a Polish [[mathematician]] famous for his solutions to two iconic problems posed by [[Hugo Steinhaus]]: the Three-Distance (or Three-Gaps) Theorem and the Non-Tetratorus Theorem.
'''Stanisław (Stash) Świerczkowski''' (16 July 1932 – 30 September 2015) was a [[Polish people|Polish]] [[mathematician]] famous for his solutions to two iconic problems posed by [[Hugo Steinhaus]]: the [[three-gap theorem]] and the non-tetratorus theorem.


==Early life and education==
==Early life and education==
Stanisław (Stash) Świerczkowski was born in [[Toruń]], 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]]. 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]] 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.
Stanisław (Stash) Świerczkowski was born in [[Toruń]], 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]]. 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]] 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 at the [[University of Wrocław]] but switched to mathematics to avoid the drudgery of astronomical calculations. He discovered a natural ability through his friendship with [[Jan Mycielski]] and was able to remain at Wrocław to complete his masters under [[Jan Mikusiński]]. 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.
Świerczkowski won a university place to study [[astronomy]] at the [[University of Wrocław]] but switched to mathematics to avoid the drudgery of astronomical calculations. He discovered a natural ability through his friendship with [[Jan Mycielski]] and was able to remain at Wrocław to complete his masters under [[Jan Mikusiński]]. He graduated with a PhD in 1960, his dissertation including the now-famous three-gap theorem, which he proved in 1956 in answer to a question of Hugo Steinhaus.


==Noted Mathematical Results==
==Noted mathematical results==
The Three-Distance (or Three-Gaps) Theorem<ref>[http://www.theoremoftheday.org/Theorems.html#78 Three-Distance Theorem at Theorem of the Day]</ref> says: take arbitrarily 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]] 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 generalized in many ways<ref>{{cite journal|author=Alessandri,P. and Berthé, V.|title=Three distance theorems and combinatorics on words|journal=L'Enseignement Mathématique|volume=44|year=1998|pages=103–132}}</ref>.
The [[three-gap theorem]]<ref>[http://www.theoremoftheday.org/Theorems.html#78 Three-Distance Theorem at Theorem of the Day]</ref> 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]] 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.<ref>{{cite journal|author=Alessandri, P., and [[Valérie Berthé|Berthé, V.]]|title=Three distance theorems and combinatorics on words|journal=L'Enseignement Mathématique|volume=44|year=1998|pages=103–132}}</ref>


The Non-Tetratorus Theorem, published by Świerczkowski in 1958<ref>{{cite journal|author=Świerczkowski, S.|title=On a free group of rotations of the Euclidean space|journal=Indagationes Mathematicae|volume=61|year=1958|pages=376-378\url=http://www.sciencedirect.com/science/article/pii/S1385725858500511}}</ref>
The non-tetratorus theorem, published by Świerczkowski in 1958,<ref>{{cite journal|author=Świerczkowski, S.|title=On a free group of rotations of the Euclidean space|journal=[[Indagationes Mathematicae]]|volume=61|year=1958|pages=376–378|doi=10.1016/s1385-7258(58)50051-1|doi-access=free}}</ref>
says that it is impossible to construct a closed chain (torus) of regular [[tetrahedra]], 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 having this property. Recent work
states that it is impossible to construct a closed chain (torus) of regular [[tetrahedra]], 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 having this property. Recent work
<ref>{{cite journal|author=Elgersma ,M. and Wagon, S.|title=Closing a Platonic gap|journal=The Mathematical Intelligencer|volume=37, no. 1|year=2015|pages=54–61}}</ref> by Michael Elgersma and [[Stan Wagon]] has sparked new interest in this result by showing that, experimentally, one can create chains of tetrahedra which are arbitrarily close to be being closed.
<ref>{{cite journal|author1=Elgersma, M. |author2=Wagon, S. |name-list-style=amp |title=An asymptotically closed loop of tetrahedra|journal=[[The Mathematical Intelligencer]]|volume=39| issue = 3|year=2017|pages=40–45|doi= 10.1007/s00283-016-9696-4|s2cid=253818257 }}</ref> by Michael Elgersma and [[Stan Wagon]] 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]], he established one of the early results on the [[axiom of determinacy]] (AD), namely that AD implies that all sets of [[real number]]s are [[Lebesgue measurable]].<ref>{{cite journal|author=Mycielski J. and Świerczkowski, S.|title=On the Lebesgue measurability and the axiom of determinateness|journal=[[Fund. Math.]]|volume=54|
year=1964|pages=67–71|doi=10.4064/fm-54-1-67-71|doi-access=free}}</ref>

Świerczkowski's last mathematical work<ref>{{cite journal|author=Świerczkowski, S.|title=Finite sets and Gödel's incompleteness theorems|journal=Dissertationes Mathematicae|volume=422|year=2003|pages=1–58|doi=10.4064/dm422-0-1|doi-access=free}}</ref> was on proving [[Gödel's incompleteness theorems]] using [[hereditarily finite set]]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.<ref>{{cite journal|author=Lawrence C. Paulson|authorlink = Lawrence Paulson|title=A Mechanised Proof of Gödel's Incompleteness Theorems Using Nominal Isabelle|journal=[[Journal of Automated Reasoning]]|volume=55| issue = 1|year=2015|pages=1–37|doi=10.1007/s10817-015-9322-8| arxiv=2104.13792 |citeseerx=10.1.1.697.5227| s2cid=254604706 }}</ref>


==Career==
==Career==
Świerczkowski had a very peripatetic career. He was allowed abroad from Poland to study at [[Dundee University]] where his work with [[Alexander Murray MacBeath]] would later attract the attention of [[André Weil]]. He then took up a lecturing post at [[Glasgow University]] before being obliged to return to Poland. When the [[Polish Academy of Sciences]] 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 lectureship in Glasgow before taking a job in the recently created [[University of Sussex]]. In 1963 he visited André Weil at the [[Institute for Advanced Studies]] and thereafter, between 1964 and 1973, held posts at the [[University of Washington]], the [[Australian National University]] and [[Queen’s University]] 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]]. His last post was at the [[University of Colorado at Boulder]] (1998-2001. Thereafter he retired to [[Tasmania]].
Świerczkowski had a very migratory career. He was allowed abroad from Poland to study at [[Dundee University]], where his work with [[Alexander Murray MacBeath]] would later attract the attention of [[André Weil]]. He then took up a research fellowship at [[Glasgow University]] before being obliged to return to Poland. When the [[Polish Academy of Sciences]] 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]]. In 1963 he visited André Weil at the [[Institute for Advanced Study]] and thereafter, between 1964 and 1973, held posts at the [[University of Washington]], the [[Australian National University]] and [[Queen's University at Kingston|Queen's University]] 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]]. His last post was at the [[University of Colorado at Boulder]] (1998–2001). Thereafter he retired to [[Tasmania]].


==References==
==References==
{{reflist}}
{{Reflist}}

<!--- After listing your sources please cite them using inline citations and place them after the information they cite. Please see https://en.wikipedia.org/wiki/Wikipedia:REFB for instructions on how to add citations. --->
==External links==
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{{Wikiquote}}
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* {{MathGenealogy|id=106488}}
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* {{MacTutor Biography|id=Swierczkowski}}

{{Authority control}}


{{DEFAULTSORT:Swierczkowski, Stanislaw}}
{{AFC submission|||ts=20160423172728|u=Charleswallingford|ns=118}}
[[Category:1932 births]]
[[Category:2015 deaths]]
[[Category:People from Toruń]]
[[Category:Polish mathematicians]]
[[Category:Alumni of the University of Glasgow]]
[[Category:University of Washington faculty]]
[[Category:Academic staff of the Australian National University]]
[[Category:Academic staff of Queen's University at Kingston]]
[[Category:Academic staff of Sultan Qaboos University]]
[[Category:University of Colorado Boulder faculty]]

Latest revision as of 19:07, 25 December 2023

Stanisław Świerczkowski
Born(1932-07-16)16 July 1932
Toruń, Poland
Died30 September 2015(2015-09-30) (aged 83)
Australia
NationalityPolish
Alma materUniversity of Wroclaw,
Known forThree-gap theorem, Non-tetratorus theorem
Children2
AwardsFoundation of Alfred Jurzykowski (1996)[1]
Scientific career
FieldsMathematics
InstitutionsGlasgow University, University of Sussex, University of Washington, Australian National University, Sultan Qaboos University, Queen's University, University of Colorado at Boulder
Doctoral advisorHugo Steinhaus

Stanisław (Stash) Świerczkowski (16 July 1932 – 30 September 2015) was a Polish mathematician famous for his solutions to two iconic problems posed by Hugo Steinhaus: the three-gap theorem and the non-tetratorus theorem.

Early life and education

[edit]

Stanisław (Stash) Świerczkowski was born in Toruń, 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. 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 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 at the University of Wrocław but switched to mathematics to avoid the drudgery of astronomical calculations. He discovered a natural ability through his friendship with Jan Mycielski and was able to remain at Wrocław to complete his masters under Jan Mikusiński. He graduated with a PhD in 1960, his dissertation including the now-famous three-gap theorem, which he proved in 1956 in answer to a question of Hugo Steinhaus.

Noted mathematical results

[edit]

The three-gap theorem[2] 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 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.[3]

The non-tetratorus theorem, published by Świerczkowski in 1958,[4] states that it is impossible to construct a closed chain (torus) of regular tetrahedra, 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 having this property. Recent work [5] by Michael Elgersma and Stan Wagon 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, he established one of the early results on the axiom of determinacy (AD), namely that AD implies that all sets of real numbers are Lebesgue measurable.[6]

Świerczkowski's last mathematical work[7] was on proving Gödel's incompleteness theorems using hereditarily finite sets 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.[8]

Career

[edit]

Świerczkowski had a very migratory career. He was allowed abroad from Poland to study at Dundee University, where his work with Alexander Murray MacBeath would later attract the attention of André Weil. He then took up a research fellowship at Glasgow University before being obliged to return to Poland. When the Polish Academy of Sciences 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. In 1963 he visited André Weil at the Institute for Advanced Study and thereafter, between 1964 and 1973, held posts at the University of Washington, the Australian National University and Queen's University 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. His last post was at the University of Colorado at Boulder (1998–2001). Thereafter he retired to Tasmania.

References

[edit]
  1. ^ Jerzy Krzywicki (2000). "Nagrody Fundacji Jurzykowskiego w matematyce" (PDF). Roczniki Polskiego Towarzystwa Matematycznego Seria II: Wiadomo Sci Matematyczne XXXVI. 73: 115–138.
  2. ^ Three-Distance Theorem at Theorem of the Day
  3. ^ Alessandri, P., and Berthé, V. (1998). "Three distance theorems and combinatorics on words". L'Enseignement Mathématique. 44: 103–132.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  4. ^ Świerczkowski, S. (1958). "On a free group of rotations of the Euclidean space". Indagationes Mathematicae. 61: 376–378. doi:10.1016/s1385-7258(58)50051-1.
  5. ^ Elgersma, M. & Wagon, S. (2017). "An asymptotically closed loop of tetrahedra". The Mathematical Intelligencer. 39 (3): 40–45. doi:10.1007/s00283-016-9696-4. S2CID 253818257.
  6. ^ Mycielski J. and Świerczkowski, S. (1964). "On the Lebesgue measurability and the axiom of determinateness". Fund. Math. 54: 67–71. doi:10.4064/fm-54-1-67-71.
  7. ^ Świerczkowski, S. (2003). "Finite sets and Gödel's incompleteness theorems". Dissertationes Mathematicae. 422: 1–58. doi:10.4064/dm422-0-1.
  8. ^ Lawrence C. Paulson (2015). "A Mechanised Proof of Gödel's Incompleteness Theorems Using Nominal Isabelle". Journal of Automated Reasoning. 55 (1): 1–37. arXiv:2104.13792. CiteSeerX 10.1.1.697.5227. doi:10.1007/s10817-015-9322-8. S2CID 254604706.
[edit]
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