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'''Craig S. Kaplan''' is a Canadian [[computer scientist]], [[mathematician]], and [[Mathematics and art|mathematical artist]]. He is an editor of the ''[[Journal of Mathematics and the Arts]]'' (formerly chief editor), and an organizer of the [[Bridges Conference]] on mathematics and art.<ref>
'''Craig S. Kaplan''' is a Canadian [[computer scientist]], [[mathematician]], and [[Mathematics and art|mathematical artist]]. He is an editor of the ''[[Journal of Mathematics and the Arts]]'' (formerly chief editor), and an organizer of the [[Bridges Conference]] on mathematics and art.{{r|fenyvesi}} He is an associate professor of computer science at the [[University of Waterloo]], Canada.
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{{cite journal |last=Fenyvesi |first=Kristóf |title=Bridges: A world community for mathematical art |journal=The Mathematical Intelligencer |volume=38 |number=2 |year=2016 |pages=35–45}}</ref> He is an associate professor of computer science at the [[University of Waterloo]], Canada.


Kaplan's work primarily focuses on applications of geometry and computer science to visual art and design. He was part of the team that proved that the tile discovered by hobbyist [[David Smith (hobbyist)|David Smith]] is a solution to the [[einstein problem]], a single shape which [[aperiodic tiling|aperiodically tiles]] the plane but cannot do so periodically.<ref name=cantor>{{Cite news |last=Cantor |first=Matthew |date=2023-04-04 |title=‘The miracle that disrupts order’: mathematicians invent new ‘einstein’ shape |language=en-GB |work=The Guardian |url=https://www.theguardian.com/science/2023/apr/03/new-einstein-shape-aperiodic-monotile |access-date=2023-08-07 |issn=0261-3077}}</ref><ref>{{Cite news |date=2023-03-28 |title=Elusive ‘Einstein’ Solves a Longstanding Math Problem |language=en |url=https://www.nytimes.com/2023/03/28/science/mathematics-tiling-einstein.html |access-date=2023-08-07}}</ref><ref>{{Cite web |date=2023-04-04 |title=Hobbyist Finds Math’s Elusive ‘Einstein’ Tile |url=https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/ |access-date=2023-09-05 |language=en}}</ref><ref>{{Cite web |date=2023-04-10 |title=Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern |url=https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/ |access-date=2023-09-05 |language=en}}</ref><ref>{{Cite web |date=2023-06-26 |title= Discovery of the Aperiodic Monotile - Numberphile |url=https://www.youtube.com/watch?v=_ZS3Oqg1AX0|access-date=2023-09-05 |language=en}}</ref>
Kaplan's work primarily focuses on applications of geometry and computer science to visual art and design. He was part of the team that proved that the tile discovered by hobbyist [[David Smith (hobbyist)|David Smith]] is a solution to the [[einstein problem]], a single shape which [[aperiodic tiling|aperiodically tiles]] the plane but cannot do so periodically.<ref name=cantor>{{Cite news |last=Cantor |first=Matthew |date=2023-04-04 |title=‘The miracle that disrupts order’: mathematicians invent new ‘einstein’ shape |language=en-GB |work=The Guardian |url=https://www.theguardian.com/science/2023/apr/03/new-einstein-shape-aperiodic-monotile |access-date=2023-08-07 |issn=0261-3077}}</ref><ref>{{Cite news |date=2023-03-28 |title=Elusive ‘Einstein’ Solves a Longstanding Math Problem |language=en |url=https://www.nytimes.com/2023/03/28/science/mathematics-tiling-einstein.html |access-date=2023-08-07}}</ref><ref>{{Cite web |date=2023-04-04 |title=Hobbyist Finds Math’s Elusive ‘Einstein’ Tile |url=https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/ |access-date=2023-09-05 |language=en}}</ref><ref>{{Cite web |date=2023-04-10 |title=Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern |url=https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/ |access-date=2023-09-05 |language=en}}</ref><ref>{{Cite web |date=2023-06-26 |title= Discovery of the Aperiodic Monotile - Numberphile |url=https://www.youtube.com/watch?v=_ZS3Oqg1AX0|access-date=2023-09-05 |language=en}}</ref>
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== References ==
== References ==
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{{cite journal |last=Fenyvesi |first=Kristóf |title=Bridges: A world community for mathematical art |journal=The Mathematical Intelligencer |volume=38 |number=2 |year=2016 |pages=35–45 |doi=10.1007/s00283-016-9630-9 |url=https://www.kristoffenyvesi.hu/documents/bridges/HistoryOfBridgesCommunityMathematicalIntelligencerFenyvesi.pdf }}
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Revision as of 17:42, 14 September 2023

Craig S. Kaplan
EducationUniversity of Waterloo (BMath), University of Washington (MSc, PhD)
OccupationAssociate Professor
Known forEinstein problem
Scientific career
FieldsMathematics, Computer Science
InstitutionsUniversity of Waterloo
Websitehttps://isohedral.ca/

Craig S. Kaplan is a Canadian computer scientist, mathematician, and mathematical artist. He is an editor of the Journal of Mathematics and the Arts (formerly chief editor), and an organizer of the Bridges Conference on mathematics and art.[1] He is an associate professor of computer science at the University of Waterloo, Canada.

Kaplan's work primarily focuses on applications of geometry and computer science to visual art and design. He was part of the team that proved that the tile discovered by hobbyist David Smith is a solution to the einstein problem, a single shape which aperiodically tiles the plane but cannot do so periodically.[2][3][4][5][6]

Education

Kaplan received BMath from the University of Waterloo in 1996. He further went on to receive MSc and PhD in computer science from University of Washington in 1998 and 2002, respectively.[7]

Work

Kaplan's research work focuses on the application of computer graphics and mathematics in art and design. He is an expert on computational applications of tiling theory.

Exotic geometries in protein assembly

In 2019, Kaplan helped to apply the concepts of Archimedean solids to protein assembly, and together with an experimental team at RIKEN demonstrated that these exotic geometries lead to ultra-stable macromolecular cages.[8][9] These new systems could have applications in targeted drug delivery systems or the design of new materials at the nanoscale.[10]

Solving the einstein problem

In 2023, Kaplan was part of the team that solved the einstein problem, a major open problem in tiling theory and Euclidean geometry. The einstein problem can be seen as a natural extension of the second part of Hilbert's eighteenth problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral.[11] The discovery is under professional review and, upon confirmation, will be credited as solving a longstanding mathematical problem.[12]

One of the infinite family of Smith–Myers–Kaplan–Goodman-Strauss tiles, found in March 2023.

'Hat' tile

In March 2023, Kaplan along with David Smith, Joseph Samuel Myers and Chaim Goodman-Strauss, announced the proof that the tile discovered by David Smith is an aperiodic monotile, i.e., a solution to the einstein problem, a problem that seeks the existence of any single shape aperiodic tile. The shape was dubbed the "hat" tile and has 13 sides.[13][2][14]

'Spectre' tile

In May 2023, the same team posted a new preprint about a family of shapes, called "spectres" (also discovered by Smith) which is related to the "hat" family of tiles. The "spectre" tile is a "strictly chiral" aperiodic monotile: even if reflections are allowed, every tiling is non-periodic and uses only one chirality of the spectre.[15][16] This new shape tiles a plane in a pattern that never repeats without the use of mirror images of the shape, hence been called a "vampire einstein".[17]

References

  1. ^ Fenyvesi, Kristóf (2016). "Bridges: A world community for mathematical art" (PDF). The Mathematical Intelligencer. 38 (2): 35–45. doi:10.1007/s00283-016-9630-9.
  2. ^ a b Cantor, Matthew (2023-04-04). "'The miracle that disrupts order': mathematicians invent new 'einstein' shape". The Guardian. ISSN 0261-3077. Retrieved 2023-08-07.
  3. ^ "Elusive 'Einstein' Solves a Longstanding Math Problem". 2023-03-28. Retrieved 2023-08-07.
  4. ^ "Hobbyist Finds Math's Elusive 'Einstein' Tile". 2023-04-04. Retrieved 2023-09-05.
  5. ^ "Newfound Mathematical 'Einstein' Shape Creates a Never-Repeating Pattern". 2023-04-10. Retrieved 2023-09-05.
  6. ^ "Discovery of the Aperiodic Monotile - Numberphile". 2023-06-26. Retrieved 2023-09-05.
  7. ^ "Craig S. Kaplan". Cheriton School of Computer Science. 2017-02-08. Retrieved 2023-08-06.
  8. ^ "An ultra-stable gold-coordinated protein cage displaying reversible assembly". Nature. 2019-05-08. Retrieved 2023-07-09.
  9. ^ "Protein assembles into Archimedean geometry". Nature. 2019-05-08. Retrieved 2023-07-09.
  10. ^ "Complex polyhedron assembled from proteins". Chemical & Engineering News. 2019-05-11. Retrieved 2023-07-09.
  11. ^ Senechal, Marjorie (1996) [1995]. Quasicrystals and Geometry (corrected paperback ed.). Cambridge University Press. pp. 22–24. ISBN 0-521-57541-9.
  12. ^ Roberts, Soibhan, Elusive 'Einstein' Solves a Longstanding Mathematical Problem, the New York Times, March 28, 2023, with image of the pattern
  13. ^ Bischoff, Manon. "Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern". Scientific American. Retrieved 2023-07-09.
  14. ^ Prisco, Jacopo (2023-04-06). "Newly discovered 'einstein' shape can do something no other tile can do". CNN. Retrieved 2023-08-07.
  15. ^ Roberts, Siobhan (2023-06-01). "With a New, Improved 'Einstein,' Puzzlers Settle a Math Problem". The New York Times. ISSN 0362-4331. Retrieved 2023-07-09.
  16. ^ "Spectre: The deceptively simple shape that's taken mathematics by storm". The Hindu. 2023-06-20. ISSN 0971-751X. Retrieved 2023-07-09.
  17. ^ "The vampire einstein". Waterloo News. 2023-07-04. Retrieved 2023-07-09.
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