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| thesis_title = Reflection and Transmission of Electromagnetic Waves by Thin Curved Shells<ref name="math">{{MathGenealogy|id=13411}}</ref>
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{{Short description|American mathematician (1923–2016)}}
{{Infobox scientist
{{Infobox scientist
| name = Joseph Bishop Keller
| name = Joseph Bishop Keller
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| birth_date = {{Birth date|1923|7|31|mf=y}}
| birth_date = {{Birth date|1923|7|31|mf=y}}
| birth_place = [[Paterson, New Jersey]], U.S.
| birth_place = [[Paterson, New Jersey]], U.S.
| residence = United States
| nationality = American
| nationality = American
| death_date = {{Death date and age|2016|9|7|1923|7|31|mf=y}}
| death_date = {{Death date and age|2016|9|7|1923|7|31|mf=y}}
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| work_institutions = [[New York University]]<br />[[Stanford University]]
| work_institutions = [[New York University]]<br />[[Stanford University]]
| alma_mater = [[New York University]]
| alma_mater = [[New York University]]
| thesis_title = [[Reflection (physics)|Reflection]] and [[Transmission (telecommunications)|Transmission]] of [[Electromagnetic Waves]] by Thin Curved Shells<ref name="math">{{MathGenealogy|id=13411}}</ref>
| thesis_title = Reflection and transmission of electromagnetic waves by thin curved shells<ref name="math">{{MathGenealogy|id=13411}}</ref>
| doctoral_advisor = [[Richard Courant]]<ref name="math"/>
| doctoral_advisor = [[Richard Courant]]<ref name="math"/>
| doctoral_students = [[Herbert Bishop Keller]]<br/>[[George C. Papanicolaou]]<br/> [[L. Mahadevan]]
| doctoral_students = [[Herbert Bishop Keller]]<br/>[[George C. Papanicolaou]]<br/>[[Bernard J. Matkowsky]]<br/> [[L. Mahadevan]]
| known_for =Geometrical theory of diffraction<br />[[Einstein–Brillouin–Keller method]]
| known_for ={{no wrap|[[Diffraction#Babinet's_principle|Geometrical theory of diffraction]]}}<br />[[Mechanism_of_sonoluminescence#Keller–Miksis_formulation|Keller–Miksis formulation]]<br/>[[Einstein–Brillouin–Keller method]]
| prizes = [[Eringen Medal]] {{small|(1981)}} <br> [[Timoshenko Medal]] {{small|(1984)}}<br>[[National Medal of Science]] (USA) in Mathematical, Statistical, and Computational Sciences {{small|(1988)}} <br />[[Nemmers Prize in Mathematics]] {{small|(1996)}}<br /> [[Wolf Prize]] {{small|(1997)}}
| prizes = [[Paul R. Halmos – Lester R. Ford Award|Lester R. Ford Award]] {{small|(1976, 1977)}}<br/>[[Josiah Willard Gibbs Lectureship|Gibbs Lecture]] {{small|(1977)}} <br/>[[Eringen Medal]] {{small|(1981)}} <br/> [[John von Neumann Prize]] {{small|(1983)}} <br/>[[Timoshenko Medal]] {{small|(1984)}}<br>[[National Medal of Science]] {{small|(1988)}} <br />[[List of International Congresses of Mathematicians Plenary and Invited Speakers|ICM Speaker]] {{small|(1994)}}<br/>{{no wrap|[[Nemmers Prize in Mathematics]] {{small|(1996)}}}}<br /> [[Wolf Prize in Mathematics|Wolf Prize]] {{small|(1997)}} <br/>[[Ig Nobel Prize]] {{small|(1999, 2012)}}
| footnotes =
| footnotes =
}}
}}


'''Joseph Bishop Keller''' (July 31, 1923 &ndash; September 7, 2016) was an American [[mathematician]] who specialized in [[applied mathematics]]. He was best known for his work on the "geometrical theory of diffraction" (GTD).<ref>{{cite journal |first=J.B. |last=Keller |title=Geometrical theory of diffraction |journal=J. Opt. Soc. Am. |volume=52 |issue=2 |pages=116–130 |year=1962 |doi=10.1364/JOSA.52.000116 |url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-52-2-116}}</ref>
'''Joseph Bishop Keller''' (July 31, 1923 &ndash; September 7, 2016) was an American [[mathematician]] who specialized in [[applied mathematics]]. He was best known for his work on the "geometrical theory of diffraction" (GTD).<ref>{{cite journal |first=J.B. |last=Keller |title=Geometrical theory of diffraction |journal=J. Opt. Soc. Am. |volume=52 |issue=2 |pages=116–130 |year=1962 |doi=10.1364/JOSA.52.000116 |pmid=14454948 }}</ref>


==Early life and education==
==Early life and education==
Born in [[Paterson, New Jersey]] on July 31, 1923, Keller attended [[Eastside High School (Paterson, New Jersey)|Eastside High School]], where he was a member of the math team.<ref>Roberts, Sam. [https://www.nytimes.com/2016/09/17/us/joseph-b-keller-mathematician-with-whimsical-curiosity-dies-at-93.html "Joseph B. Keller, Mathematician With Whimsical Curiosity, Dies at 93"], ''[[The New York Times]]'', September 16, 2016. Accessed September 19, 2016. "Joseph Bishop Keller was born in Paterson, N.J., on July 31, 1923. His father, Isaac Keiles — whose name, he said, was changed when he arrived in the United States — was a Russian refugee who fled pogroms against Jews.... Joseph Keller competed on the math team at East Side High School in Paterson."</ref> After earning his undergraduate degree in 1943 at [[New York University]], Keller obtained his PhD in 1948 from NYU under the supervision of [[Richard Courant]]. He was a Professor of Mathematics in the [[Courant Institute]] at New York University until 1979. Then he was Professor of Mathematics and Mechanical Engineering at [[Stanford University]] until 1993, when he became [[Professor Emeritus]].
Born in [[Paterson, New Jersey]] on July 31, 1923, Keller attended [[Eastside High School (Paterson, New Jersey)|Eastside High School]], where he was a member of the math team.<ref>Roberts, Sam. [https://www.nytimes.com/2016/09/17/us/joseph-b-keller-mathematician-with-whimsical-curiosity-dies-at-93.html "Joseph B. Keller, Mathematician With Whimsical Curiosity, Dies at 93"], ''[[The New York Times]]'', September 16, 2016. Accessed September 19, 2016. "Joseph Bishop Keller was born in Paterson, N.J., on July 31, 1923. His father, Isaac Keiles — whose name, he said, was changed when he arrived in the United States — was a Russian refugee who fled pogroms against Jews.... Joseph Keller competed on the math team at East Side High School in Paterson."</ref> After earning his undergraduate degree in 1943 at [[New York University]], Keller obtained his PhD in 1948 from NYU under the supervision of [[Richard Courant]]. He was a professor of mathematics in the [[Courant Institute]] at New York University until 1979. Then he was Professor of Mathematics and Mechanical Engineering at [[Stanford University]] until 1993, when he became [[professor emeritus]].


==Research==
==Research==
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==Awards and honors==
==Awards and honors==
Keller was awarded a [[Lester R. Ford Award]] (shared with David W. McLaughlin) in 1976<ref>{{cite journal|author=Keller, Joseph B.|author2=McLaughlin, David W.|title=The Feynman Integral|journal=Amer. Math. Monthly|year=1975|volume=82|issue=5|pages=451–465|url=http://www.maa.org/programs/maa-awards/writing-awards/the-feynman-integral|doi=10.2307/2319736|jstor=2319736}}</ref> and unshared in 1977.<ref>{{cite journal|author=Keller, Joseph B.|title=Inverse Problem|journal=Amer. Math. Monthly|year=1976|volume=83|pages=107–118|url=http://www.maa.org/programs/maa-awards/writing-awards/inverse-problems}}</ref> In 1988 he was awarded the U.S. [[National Medal of Science]], and in 1997 he was awarded the [[Wolf Prize]] by the Israel-based [[Wolf Foundation]]. In 1996, he was awarded the [[Nemmers Prize in Mathematics]]. In 1999 he was awarded the [[Ig Nobel Prize]] for calculating how to make a teapot spout that does not drip. With Patrick B. Warren, Robin C. Ball and [[Raymond E. Goldstein]], Keller was awarded an [[Ig Nobel Prize]] in 2012 for calculating the forces that shape and move [[ponytail]] hair.<ref name=ignobelpaper>{{Cite journal | last1 = Goldstein | first1 = R. | authorlink1 = Raymond E. Goldstein| last2 = Warren | first2 = P. | last3 = Ball | first3 = R. | title = Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles | doi = 10.1103/PhysRevLett.108.078101 | journal = Physical Review Letters | volume = 108 | issue = 7 | year = 2012 | pmid = 22401258| pmc = | url = http://www.damtp.cam.ac.uk/user/gold/pdfs/ponytail_prl.pdf|arxiv = 1204.0371 |bibcode = 2012PhRvL.108g8101G | page=078101}}</ref><ref name=ignobelcam>{{cite web|archiveurl=https://web.archive.org/web/20130203233116/http://www.damtp.cam.ac.uk/comms/110.html|archivedate=2013-02-03|url=http://www.damtp.cam.ac.uk/comms/110.html|publisher=University of Cambridge|title=Ray Goldstein Shares 2012 Ig Nobel Prize for Physics}}</ref>
Keller was awarded a [[Lester R. Ford Award]] (shared with David W. McLaughlin) in 1976<ref>{{cite journal|author=Keller, Joseph B.|author2=McLaughlin, David W.|title=The Feynman Integral|journal=Amer. Math. Monthly|year=1975|volume=82|issue=5|pages=451–465|url=http://www.maa.org/programs/maa-awards/writing-awards/the-feynman-integral|doi=10.2307/2319736|jstor=2319736|access-date=2015-02-02|archive-date=2023-06-04|archive-url=https://web.archive.org/web/20230604164332/https://www.maa.org/programs/maa-awards/writing-awards/the-feynman-integral|url-status=dead}}</ref> and (not shared) in 1977.<ref>{{cite journal|author=Keller, Joseph B.|title=Inverse Problem|journal=Amer. Math. Monthly|year=1976|volume=83|issue=2|pages=107–118|url=http://www.maa.org/programs/maa-awards/writing-awards/inverse-problems|doi=10.2307/2976988|jstor=2976988|access-date=2015-02-02|archive-date=2023-03-24|archive-url=https://web.archive.org/web/20230324120444/https://www.maa.org/programs/maa-awards/writing-awards/inverse-problems|url-status=dead}}</ref> In 1988 he was awarded the U.S. [[National Medal of Science]], and in 1997 he was awarded the [[Wolf Prize]] by the Israel-based [[Wolf Foundation]]. In 1996, he was awarded the [[Nemmers Prize in Mathematics]]. In 1999 he was awarded the [[Ig Nobel Prize]] for calculating how to make a teapot spout that does not drip. With Patrick B. Warren, Robin C. Ball and [[Raymond E. Goldstein]], Keller was awarded an [[Ig Nobel Prize]] in 2012 for calculating the forces that shape and move [[ponytail]] hair.<ref name=ignobelpaper>{{Cite journal | last1 = Goldstein | first1 = R. | author-link1 = Raymond E. Goldstein| last2 = Warren | first2 = P. | last3 = Ball | first3 = R. | title = Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles | doi = 10.1103/PhysRevLett.108.078101 | journal = Physical Review Letters | volume = 108 | issue = 7 | year = 2012 | pmid = 22401258| url = http://www.damtp.cam.ac.uk/user/gold/pdfs/ponytail_prl.pdf|arxiv = 1204.0371 |bibcode = 2012PhRvL.108g8101G | page=078101| s2cid = 31964168 }}</ref><ref name=ignobelcam>{{cite web|archive-url=https://web.archive.org/web/20130203233116/http://www.damtp.cam.ac.uk/comms/110.html|archive-date=2013-02-03|url=http://www.damtp.cam.ac.uk/comms/110.html|publisher=University of Cambridge|title=Ray Goldstein Shares 2012 Ig Nobel Prize for Physics}}</ref>
This makes him the only person to win more than one Ig Nobel Prize. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref>
In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref>


==Personal life==
==Personal life==
Keller's second wife, [[Alice S. Whittemore]], started her career as a pure mathematician but shifted her interests to [[epidemiology]] and [[biostatistics]].
Keller had a brother who was also a mathematician, [[Herbert Keller|Herbert B. Keller]], who has studied numerical analysis, [[scientific computing]], [[bifurcation theory]], path following and homotopy methods, and [[computational fluid dynamics]]. Herbert Keller was a professor at [[Caltech]]. Both brothers contributed to the fields of [[electromagnetics]] and [[fluid dynamics]]. Joseph Keller died in [[Stanford, California|Stanford]], [[California]] on September 7, 2016 from a recurrence of kidney cancer first diagnosed in 2003.<ref>{{cite web
Keller had a brother who was also a mathematician, [[Herbert Keller|Herbert B. Keller]], who studied numerical analysis, [[scientific computing]], [[bifurcation theory]], path following and homotopy methods, and [[computational fluid dynamics]]; Keller was the co-advisor of his Herbert's PhD thesis. Herbert Keller was a professor at [[Caltech]]. Both brothers contributed to the fields of [[electromagnetics]] and [[fluid dynamics]]. Joseph Keller died in [[Stanford, California|Stanford]], [[California]] on September 7, 2016, from a recurrence of kidney cancer first diagnosed in 2003.<ref>{{cite news
| title = Stanford Professor Emeritus Joseph Keller, an applied mathematician whose work investigated atomic explosions and oscillating ponytails, dies at 93
| title = Stanford Professor Emeritus Joseph Keller, an applied mathematician whose work investigated atomic explosions and oscillating ponytails, dies at 93
| url = http://news.stanford.edu/2016/09/08/joseph-keller-applied-mathematician-dies-93/
| url = http://news.stanford.edu/2016/09/08/joseph-keller-applied-mathematician-dies-93/
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| access-date = September 8, 2016}}
| access-date = September 8, 2016}}
</ref>
</ref>

==Major publications==
* J.B. Keller. ''On solutions of Δu=f(u).'' Comm. Pure Appl. Math. 10 (1957), 503–510.
* Edward W. Larsen and Joseph B. Keller. ''Asymptotic solution of neutron transport problems for small mean free paths.'' J. Mathematical Phys. 15 (1974), 75–81.
* Joseph B. Keller and Dan Givoli. ''Exact nonreflecting boundary conditions.'' J. Comput. Phys. 82 (1989), no. 1, 172–192.
* Jacob Rubinstein, Peter Sternberg, and Joseph B. Keller. ''Fast reaction, slow diffusion, and curve shortening.'' SIAM J. Appl. Math. 49 (1989), no. 1, 116–133.
* Marcus J. Grote and Joseph B. Keller. ''On nonreflecting boundary conditions.'' J. Comput. Phys. 122 (1995), no. 2, 231–243.
* Leonid Ryzhik, George Papanicolaou, and Joseph B. Keller. ''Transport equations for elastic and other waves in random media.'' Wave Motion 24 (1996), no. 4, 327–370.


== References ==
== References ==
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== External links ==
== External links ==
* [http://math.stanford.edu/~keller/JBK_BIO.htm Official biography]
* [http://math.stanford.edu/~keller/JBK_BIO.htm Official biography] {{Webarchive|url=https://web.archive.org/web/20171123080411/http://math.stanford.edu/~keller/JBK_BIO.htm |date=2017-11-23 }}
* [http://math.stanford.edu/~keller/JBK_CV.htm Curriculum vitae]
* [http://math.stanford.edu/~keller/JBK_CV.htm Curriculum vitae] {{Webarchive|url=https://web.archive.org/web/20171024195859/http://math.stanford.edu/~keller/JBK_CV.htm |date=2017-10-24 }}
* {{MacTutor Biography|id=Keller_Joseph}}
* {{MacTutor Biography|id=Keller_Joseph}}
* {{MathGenealogy|13411}}
* {{MathGenealogy|13411}}
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| issue = 7
| issue = 7
| pages = 751–760
| pages = 751–760
| url = http://www.ams.org/notices/200407/fea-keller.pdf
| url = https://www.ams.org/notices/200407/fea-keller.pdf
| format = [[PDF]]
| access-date = 2008-01-17 }}
{{FRS 1986}}
| accessdate = 2008-01-17 }}

{{Wolf Prize in Mathematics}}
{{Wolf Prize in Mathematics}}
{{Winners of the National Medal of Science|math-stat-comp}}
{{Winners of the National Medal of Science|math-stat-comp}}
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[[Category:1923 births]]
[[Category:1923 births]]
[[Category:2016 deaths]]
[[Category:2016 deaths]]
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[[Category:People from Paterson, New Jersey]]
[[Category:20th-century American mathematicians]]
[[Category:20th-century American mathematicians]]
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[[Category:21st-century American Jews]]
[[Category:21st-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Jewish American scientists]]
[[Category:Courant Institute of Mathematical Sciences alumni]]
[[Category:Courant Institute of Mathematical Sciences faculty]]
[[Category:Courant Institute of Mathematical Sciences faculty]]
[[Category:Stanford University School of Engineering faculty]]
[[Category:Eastside High School (Paterson, New Jersey) alumni]]
[[Category:Foreign Members of the Royal Society]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the American Physical Society]]
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[[Category:Fellows of the Society for Industrial and Applied Mathematics]]
[[Category:Foreign members of the Royal Society]]
[[Category:Ig Nobel laureates]]
[[Category:Jewish American scientists]]
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[[Category:Members of the United States National Academy of Sciences]]
[[Category:National Medal of Science laureates]]
[[Category:National Medal of Science laureates]]
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[[Category:Scientists from Paterson, New Jersey]]
[[Category:Stanford University School of Engineering faculty]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Courant Institute of Mathematical Sciences alumni]]
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[[Category:Members of the United States National Academy of Sciences]]
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[[Category:Fellows of the Society for Industrial and Applied Mathematics]]
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[[Category:Fellows of the American Mathematical Society]]

Latest revision as of 23:58, 3 December 2024

Joseph Bishop Keller
Born(1923-07-31)July 31, 1923
Paterson, New Jersey, U.S.
DiedSeptember 7, 2016(2016-09-07) (aged 93)
Stanford, California, U.S.
NationalityAmerican
Alma materNew York University
Known forGeometrical theory of diffraction
Keller–Miksis formulation
Einstein–Brillouin–Keller method
AwardsLester R. Ford Award (1976, 1977)
Gibbs Lecture (1977)
Eringen Medal (1981)
John von Neumann Prize (1983)
Timoshenko Medal (1984)
National Medal of Science (1988)
ICM Speaker (1994)
Nemmers Prize in Mathematics (1996)
Wolf Prize (1997)
Ig Nobel Prize (1999, 2012)
Scientific career
FieldsMathematics
InstitutionsNew York University
Stanford University
Thesis Reflection and transmission of electromagnetic waves by thin curved shells[1]
Doctoral advisorRichard Courant[1]
Doctoral studentsHerbert Bishop Keller
George C. Papanicolaou
Bernard J. Matkowsky
L. Mahadevan

Joseph Bishop Keller (July 31, 1923 – September 7, 2016) was an American mathematician who specialized in applied mathematics. He was best known for his work on the "geometrical theory of diffraction" (GTD).[2]

Early life and education

[edit]

Born in Paterson, New Jersey on July 31, 1923, Keller attended Eastside High School, where he was a member of the math team.[3] After earning his undergraduate degree in 1943 at New York University, Keller obtained his PhD in 1948 from NYU under the supervision of Richard Courant. He was a professor of mathematics in the Courant Institute at New York University until 1979. Then he was Professor of Mathematics and Mechanical Engineering at Stanford University until 1993, when he became professor emeritus.

Research

[edit]

Keller worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein–Brillouin–Keller method for computing eigenvalues in quantum mechanical systems.

Awards and honors

[edit]

Keller was awarded a Lester R. Ford Award (shared with David W. McLaughlin) in 1976[4] and (not shared) in 1977.[5] In 1988 he was awarded the U.S. National Medal of Science, and in 1997 he was awarded the Wolf Prize by the Israel-based Wolf Foundation. In 1996, he was awarded the Nemmers Prize in Mathematics. In 1999 he was awarded the Ig Nobel Prize for calculating how to make a teapot spout that does not drip. With Patrick B. Warren, Robin C. Ball and Raymond E. Goldstein, Keller was awarded an Ig Nobel Prize in 2012 for calculating the forces that shape and move ponytail hair.[6][7] In 2012 he became a fellow of the American Mathematical Society.[8]

Personal life

[edit]

Keller's second wife, Alice S. Whittemore, started her career as a pure mathematician but shifted her interests to epidemiology and biostatistics. Keller had a brother who was also a mathematician, Herbert B. Keller, who studied numerical analysis, scientific computing, bifurcation theory, path following and homotopy methods, and computational fluid dynamics; Keller was the co-advisor of his Herbert's PhD thesis. Herbert Keller was a professor at Caltech. Both brothers contributed to the fields of electromagnetics and fluid dynamics. Joseph Keller died in Stanford, California on September 7, 2016, from a recurrence of kidney cancer first diagnosed in 2003.[9]

Major publications

[edit]
  • J.B. Keller. On solutions of Δu=f(u). Comm. Pure Appl. Math. 10 (1957), 503–510.
  • Edward W. Larsen and Joseph B. Keller. Asymptotic solution of neutron transport problems for small mean free paths. J. Mathematical Phys. 15 (1974), 75–81.
  • Joseph B. Keller and Dan Givoli. Exact nonreflecting boundary conditions. J. Comput. Phys. 82 (1989), no. 1, 172–192.
  • Jacob Rubinstein, Peter Sternberg, and Joseph B. Keller. Fast reaction, slow diffusion, and curve shortening. SIAM J. Appl. Math. 49 (1989), no. 1, 116–133.
  • Marcus J. Grote and Joseph B. Keller. On nonreflecting boundary conditions. J. Comput. Phys. 122 (1995), no. 2, 231–243.
  • Leonid Ryzhik, George Papanicolaou, and Joseph B. Keller. Transport equations for elastic and other waves in random media. Wave Motion 24 (1996), no. 4, 327–370.

References

[edit]
  1. ^ a b Joseph Keller at the Mathematics Genealogy Project
  2. ^ Keller, J.B. (1962). "Geometrical theory of diffraction". J. Opt. Soc. Am. 52 (2): 116–130. doi:10.1364/JOSA.52.000116. PMID 14454948.
  3. ^ Roberts, Sam. "Joseph B. Keller, Mathematician With Whimsical Curiosity, Dies at 93", The New York Times, September 16, 2016. Accessed September 19, 2016. "Joseph Bishop Keller was born in Paterson, N.J., on July 31, 1923. His father, Isaac Keiles — whose name, he said, was changed when he arrived in the United States — was a Russian refugee who fled pogroms against Jews.... Joseph Keller competed on the math team at East Side High School in Paterson."
  4. ^ Keller, Joseph B.; McLaughlin, David W. (1975). "The Feynman Integral". Amer. Math. Monthly. 82 (5): 451–465. doi:10.2307/2319736. JSTOR 2319736. Archived from the original on 2023-06-04. Retrieved 2015-02-02.
  5. ^ Keller, Joseph B. (1976). "Inverse Problem". Amer. Math. Monthly. 83 (2): 107–118. doi:10.2307/2976988. JSTOR 2976988. Archived from the original on 2023-03-24. Retrieved 2015-02-02.
  6. ^ Goldstein, R.; Warren, P.; Ball, R. (2012). "Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles" (PDF). Physical Review Letters. 108 (7): 078101. arXiv:1204.0371. Bibcode:2012PhRvL.108g8101G. doi:10.1103/PhysRevLett.108.078101. PMID 22401258. S2CID 31964168.
  7. ^ "Ray Goldstein Shares 2012 Ig Nobel Prize for Physics". University of Cambridge. Archived from the original on 2013-02-03.
  8. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
  9. ^ "Stanford Professor Emeritus Joseph Keller, an applied mathematician whose work investigated atomic explosions and oscillating ponytails, dies at 93". Stanford News. September 8, 2016. Retrieved September 8, 2016.
[edit]
Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Joseph_Keller&oldid=1261052035"