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{{Short description|American historian of mathematics (1945–1997)}}{{Infobox academic
| occupation = [[Historian of mathematics]]
| discipline = [[History of mathematics]]
| sub_discipline = [[Ancient Greek mathematics]]
| workplaces = [[Stanford University]] {{small|(1979–1997)}}
| image = Wilbur Knorr 1973 headshot.jpg
| caption = Dr. Wilbur Knorr in his 30s
| education = [[Harvard University]] {{small|([[Bachelor of Arts|BA]]{{nbsp}}1966; [[PhD]]{{nbsp}}1973)}}
| academic_advisors = [[John E. Murdoch]] and [[G. E. L. Owen]]
| birth_date = {{birth date|1945|08|29}}
| death_date = {{death date and age|1997|03|18|1945|08|29}}
| birth_place = [[Richmond Hill, Queens]]
| death_place = [[Palo Alto, California]]
⚫
}}

'''Wilbur Richard Knorr''' (August 29, 1945 – March 18, 1997) was an American [[history of mathematics|historian of mathematics]] and a professor in the departments of philosophy and classics at [[Stanford University]]. He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century.<ref name="isis"/>
'''Wilbur Richard Knorr''' (August 29, 1945 – March 18, 1997) was an American [[history of mathematics|historian of mathematics]] and a professor in the departments of philosophy and classics at [[Stanford University]]. He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century.<ref name="isis"/>


==Biography==
==Biography==
Knorr was born August 29, 1945, in [[Richmond Hill, New York]].<ref name="sns"/> He did his undergraduate studies at [[Harvard University]] from 1963 to 1966 and stayed there for his Ph.D., which he received in 1973 under the supervision of John Emery Murdoch and [[Gwilym Ellis Lane Owen|G. E. L. Owen]].<ref name="isis">{{citation|title=Eloge: Wilbur Knorr, 29 August 1945–18 March 1997|journal=[[Isis (journal)|Isis]]|first=Henry R.|last=Mendell|volume=92|issue=2|year=2001|pages=339–343|jstor=3080632|doi=10.1086/385185}}.</ref><ref name="fowler">{{citation|title=Wilbur Richard Knorr (1945–1997): An Appreciation|first=David|last=Fowler|journal=[[Historia Mathematica]]|volume=25|issue=2|pages=123–132|year=1998|doi=10.1006/hmat.1998.2199}}.</ref> After postdoctoral studies at [[Cambridge University]], he taught at [[Brooklyn College]], but lost his position when the college's Downtown Brooklyn campus was closed as part of [[History of New York City (1946–1977)#1970s|New York's mid-1970s fiscal crisis]].<ref name="isis"/> After taking a temporary position at the [[Institute for Advanced Study]],<ref name="isis"/> he joined the Stanford faculty as an assistant professor in 1979, was tenured there in 1983, and was promoted to full professor in 1990.<ref name="sns"/>
Knorr was born August 29, 1945, in [[Richmond Hill, Queens]].<ref name="sns"/> He did his undergraduate studies at [[Harvard University]] from 1963 to 1966 and stayed there for his Ph.D., which he received in 1973 under the supervision of [[John E. Murdoch|John Emery Murdoch]] and [[Gwilym Ellis Lane Owen|G. E. L. Owen]].<ref name="isis">{{citation|title=Eloge: Wilbur Knorr, 29 August 1945–18 March 1997|journal=[[Isis (journal)|Isis]]|first=Henry R.|last=Mendell|volume=92|issue=2|year=2001|pages=339–343|jstor=3080632|doi=10.1086/385185|s2cid=144610643 }}.</ref><ref name="fowler">{{citation|title=Wilbur Richard Knorr (1945–1997): An Appreciation|first=David|last=Fowler|journal=[[Historia Mathematica]]|volume=25|issue=2|pages=123–132|year=1998|doi=10.1006/hmat.1998.2199|doi-access=free}}.</ref> After postdoctoral studies at [[Cambridge University]], he taught at [[Brooklyn College]], but lost his position when the college's [[Downtown Brooklyn]] campus was closed as part of [[History of New York City (1946–1977)#1970s|New York's mid-1970s fiscal crisis]].<ref name="isis"/> After taking a temporary position at the [[Institute for Advanced Study]],<ref name="isis"/> he joined the Stanford faculty as an assistant professor in 1979, was tenured there in 1983, and was promoted to full professor in 1990.<ref name="sns"/>
He died March 18, 1997 in [[Palo Alto, California]], of [[melanoma]].<ref name="sns">{{citation|url=http://news.stanford.edu/pr/97/970319knorr.html|title=Wilbur Knorr, professor of philosophy and classics, dies at 51|publisher=Stanford News Service|date=March 19, 1997}}.</ref><ref name="nyt">{{citation|url=http://www.nytimes.com/1997/03/31/us/wilbur-knorr-51-mathematics-historian.html|title=Wilbur Knorr, 51, Mathematics Historian|journal=[[New York Times]]|first=Wolfgang|last=Saxon|date=March 31, 1997}}.</ref>
He died March 18, 1997, in [[Palo Alto, California]], of [[melanoma]].<ref name="sns">{{citation|url=http://news.stanford.edu/pr/97/970319knorr.html|title=Wilbur Knorr, professor of philosophy and classics, dies at 51|publisher=Stanford News Service|date=March 19, 1997}}.</ref><ref name="nyt">{{citation|url=https://www.nytimes.com/1997/03/31/us/wilbur-knorr-51-mathematics-historian.html|title=Wilbur Knorr, 51, Mathematics Historian|journal=[[New York Times]]|first=Wolfgang|last=Saxon|date=March 31, 1997}}.</ref>


Knorr was a talented violinist, and played first violin in the Harvard Orchestra, but he gave up his music when he came to Stanford, as the pressures of the tenure process did not allow him adequate practice time.<ref name="isis"/><ref name="fowler"/>
Knorr was a talented violinist, and played first violin in the Harvard Orchestra, but he gave up his music when he came to Stanford, as the pressures of the tenure process did not allow him adequate practice time.<ref name="isis"/><ref name="fowler"/>


==Books==
==Books==
;''The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry''.:<ref>Dordrecht: D. Reidel Publishing Co., 1975.</ref> This work incorporates Knorr's Ph.D. thesis. It traces the early history of [[irrational number]]s from their first discovery (in [[Thebes, Greece|Thebes]] between 430 and 410 BC, Knorr speculates), through the work of [[Theodorus of Cyrene]], who showed the irrationality of the square roots of the integers up to 17, and Theodorus' student [[Theaetetus (mathematician)|Theaetetus]], who showed that all non-square integers have irrational square roots. Knorr reconstructs an argument based on [[Pythagorean triple]]s and [[Parity (mathematics)|parity]] that matches the story in [[Plato]]'s ''[[Theaetetus (dialogue)|Theaetetus]]'' of Theodorus' difficulties with the number 17, and shows that switching from parity to a different dichotomy in terms of whether a number is square or not was the key to Theaetetus' success. Theaetetus classified the known irrational numbers into three types, based on analogies to the [[geometric mean]], [[arithmetic mean]], and [[harmonic mean]], and this classification was then greatly extended by [[Eudoxus of Cnidus]]; Knorr speculates that this extension stemmed out of Eudoxus' studies of the [[golden section]].<ref name="isis"/><ref name="fowler"/><ref name="u1">[http://www.jstor.org/stable/230094 Review] of ''The Evolution of the Euclidean Elements'' by Sabetai Unguru (1977), ''[[Isis (journal)|Isis]]'' 68: 314–316, {{doi|10.1086/351791}}.</ref><ref name="u2">{{citation|title=Incommensurability and irrationality: A new historical interpretation|first=Sabetai|last=Unguru|journal=History of Science|year=1977|volume=15|pages=216–227}}. Although published as a regular paper, this is an extended review of ''The Evolution of the Euclidean Elements'', for which Unguru's review in ''Isis'' is a precis.</ref>
;''The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry''.<ref>Dordrecht: D. Reidel Publishing Co., 1975.</ref>
:This work incorporates Knorr's Ph.D. thesis. It traces the early history of [[irrational number]]s from their first discovery (in [[Thebes, Greece|Thebes]] between 430 and 410 BC, Knorr speculates), through the work of [[Theodorus of Cyrene]], who showed the irrationality of the square roots of the integers up to 17, and Theodorus' student [[Theaetetus (mathematician)|Theaetetus]], who showed that all non-square integers have irrational square roots. Knorr reconstructs an argument based on [[Pythagorean triple]]s and [[Parity (mathematics)|parity]] that matches the story in [[Plato]]'s ''[[Theaetetus (dialogue)|Theaetetus]]'' of Theodorus' difficulties with the number 17, and shows that switching from parity to a different dichotomy in terms of whether a number is square or not was the key to Theaetetus' success. Theaetetus classified the known irrational numbers into three types, based on analogies to the [[geometric mean]], [[arithmetic mean]], and [[harmonic mean]], and this classification was then greatly extended by [[Eudoxus of Cnidus]]; Knorr speculates that this extension stemmed out of Eudoxus' studies of the [[golden section]].<ref name="isis"/><ref name="fowler"/><ref name="u1">[https://www.jstor.org/stable/230094 Review] of ''The Evolution of the Euclidean Elements'' by [[Sabetai Unguru]] (1977), ''[[Isis (journal)|Isis]]'' 68: 314–316, {{doi|10.1086/351791}}.</ref><ref name="u2">{{citation|title=Incommensurability and irrationality: A new historical interpretation|first=Sabetai|last=Unguru|author-link=Sabetai Unguru|journal=History of Science|year=1977|volume=15|pages=216–227|doi=10.1177/007327537701500303 |s2cid=220854110 }}. Although published as a regular paper, this is an extended review of ''The Evolution of the Euclidean Elements'', for which Unguru's review in ''Isis'' is a precis.</ref>

:Along with this history of irrational numbers, Knorr reaches several conclusions about the history of [[Euclid]]'s [[Euclid's Elements|''Elements'']] and of other related mathematical documents; in particular, he ascribes the origin of the material in Books 1, 3, and 6 of the ''Elements'' to the time of [[Hippocrates of Chios]], and of the material in books 2, 4, 10, and 13 to the later period of Theodorus, Theaetetus, and Eudoxos. However, this suggested history has been criticized by [[Bartel Leendert van der Waerden|van der Waerden]], who believed that books 1 through 4 were largely due to the much earlier [[Pythagoras|Pythagorean school]].<ref name="vdw">Review of ''The Evolution of the Euclidean Elements'' by [[Bartel Leendert van der Waerden]] (1976), ''[[Historia Mathematica]]'' '''3''' (4): 497–499, {{doi|10.1016/0315-0860(76)90092-6}}.</ref>
:Along with this history of irrational numbers, Knorr reaches several conclusions about the history of [[Euclid]]'s [[Euclid's Elements|''Elements'']] and of other related mathematical documents; in particular, he ascribes the origin of the material in Books 1, 3, and 6 of the ''Elements'' to the time of [[Hippocrates of Chios]], and of the material in books 2, 4, 10, and 13 to the later period of Theodorus, Theaetetus, and Eudoxos. However, this suggested history has been criticized by [[Bartel Leendert van der Waerden|van der Waerden]], who believed that books 1 through 4 were largely due to the much earlier [[Pythagoras|Pythagorean school]].<ref name="vdw">Review of ''The Evolution of the Euclidean Elements'' by [[Bartel Leendert van der Waerden]] (1976), ''[[Historia Mathematica]]'' '''3''' (4): 497–499, {{doi|10.1016/0315-0860(76)90092-6}}.</ref>
;''Ancient Sources of the Medieval Tradition of Mechanics: Greek, Arabic, and Latin studies of the balance''.<ref>Florence: Istituto e museo di storia della scienza, 1982.</ref>
;''Ancient Sources of the Medieval Tradition of Mechanics: Greek, Arabic, and Latin studies of the balance''.<ref>Florence: Istituto e museo di storia della scienza, 1982.</ref>
;''The Ancient Tradition of Geometric Problems''.:<ref>Boston: Birkhaüser, 1986. Reprinted by [[Dover Publications]], 1993, ISBN 978-0-486-67532-9.</ref> This book, aimed at a general audience, examines the history of three classical problems from [[Greek mathematics]]: [[doubling the cube]], [[squaring the circle]], and [[angle trisection]]. It is now known that none of these problems can be solved by [[compass and straightedge]], but Knorr argues that emphasizing these impossibility results is an anachronism due in part to the [[Foundations of mathematics#Foundational crisis|foundational crisis]] in 1930s mathematics.<ref name="drucker">[http://www.jstor.org/stable/233339 Review] of both ''The Ancient Tradition of Geometric Problems'' and ''Textual Studies in Ancient and Medieval Geometry'' by Thomas Drucker (1991), ''[[Isis (journal)|Isis]]'' '''82''': 718–720, {{doi|10.1086/355947}}.</ref> Instead, Knorr argues, the Greek mathematicians were primarily interested in how to solve these problems by whatever means they could, and viewed theorem and proofs as tools for problem-solving more than as ends in their own right.<ref name="isis"/>
;''[[The Ancient Tradition of Geometric Problems]]''.<ref>Boston: Birkhaüser, 1986. Reprinted by [[Dover Publications]], 1993, {{ISBN|978-0-486-67532-9}}.</ref>
:This book, aimed at a general audience, examines the history of three classical problems from [[Greek mathematics]]: [[doubling the cube]], [[squaring the circle]], and [[angle trisection]]. It is now known that none of these problems can be solved by [[compass and straightedge]], but Knorr argues that emphasizing these impossibility results is an anachronism due in part to the [[Foundations of mathematics#Foundational crisis|foundational crisis]] in 1930s mathematics.<ref name="drucker">[https://www.jstor.org/stable/233339 Review] of both ''The Ancient Tradition of Geometric Problems'' and ''Textual Studies in Ancient and Medieval Geometry'' by Thomas Drucker (1991), ''[[Isis (journal)|Isis]]'' '''82''': 718–720, {{doi|10.1086/355947}}.</ref> Instead, Knorr argues, the Greek mathematicians were primarily interested in how to solve these problems by whatever means they could, and viewed theorem and proofs as tools for problem-solving more than as ends in their own right.<ref name="isis"/>
;''Textual Studies in Ancient and Medieval Geometry''.:<ref>Boston: Birkhäuser, 1989, ISBN 978-0-8176-3387-5.</ref> This is a longer and more technical "appendix" to ''The Ancient Tradition of Geometric Problems'' in which Knorr examines the similarities and differences between ancient mathematical texts carefully in order to determine how they influenced each other and untangle their editorial history.<ref name="isis"/><ref name="drucker"/> One of Knorr's more provocative speculations in this work is that [[Hypatia]] may have played a role in editing [[Archimedes]]' ''Dimension of a Circle''.<ref name="fowler"/>
;''Textual Studies in Ancient and Medieval Geometry''.<ref>Boston: Birkhäuser, 1989, {{ISBN|978-0-8176-3387-5}}.</ref>
:This is a longer and more technical "appendix" to ''The Ancient Tradition of Geometric Problems'' in which Knorr examines the similarities and differences between ancient mathematical texts carefully in order to determine how they influenced each other and untangle their editorial history.<ref name="isis"/><ref name="drucker"/> One of Knorr's more provocative speculations in this work is that [[Hypatia]] may have played a role in editing [[Archimedes]]' ''[[Measurement of a Circle]]''.<ref name="fowler"/>


==References==
==References==
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{{Authority control}}
{{Authority control}}


{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME =Knorr, Wilbur
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American historian
| DATE OF BIRTH = August 29, 1945
| PLACE OF BIRTH =
| DATE OF DEATH = March 18, 1997
| PLACE OF DEATH =
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}}
{{DEFAULTSORT:Knorr, Wilbur}}
{{DEFAULTSORT:Knorr, Wilbur}}
[[Category:1945 births]]
[[Category:1945 births]]
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[[Category:Harvard University alumni]]
[[Category:Harvard University alumni]]
[[Category:Brooklyn College faculty]]
[[Category:Brooklyn College faculty]]
[[Category:Historians of mathematics]]
[[Category:American historians of mathematics]]
⚫
[[Category:American historians]]
[[Category:Stanford University Department of Philosophy faculty]]
[[Category:Stanford University Department of Philosophy faculty]]
[[Category:20th-century historians]]
[[Category:20th-century American historians]]
[[Category:20th-century mathematicians]]
[[Category:20th-century American male writers]]
[[Category:People from Richmond Hill, Queens]]
[[Category:Historians from New York (state)]]
⚫
[[Category:American male non-fiction writers]]

Latest revision as of 00:51, 6 December 2024

Wilbur Knorr
Dr. Wilbur Knorr in his 30s
Born(1945-08-29)August 29, 1945
Richmond Hill, Queens
DiedMarch 18, 1997(1997-03-18) (aged 51)
Palo Alto, California
OccupationHistorian of mathematics
Academic background
EducationHarvard University (BA 1966; PhD 1973)
Academic advisorsJohn E. Murdoch and G. E. L. Owen
Academic work
DisciplineHistory of mathematics
Sub-disciplineAncient Greek mathematics
InstitutionsStanford University (1979–1997)

Wilbur Richard Knorr (August 29, 1945 – March 18, 1997) was an American historian of mathematics and a professor in the departments of philosophy and classics at Stanford University. He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century.[1]

Biography

[edit]

Knorr was born August 29, 1945, in Richmond Hill, Queens.[2] He did his undergraduate studies at Harvard University from 1963 to 1966 and stayed there for his Ph.D., which he received in 1973 under the supervision of John Emery Murdoch and G. E. L. Owen.[1][3] After postdoctoral studies at Cambridge University, he taught at Brooklyn College, but lost his position when the college's Downtown Brooklyn campus was closed as part of New York's mid-1970s fiscal crisis.[1] After taking a temporary position at the Institute for Advanced Study,[1] he joined the Stanford faculty as an assistant professor in 1979, was tenured there in 1983, and was promoted to full professor in 1990.[2] He died March 18, 1997, in Palo Alto, California, of melanoma.[2][4]

Knorr was a talented violinist, and played first violin in the Harvard Orchestra, but he gave up his music when he came to Stanford, as the pressures of the tenure process did not allow him adequate practice time.[1][3]

Books

[edit]
The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry.[5]
This work incorporates Knorr's Ph.D. thesis. It traces the early history of irrational numbers from their first discovery (in Thebes between 430 and 410 BC, Knorr speculates), through the work of Theodorus of Cyrene, who showed the irrationality of the square roots of the integers up to 17, and Theodorus' student Theaetetus, who showed that all non-square integers have irrational square roots. Knorr reconstructs an argument based on Pythagorean triples and parity that matches the story in Plato's Theaetetus of Theodorus' difficulties with the number 17, and shows that switching from parity to a different dichotomy in terms of whether a number is square or not was the key to Theaetetus' success. Theaetetus classified the known irrational numbers into three types, based on analogies to the geometric mean, arithmetic mean, and harmonic mean, and this classification was then greatly extended by Eudoxus of Cnidus; Knorr speculates that this extension stemmed out of Eudoxus' studies of the golden section.[1][3][6][7]
Along with this history of irrational numbers, Knorr reaches several conclusions about the history of Euclid's Elements and of other related mathematical documents; in particular, he ascribes the origin of the material in Books 1, 3, and 6 of the Elements to the time of Hippocrates of Chios, and of the material in books 2, 4, 10, and 13 to the later period of Theodorus, Theaetetus, and Eudoxos. However, this suggested history has been criticized by van der Waerden, who believed that books 1 through 4 were largely due to the much earlier Pythagorean school.[8]
Ancient Sources of the Medieval Tradition of Mechanics: Greek, Arabic, and Latin studies of the balance.[9]
The Ancient Tradition of Geometric Problems.[10]
This book, aimed at a general audience, examines the history of three classical problems from Greek mathematics: doubling the cube, squaring the circle, and angle trisection. It is now known that none of these problems can be solved by compass and straightedge, but Knorr argues that emphasizing these impossibility results is an anachronism due in part to the foundational crisis in 1930s mathematics.[11] Instead, Knorr argues, the Greek mathematicians were primarily interested in how to solve these problems by whatever means they could, and viewed theorem and proofs as tools for problem-solving more than as ends in their own right.[1]
Textual Studies in Ancient and Medieval Geometry.[12]
This is a longer and more technical "appendix" to The Ancient Tradition of Geometric Problems in which Knorr examines the similarities and differences between ancient mathematical texts carefully in order to determine how they influenced each other and untangle their editorial history.[1][11] One of Knorr's more provocative speculations in this work is that Hypatia may have played a role in editing Archimedes' Measurement of a Circle.[3]

References

[edit]
  1. ^ a b c d e f g h Mendell, Henry R. (2001), "Eloge: Wilbur Knorr, 29 August 1945–18 March 1997", Isis, 92 (2): 339–343, doi:10.1086/385185, JSTOR 3080632, S2CID 144610643.
  2. ^ a b c Wilbur Knorr, professor of philosophy and classics, dies at 51, Stanford News Service, March 19, 1997.
  3. ^ a b c d Fowler, David (1998), "Wilbur Richard Knorr (1945–1997): An Appreciation", Historia Mathematica, 25 (2): 123–132, doi:10.1006/hmat.1998.2199.
  4. ^ Saxon, Wolfgang (March 31, 1997), "Wilbur Knorr, 51, Mathematics Historian", New York Times.
  5. ^ Dordrecht: D. Reidel Publishing Co., 1975.
  6. ^ Review of The Evolution of the Euclidean Elements by Sabetai Unguru (1977), Isis 68: 314–316, doi:10.1086/351791.
  7. ^ Unguru, Sabetai (1977), "Incommensurability and irrationality: A new historical interpretation", History of Science, 15: 216–227, doi:10.1177/007327537701500303, S2CID 220854110. Although published as a regular paper, this is an extended review of The Evolution of the Euclidean Elements, for which Unguru's review in Isis is a precis.
  8. ^ Review of The Evolution of the Euclidean Elements by Bartel Leendert van der Waerden (1976), Historia Mathematica 3 (4): 497–499, doi:10.1016/0315-0860(76)90092-6.
  9. ^ Florence: Istituto e museo di storia della scienza, 1982.
  10. ^ Boston: Birkhaüser, 1986. Reprinted by Dover Publications, 1993, ISBN 978-0-486-67532-9.
  11. ^ a b Review of both The Ancient Tradition of Geometric Problems and Textual Studies in Ancient and Medieval Geometry by Thomas Drucker (1991), Isis 82: 718–720, doi:10.1086/355947.
  12. ^ Boston: Birkhäuser, 1989, ISBN 978-0-8176-3387-5.
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