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Neal Koblitz
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<h2 id="biography">Biography</h2> <p>Koblitz received his <a href="/facts/Bachelor_of_Arts/2pa1nwfR">B.A.</a> in mathematics from <a href="/facts/Harvard_University/Lhy9L1cx">Harvard University</a> in 1969.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> While at Harvard, he was a <a href="/facts/Putnam_Fellow/wTJSGQHM">Putnam Fellow</a> in 1968.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> He received his Ph.D. from <a href="/facts/Princeton_University/n3EPGHBM">Princeton University</a> in 1974 under the direction of <a href="/facts/Nick_Katz/lXpyyM80">Nick Katz</a>. From 1975 to 1979 he was an instructor at Harvard University.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> In 1979 he began working at the University of Washington. </p><p>Koblitz's 1981 article "Mathematics as Propaganda"<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> criticized the misuse of mathematics in the <a href="/facts/Social_science/hAbm1xtD">social sciences</a> and helped motivate <a href="/facts/Serge_Lang/I7MW2rUu">Serge Lang</a>'s successful challenge to the nomination of <a href="/facts/Political_scientist/Gqy5EoRX">political scientist</a> <a href="/facts/Samuel_P._Huntington/Y5QY8bXP">Samuel P. Huntington</a> to the <a href="/facts/United_States_National_Academy_of_Sciences/M3oePVeG">National Academy of Sciences</a>.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> In <i><a href="/facts/The_Mathematical_Intelligencer/tr4EnU3C">The Mathematical Intelligencer</a></i>, Koblitz,<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a><a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> Steven Weintraub,<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> and <a href="/facts/Saunders_Mac_Lane/rjgUqfkA">Saunders Mac Lane</a> later criticized the arguments of <a href="/facts/Herbert_A._Simon/NNHhQ2bS">Herbert A. Simon</a>, who had attempted to defend Huntington's work.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> </p><p>He co-invented <a href="/facts/Elliptic-curve_cryptography/YbjcXIWk">elliptic-curve cryptography</a> in 1985<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> with <a href="/facts/Victor_S._Miller/W25VdAe3">Victor S. Miller</a>, and for this was awarded the Levchin Prize<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> in 2021. </p><p>With his wife <a href="/facts/Ann_Hibner_Koblitz/CptbA1js">Ann Hibner Koblitz</a>, he in 1985 founded the Kovalevskaia Prize to honor women scientists in <a href="/facts/Developing_countries/eTfS4kxl">developing countries</a>. It was financed from the royalties of Ann Hibner Koblitz's 1983 biography of <a href="/facts/Sofia_Kovalevskaia/gvPMMXx1">Sofia Kovalevskaia</a>.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> Although the awardees have ranged over many fields of <a href="/facts/Science/IJoaD7rs">science</a>, one of the 2011 winners was a Vietnamese mathematician, <a href="/facts/L%C3%AA_Th%E1%BB%8B_Thanh_Nh%C3%A0n/qL2e4J1c">Lê Thị Thanh Nhàn</a>.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> </p><p>Koblitz's 2007 article "The uneasy relationship between mathematics and cryptography" discusses the increased contact between mathematics and cryptography in the 1990s. He argues that there is an unjustified "aura" placed onto mathematical proofs in cryptographic competitions and received much ire for the view.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> Koblitz, in co-operation with <a href="/facts/Alfred_Menezes/nduu6dew">Alfred Menezes</a>, went on to write a series of <i>Another Look</i> papers that describe errors or weaknesses in existing security proofs, the first being <i>Another look at HMAC</i> (2013). The two now maintain a website dedicated to this type of papers.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> </p><p>In 2011, Koblitz published "Elliptic curve cryptography: The serpentine course of a paradigm shift" with Ann Hibner Koblitz and Alfred Menezes. Using the history of ECC and shifting attitudes in the cryptographic community, the article argues that the field of cryptography is not as scientific and meritocratic as cryptographers want to show to the outside world; the field is <a href="/facts/Technological_constructivism/z770nHcA">controlled by social factors</a>, especially path dependence.<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/List_of_University_of_Waterloo_people/qL65vjrJ">List of University of Waterloo people</a></li> <li><a href="/facts/Gross%E2%80%93Koblitz_formula/XR5pdp80">Gross–Koblitz formula</a></li></ul> <h2 id="selected-publications">Selected publications</h2> <ul><li>— (1984) [1977]. <i></i>p<i>-adic Numbers, </i>p<i>-adic Analysis, and Zeta-Functions</i>. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 58 (Second ed.). New York: Springer-Verlag. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4612-1112-9">10.1007/978-1-4612-1112-9</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-4612-1112-9.</li> <li>— (1980). <a href="https://www.cambridge.org/sg/academic/subjects/mathematics/number-theory/p-adic-analysis-short-course-recent-work"><i>p-adic Analysis: a Short Course on Recent Work</i></a>. London Mathematical Society Lecture Note Series. Vol. 46. Cambridge: Cambridge University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780521280600. Retrieved 10 August 2022.</li> <li>— (1993) [1984]. <i>Introduction to Elliptic Curves and Modular Forms</i>. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 97 (Second ed.). New York: Springer-Verlag. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4612-0909-6">10.1007/978-1-4612-0909-6</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-4612-0909-6.</li> <li>— (1994) [1987]. <i>A Course in Number Theory and Cryptography</i>. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 114 (Second ed.). New York: Springer-Verlag. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4419-8592-7">10.1007/978-1-4419-8592-7</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-4419-8592-7.</li> <li>— (1998). <i>Algebraic Aspects of Cryptography</i>. Algorithms and Computation in Mathematics. Vol. 3. New York: <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-3-662-03642-6">10.1007/978-3-662-03642-6</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-662-03642-6.</li> <li>— (2008). <i>Random Curves: Journeys of a Mathematician</i>. Springer-Verlag. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-3-540-74078-0">10.1007/978-3-540-74078-0</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3540740773.</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="http://www.math.washington.edu/~koblitz/">Neal Koblitz's home page</a></li> <li><a href="https://mathgenealogy.org/id.php?id=28312">Neal Koblitz</a> at the <a href="/facts/Mathematics_Genealogy_Project/J7AFo1Do">Mathematics Genealogy Project</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Engquist, Björn; Schmid, Wilfried, eds. (2001), Mathematics Unlimited: 2001 and Beyond, Berlin: Springer, p. 1225, ISBN 978-3-540-66913-5 <a href="978-3-540-66913-5" target="_blank">978-3-540-66913-5</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Engquist, Björn; Schmid, Wilfried, eds. (2001), Mathematics Unlimited: 2001 and Beyond, Berlin: Springer, p. 1225, ISBN 978-3-540-66913-5 <a href="978-3-540-66913-5" target="_blank">978-3-540-66913-5</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>"Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved December 13, 2021. <a href="http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners" target="_blank">http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Koblitz, Neal (2008), Random Curves: Journeys of a Mathematician, Berlin: Springer-Verlag, p. 123, doi:10.1007/978-3-540-74078-0, ISBN 978-3540740773 <a href="978-3540740773" target="_blank">978-3540740773</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Koblitz, Neal (1981), "Mathematics as Propaganda", in Steen, Lynn Arthur (ed.), Mathematics Tomorrow, Springer Verlag, pp. 111–120, doi:10.1007/978-1-4613-8127-3_12, ISBN 0-387-90564-2 <a href="0-387-90564-2" target="_blank">0-387-90564-2</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Krantz, Steven George (2005), Mathematical apocrypha redux, Cambridge University Press, ISBN 0-88385-554-2 <a href="0-88385-554-2" target="_blank">0-88385-554-2</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Koblitz, Neal (Winter 1988), "A Tale of Three Equations; or The Emperors Have No Clothes", The Mathematical Intelligencer, 10 (1), New York, NY: 4–10, doi:10.1007/BF03023843, S2CID 121312716 <a href="/wiki/The_Mathematical_Intelligencer" target="_blank">/wiki/The_Mathematical_Intelligencer</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Koblitz, Neal (Winter 1988), "Reply to Unclad Emperors", The Mathematical Intelligencer, 10 (1), New York, NY: 14–16, doi:10.1007/BF03023845, S2CID 123030288 <a href="/wiki/The_Mathematical_Intelligencer" target="_blank">/wiki/The_Mathematical_Intelligencer</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Koblitz, Neal (Spring 1988), "Simon Falls off the Wall", The Mathematical Intelligencer, 10 (2), New York, NY: 11–12, doi:10.1007/bf03028350 <a href="/wiki/The_Mathematical_Intelligencer" target="_blank">/wiki/The_Mathematical_Intelligencer</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Weintraub, Steven H. (Summer 1988), "Trivial Pseudomathematics", The Mathematical Intelligencer, 10 (3), New York, NY: 3–4, doi:10.1007/bf03026633, S2CID 189883909 <a href="/wiki/The_Mathematical_Intelligencer" target="_blank">/wiki/The_Mathematical_Intelligencer</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Brown, James Robert (1999), Philosophy of mathematics, Routledge, ISBN 0-415-12275-9 <a href="0-415-12275-9" target="_blank">0-415-12275-9</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Koblitz, N. (1987). "Elliptic curve cryptosystems". Mathematics of Computation. 48 (177): 203–209. doi:10.2307/2007884. JSTOR 2007884. <a href="https://doi.org/10.2307%2F2007884" target="_blank">https://doi.org/10.2307%2F2007884</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Levchin Prize <a href="https://rwc.iacr.org/LevchinPrize/#Winners" target="_blank">https://rwc.iacr.org/LevchinPrize/#Winners</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Hickey, Hannah (2007-11-08), Neal Koblitz: Deciphering the cryptographer, University Week <a href="http://www.washington.edu/news/2007/11/08/neal-koblitz-deciphering-the-cryptographer/" target="_blank">http://www.washington.edu/news/2007/11/08/neal-koblitz-deciphering-the-cryptographer/</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Nguyen, Ha (March 13, 2012), "Women make their mark in sciences", Việt Nam News. <a href="http://vietnamnews.vn/sunday/features/222076/women-make-their-mark-in-sciences.html" target="_blank">http://vietnamnews.vn/sunday/features/222076/women-make-their-mark-in-sciences.html</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Koblitz, Neal (2007). "The uneasy relationship between mathematics and cryptography". Notices of the AMS. 54: 972–979. <a href="https://www.math.uwaterloo.ca/~ajmeneze/anotherlook/ams.shtml" target="_blank">https://www.math.uwaterloo.ca/~ajmeneze/anotherlook/ams.shtml</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Neal, Koblitz; Alfred, Menezes. "Another Look at Provable Security". www.math.uwaterloo.ca. <a href="https://www.math.uwaterloo.ca/~ajmeneze/anotherlook/index.shtml" target="_blank">https://www.math.uwaterloo.ca/~ajmeneze/anotherlook/index.shtml</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Koblitz, Ann Hibner; Koblitz, Neal; Menezes, Alfred (May 2011). "Elliptic curve cryptography: The serpentine course of a paradigm shift". Journal of Number Theory. 131 (5): 781–814. doi:10.1016/j.jnt.2009.01.006. <a href="https://doi.org/10.1016%2Fj.jnt.2009.01.006" target="_blank">https://doi.org/10.1016%2Fj.jnt.2009.01.006</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> </ol>