Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Leonid Kantorovich
open-in-new
<h2 id="biography">Biography</h2> <p>Kantorovich was born on 19 January 1912, to a <a href="/facts/History_of_the_Jews_in_Russia/q6sN2WA8">Russian Jewish</a> family.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> His father was a doctor practicing in <a href="/facts/Saint_Petersburg/pNuCBxaM">Saint Petersburg</a>.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> In 1926, at the age of fourteen, he began his studies at <a href="/facts/Saint_Petersburg_State_University/s9purC6t">Leningrad State University</a>. He graduated from the Faculty of Mathematics and Mechanics in 1930, and began his graduate studies. In 1934, at the age of 22 years, he became a full professor. In 1935 he received his <a href="/facts/Doctoral_degree/hb3AGQ6A">doctoral degree</a>.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> </p><p>Later, Kantorovich worked for the <a href="/facts/Government_of_the_Soviet_Union/TUzn71Pa">Soviet government</a>. He was given the task of <a href="/facts/Mathematical_optimization/oRn8Iv5I">optimizing</a> production in a <a href="/facts/Plywood/eM5WFvER">plywood</a> industry. He devised the mathematical technique now known as <a href="/facts/Linear_programming/GduXFQxT">linear programming</a> in 1939, some years before it was advanced by <a href="/facts/George_Dantzig/04se7h0M">George Dantzig</a>. He authored several books including <i>The Mathematical Method of Production Planning and Organization</i> (Russian original 1939), <i>The Best Uses of Economic Resources</i> (Russian original 1959), and, with Vladimir Ivanovich Krylov, <i>Approximate methods of higher analysis</i> (Russian original 1936).<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> For his work, Kantorovich was awarded the <a href="/facts/USSR_State_Prize/9fu2Ewjt">Stalin Prize</a> in 1949. </p><p>After 1939, he became a professor at <a href="/facts/Military_Engineering-Technical_University/zu82Cr34">Military Engineering-Technical University</a>. During the <a href="/facts/Siege_of_Leningrad/uCkWCzu0">Siege of Leningrad</a>, Kantorovich was a professor at <a href="/facts/Military_Engineering-Technical_University/zu82Cr34">VITU of Navy</a> and worked on safety of the <a href="/facts/Road_of_Life/EJxlYkb8">Road of Life</a>. He calculated the optimal distance between cars on ice in dependence of the thickness of ice and the temperature of the air. In December 1941 and January 1942, Kantorovich walked himself between cars driving on the ice of <a href="/facts/Lake_Ladoga/7pte777E">Lake Ladoga</a> on the Road of Life to ensure that cars did not sink. However, many cars with food for survivors of the siege were destroyed by the <a href="/facts/Luftwaffe/k7PAsBlo">German</a> airstrikes. For his feat and courage Kantorovich was awarded the <a href="/facts/Order_of_the_Patriotic_War/oMXpedKr">Order of the Patriotic War</a>, and was decorated with the medal <i>For Defense of Leningrad</i>. </p><p>In 1948 Kantorovich was assigned to the atomic project of the USSR. </p><p>After 1960, Kantorovich lived and worked in <a href="/facts/Novosibirsk/8UImC3vI">Novosibirsk</a>, where he created and took charge of the Department of Computational Mathematics in <a href="/facts/Novosibirsk_State_University/XjvN5qLN">Novosibirsk State University</a>.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p><p>The <a href="/facts/Nobel_Memorial_Prize_in_Economic_Sciences/8BBwNwre">Nobel Memorial Prize</a>, which he shared with <a href="/facts/Tjalling_Koopmans/1Woq9W7Y">Tjalling Koopmans</a>, was given "for their contributions to the theory of optimum allocation of resources." </p> <h2 id="mathematics">Mathematics</h2> <p>In <a href="/facts/Mathematical_analysis/XXeR26Ih">mathematical analysis</a>, Kantorovich had important results in <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a>, <a href="/facts/Approximation_theory/87AaPXLp">approximation theory</a>, and <a href="/facts/Operator_theory/Ays1ofel">operator theory</a>. </p><p>In particular, Kantorovich formulated some fundamental results in the theory of <a href="/facts/Normed_vector_space/rmDljfyE">normed</a> <a href="/facts/Riesz_space/FX7Mwfxe">vector lattices</a>, especially in Dedekind complete vector lattices called "K-spaces" which are now referred to as "Kantorovich spaces" in his honor. </p><p>Kantorovich showed that <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a> could be used in the analysis of <a href="/facts/Iterative_method/uKMAJhEh">iterative methods</a>, obtaining the <a href="/facts/Kantorovich_inequality/gr217YAL">Kantorovich inequalities</a> on the <a href="/facts/Rate_of_convergence/JVGuzPoS">convergence rate</a> of the <a href="/facts/Gradient_method/xwxAR6hM">gradient method</a> and of <a href="/facts/Newton%2527s_method/VlRhI2FL">Newton's method</a> (see the <a href="/facts/Kantorovich_theorem/Grtj9yBF">Kantorovich theorem</a>). </p><p>Kantorovich considered <a href="/facts/Infinite-dimensional_optimization/S18f9Byd">infinite-dimensional optimization</a> problems, such as the Kantorovich-Monge problem in <a href="/facts/Transportation_theory_(mathematics)/DRoHNtde">transport theory</a>. His analysis proposed the <a href="/facts/Wasserstein_metric/r0tB6sXm">Kantorovich–Rubinstein metric</a>, which is used in <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, in the theory of the <a href="/facts/Weak_convergence_of_measures/fb0I0KAL">weak convergence</a> of <a href="/facts/Probability_measure/8BjhgoPR">probability measures</a>. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/List_of_Russian_mathematicians/FIzXqhLY">List of Russian mathematicians</a></li> <li><a href="/facts/List_of_economists/dlnGBI5Q">List of economists</a></li> <li><a href="/facts/Shadow_price/gpHIueEC">Shadow price</a></li> <li><a href="/facts/List_of_Jewish_Nobel_laureates/nNekdQTP">List of Jewish Nobel laureates</a></li></ul> <h2 id="notes">Notes</h2> <ul><li>Makarov, V. (1987). "Kantorovich, Leonid Vitaliyevich". <i><a href="/facts/The_New_Palgrave%3a_A_Dictionary_of_Economics/3VDv8Bdp">The New Palgrave: A Dictionary of Economics</a></i>. 3: 14–15.</li> <li>Kantorovich, L.V. (1939). "Mathematical Methods of Organizing and Planning Production". <i>Management Science</i>. 6 (4): 366–422. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1287%2Fmnsc.6.4.366">10.1287/mnsc.6.4.366</a>. <a href="/facts/JSTOR_(identifier)/YTeVmaJ7">JSTOR</a> <a href="https://www.jstor.org/stable/2627082">2627082</a>.</li> <li>Kantorovich, L.V. (1959). <i><a href="https://drive.google.com/file/d/1h8VXbMkPRWehB7khZr2lnATdOCPle03I/view">"The Best Use of Economic Resources"</a></i>(<a href="/facts/Portable_Document_Format/C9Mn1vYL"></a>). <a href="/facts/Pergamon_Press/qe6ctSTB">Pergamon Press</a>, 1965.</li> <li>Klaus Hagendorf (2008). <a href="http://eurodos.free.fr/docu/econ/Kantorovich1939.zip">Spreadsheet presenting all examples of Kantorovich</a>, 1939 with the <a href="/facts/OpenOffice.org/561WcNgg">OpenOffice.org</a> Calc Solver as well as the lp_solver.</li></ul> Nobel prize lecture <ul><li>Kantorovich, Leonid, <a href="http://nobelprize.org/nobel_prizes/economics/laureates/1975/kantorovich-lecture.html">"Mathematics in Economics: Achievements, Difficulties, Perspectives"</a>, Nobel Prize lecture, December 11, 1975</li> <li><a href="http://nobelprize.org/nobel_prizes/economics/laureates/1975/kantorovich-autobio.html">"Autobiography: Leonid Kantorovich"</a>, Nobel Prize website</li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Ivan Boldyrev, <a href="https://read.dukeupress.edu/hope/article/56/3/467/386155/The-Frame-for-the-Not-Yet-Existent-How-American">The Frame for the Not-Yet Existent: How American, European, and Soviet Scholars Jointly Shaped Modern Mathematical Economics</a>, History of Political Economy (2024) 56 (3): 467–488.</li> <li>Ivan Boldyrev, <a href="https://arxiv.org/abs/2407.14315">Soviet Mathematics and Economic Theory in the Past Century: A Historical Reappraisal</a>, Journal of Economic Literature, 2024.</li> <li><a href="/facts/George_Dantzig/04se7h0M">Dantzig, George</a>, <i><a href="https://books.google.com/books?id=2j46uCX5ZAYC">Linear programming and extensions</a></i>. Princeton University Press and the RAND Corporation, 1963. Cf. <a href="https://books.google.com/books?id=2j46uCX5ZAYC&q=kantorovich">p.22</a> for the work of Kantorovich.</li> <li><a href="/facts/John_R._Isbell/Pjyygred">Isbell, J.R.</a>; Marlow, W.H., <a href="https://www.jstor.org/stable/2627271">"On an Industrial Programming Problem of Kantorovich"</a>, <i>Management Science</i>, Vol. 8, No. 1 (Oct., 1961), pp. 13–17</li> <li>Kantorovich, L. V. <i>"My journey in science (supposed report to the Moscow Mathematical Society)" [expanding </i>Russian Math. Surveys<i> 42 (1987), no. 2, pp. 233–270]</i>. pp. 8–45. <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0898626">0898626</a>.</li> <li>Koopmans, Tjalling C., <a href="http://nobelprize.org/nobel_prizes/economics/laureates/1975/koopmans-lecture.pdf">"Concepts of optimality and their uses"</a>, Nobel Memorial Lecture, December 11, 1975</li> <li><a href="/facts/S._S._Kutateladze/Bq99vQUf">Kutateladze, S.S.</a>, <a href="http://www.jams.or.jp/notice/Notices0701.pdf">"The World Line of Kantorovich"</a>, <i>Notices of the ISMS</i>, International Society for Mathematical Sciences, Osaka, Japan, January 2007</li> <li><a href="/facts/S._S._Kutateladze/Bq99vQUf">Kutateladze, S.S.</a>, <a href="http://www.math.nsc.ru/LBRT/g2/english/ssk/lvk_phenomenon_e.html">"Kantorovich's Phenomenon"</a>, <i>Siberian Math. J.</i> (Сибирский мат. журн.), 2007, V. 48, No. 1, 3–4, November 29, 2006.</li> <li><a href="/facts/S._S._Kutateladze/Bq99vQUf">Kutateladze, S.S.</a>, <a href="http://www.math.nsc.ru/LBRT/g2/english/ssk/lvk100_e.html">"Mathematics and Economics of Kantorovich"</a></li> <li><a href="/facts/S._S._Kutateladze/Bq99vQUf">Kutateladze, S.S.</a>, <a href="http://www.math.nsc.ru/LBRT/g2/english/ssk/lvk110_e.html">"My Kantorovich"</a></li> <li>Leifman, Lev J., ed. (1990). <i>Functional analysis, optimization, and mathematical economics: A collection of papers dedicated to the memory of Leonid Vitalʹevich Kantorovich</i>. New York: The Clarendon Press, Oxford University Press. pp. xvi+341. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-19-505729-5. <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1082562">1082562</a>.{{cite book}}: CS1 maint: multiple names: authors list (link)</li> <li>Makarov, V. L. [Valery Leonidovich]; Sobolev, S. L. "Academician L. V. Kantorovich (19 January 1912 to 7 April 1986)". <i></i>In:<i> Functional analysis, optimization, and mathematical economics: A collection of papers dedicated to the memory of Leonid Vital'evich Kantorovich</i>. pp. 1–7. <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1082564">1082564</a>.</li> <li>Polyak, B. T. (2002). "History of mathematical programming in the USSR: Analyzing the phenomenon (Chapter 3 The pioneer: L. V. Kantorovich, 1912–1986, pp. 405–407)". <i>Mathematical Programming</i>. Series B. 91 (3): 401–416. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2Fs101070100258">10.1007/s101070100258</a>. <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1888984">1888984</a>. <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:13089965">13089965</a>.</li> <li>Ivan Boldyrev and Till Düppe, <a href="https://www.cambridge.org/core/journals/british-journal-for-the-history-of-science/article/programming-the-ussr-leonid-v-kantorovich-in-context/4BF0F0D89079DD94AF595EA25A991299">Programming the USSR: Leonid V. Kantorovich in context</a>, The British Journal for the History of Science. 2020. 53(2): 255-278.</li> <li>Spufford, Francis (2010). <i>Red plenty</i>. London: Faber.</li> <li>(in Russian) <a href="/facts/S._S._Kutateladze/Bq99vQUf">Kutateladze, S.S.</a>, et al., <a href="http://math.nsc.ru/LBRT/u2/nauka/kant.html">"Leonid V. Kantorovich (1912–1986)"</a>, Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences. Also published in the <i>Siberian Mathematical Journal</i>, Volume 43 (2002), No. 1, pp. 3–8</li> <li>(in Russian) Vershik, Anatoly, <a href="http://www.mmonline.ru/articles.php?mid=1893">"On Leonid Kantorovich and linear programming"</a></li></ul> <h2 id="external-links">External links</h2> Wikiquote has quotations related to <i>Leonid Kantorovich</i>. <ul><li><a href="https://mathgenealogy.org/id.php?id=58665">Leonid Kantorovich</a> at the <a href="/facts/Mathematics_Genealogy_Project/J7AFo1Do">Mathematics Genealogy Project</a></li> <li>O'Connor, John J.; <a href="/facts/Edmund_F._Robertson/jQMcnY79">Robertson, Edmund F.</a>, <a href="https://mathshistory.st-andrews.ac.uk/Biographies/Kantorovich.html">"Leonid Kantorovich"</a>, <i><a href="/facts/MacTutor_History_of_Mathematics_Archive/xtwLmN5q">MacTutor History of Mathematics Archive</a></i>, <a href="/facts/University_of_St_Andrews/IwXjmljw">University of St Andrews</a> (With additional photos.)</li> <li><a href="https://ideas.repec.org/e/pka32.html">Information about: Leonid Vitaliyevich Kantorovich</a> – IDEAS/RePEc</li> <li><a href="https://www.informs.org/About-INFORMS/History-and-Traditions/Biographical-Profiles/Kantorovich-Leonid-V">Biography Leonid Kantorovich</a> from the Institute for Operations Research and the Management Sciences</li> <li><a href="https://player.vgtrk.com/iframe/video/id/1620875/start_zoom/true/showZoomBtn/false/sid/kultura/?acc_video_id=episode_id/1457551/video_id/1575169/brand_id/21101">Biographical documentary about L.Kantorovich</a> by <i><a href="/facts/Rossiya_K/5DwSJDNV">Rossiya-Culture</a></i></li> <li><a href="https://www.nobelprize.org/laureate/686">Leonid Kantorovich</a> on Nobelprize.org </li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>The Soviet Union: empire, nation, and system, By Aron Kat︠s︡enelinboĭgen, page 406, Transaction Publishers, 1990 <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Gass, Saul I.; Rosenhead, J. (2011). "Leonid Vital'evich Kantorovich". Profiles in Operations Research. International Series in Operations Research & Management Science. Vol. 147. pp. 157–170. doi:10.1007/978-1-4419-6281-2_10. ISBN 978-1-4419-6280-5. <a href="978-1-4419-6280-5" target="_blank">978-1-4419-6280-5</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>"The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1975". NobelPrize.org. Retrieved 2025-02-19. <a href="https://www.nobelprize.org/prizes/economic-sciences/1975/kantorovich/biographical/" target="_blank">https://www.nobelprize.org/prizes/economic-sciences/1975/kantorovich/biographical/</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Kaplan, W. (1960). "Review of Approximate methods of higher analysis by L. V. Kantorovich and V. I. Krylov". Bull. Amer. Math. Soc. 66 (3): 146–147. doi:10.1090/S0002-9904-1960-10408-9. <a href="/wiki/Wilfred_Kaplan" target="_blank">/wiki/Wilfred_Kaplan</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Kantorovich`s biography in Russian <a href="http://www.nsu.ru/xmlui/bitstream/handle/nsu/2145/01.pdf" target="_blank">http://www.nsu.ru/xmlui/bitstream/handle/nsu/2145/01.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> </ol>