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Hans Freudenthal
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<h2 id="biography">Biography</h2> <p>Freudenthal was born in <a href="/facts/Luckenwalde/fx4Dd9jm">Luckenwalde</a>, <a href="/facts/Province_of_Brandenburg/pMn2ylrx">Brandenburg</a>, on 17 September 1905, the son of a Jewish teacher. He was interested in both mathematics and literature as a child, and studied mathematics at the <a href="/facts/Humboldt_University_of_Berlin/QE2lhhkd">University of Berlin</a> beginning in 1923.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> He met <a href="/facts/L._E._J._Brouwer/6q6ULf3b">L. E. J. Brouwer</a> in 1927, when Brouwer came to Berlin to give a lecture, and in the same year Freudenthal also visited the <a href="/facts/University_of_Paris/yXAx8nlG">University of Paris</a>.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> He completed his thesis work with <a href="/facts/Heinz_Hopf/PMks10NV">Heinz Hopf</a> at Berlin, defended a thesis on the <a href="/facts/End_(topology)/Rtwywetf">ends</a> of <a href="/facts/Topological_group/cAgNMMRU">topological groups</a> in 1930, and was officially awarded a degree in October 1931.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><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> After defending his thesis in 1930, he moved to Amsterdam to take up a position as assistant to Brouwer.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a><a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> In this pre-war period in Amsterdam, he was promoted to lecturer at the <a href="/facts/University_of_Amsterdam/VqQ6q6QK">University of Amsterdam</a>,<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> and married his wife, Suus Lutter, a Dutch teacher.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> </p><p>Although he was a German Jew, Freudenthal's position in the Netherlands insulated him from the <a href="/facts/Nuremberg_Laws/qhRVUSPd">anti-Jewish laws</a> that had been passed in Germany beginning with the <a href="/facts/Nazi/JjsMI4lE">Nazi</a> rise to power in 1933.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> However, in 1940 the Germans <a href="/facts/Battle_of_the_Netherlands/q81KKes7">invaded the Netherlands</a>, following which Freudenthal was suspended from duties at the <a href="/facts/University_of_Amsterdam/VqQ6q6QK">University of Amsterdam</a> by the Nazis.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a><a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> In 1943 Freudenthal was sent to a labor camp in the village of <a href="/facts/Havelte/qbWJgFo4">Havelte</a> in the Netherlands, but with the help of his wife (who, as a non-Jew, had not been deported) he escaped in 1944 and went into hiding with his family in occupied Amsterdam.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> During this period Freudenthal occupied his time in literary pursuits, including winning first prize under a false name in a novel-writing contest.<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> </p><p>With the war over, Freudenthal's position at the University of Amsterdam was returned to him, but in 1946 he was given a chair in pure and applied mathematics and <a href="/facts/Foundations_of_mathematics/yjpbbUkt">foundations of mathematics</a> at <a href="/facts/Utrecht_University/SfvqmD0l">Utrecht University</a>, where he remained for the rest of his career.<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a><a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> He served as the 8th president of the <a href="/facts/International_Commission_on_Mathematical_Instruction/T0LCUjam">International Commission on Mathematical Instruction</a> from 1967 to 1970.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> In 1971 he founded the Institute for the Development of Mathematical Education (IOWO) at Utrecht University, which after his death was renamed the <a href="/facts/Freudenthal_Institute/2st8JDIe">Freudenthal Institute</a>.<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a> In 1972 he founded and became editor-in-chief of the journal <i><a href="/facts/Geometriae_Dedicata/8sNcnkJs">Geometriae Dedicata</a></i>.<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a> He retired from his professorship in 1975<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a> and from his journal editorship in 1981.<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a> He died in <a href="/facts/Utrecht/49YgvgXJ">Utrecht</a> in 1990, sitting on a bench in a park where he always took a morning walk.<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a> </p> <h2 id="contributions">Contributions</h2> <p>In his thesis work, published as a journal article in 1931, Freudenthal introduced the concept of an <a href="/facts/End_(topology)/Rtwywetf">end</a> of a <a href="/facts/Topological_space/v2ut7CbK">topological space</a>.<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a> Ends are intended to capture the intuitive idea of a direction in which the space extends to infinity, but have a precise mathematical formulation in terms of covers of the space by nested sequences of <a href="/facts/Compact_set/d0cgXJH7">compact sets</a>. Ends remain of great importance in <a href="/facts/Topological_group/cAgNMMRU">topological group</a> theory, Freudenthal's motivating application,<a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a> and also in other areas of mathematics such as the study of <a href="/facts/Minimal_surface/Fy7VkrLQ">minimal surfaces</a>. </p><p>In 1936, while working with Brouwer, Freudenthal proved the <a href="/facts/Freudenthal_spectral_theorem/t9oFUqsN">Freudenthal spectral theorem</a> on the existence of uniform approximations by <a href="/facts/Simple_function/hWAJkmDQ">simple functions</a> in <a href="/facts/Riesz_space/FX7Mwfxe">Riesz spaces</a>.<a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a> In 1937 he proved the <a href="/facts/Freudenthal_suspension_theorem/qGCDXhgl">Freudenthal suspension theorem</a>, showing that the <a href="/facts/Suspension_(topology)/pIWr58dM">suspension</a> operation on topological spaces shifts by one their low-dimensional <a href="/facts/Homotopy_group/xjogL95Y">homotopy groups</a>; this result was important in understanding the <a href="/facts/Homotopy_groups_of_spheres/YMENlGgd">homotopy groups of spheres</a> (since every sphere can be formed topologically as a suspension of a lower-dimensional sphere) and eventually formed the basis of <a href="/facts/Stable_homotopy_theory/wnedyf7K">stable homotopy theory</a>.<a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a> The <a href="/facts/Freudenthal_magic_square/7b1c35f6">Freudenthal magic square</a> is a construction in <a href="/facts/Lie_algebra/n2gAUkNq">Lie algebra</a> developed by Freudenthal (and independently by <a href="/facts/Jacques_Tits/QyJlDmlE">Jacques Tits</a>) in the 1950s and 1960s, associating each Lie algebra to a pair of <a href="/facts/Division_algebra/xp5Bepx3">division algebras</a>.<a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a> </p><p>In 1968, Freudenthal founded the journal, <i><a href="/facts/Educational_Studies_in_Mathematics/eH1HIWI8">Educational Studies in Mathematics</a></i> (ESM). Becoming one of the top-rated journals in the field of mathematics education, ESM was focused on publishing research around finding better ways to teach mathematics.<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a> </p><p>Later in his life, Freudenthal focused on elementary <a href="/facts/Mathematics_education/6hXltmmF">mathematics education</a>. In the 1970s, his single-handed intervention prevented the Netherlands from following the worldwide trend of "<a href="/facts/New_math/aREUYdXe">new math</a>".<a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a> He was also a fervent critic of one of the first international school achievement studies.<a class="footnote-ref" id="fnref:34" href="#fn:34"><sup>34</sup></a> He interpreted mathematics as a human activity where students should open a scientific eye on the world around them, mathematizing real situations, in a context that makes sense for the students. This approach is called <i>Realistic Mathematics Education</i> (RME).<a class="footnote-ref" id="fnref:35" href="#fn:35"><sup>35</sup></a> </p><p>Freudenthal published the <a href="/facts/Impossible_Puzzle/pflz6bPp">Impossible Puzzle</a>, a mathematical puzzle that appears to lack sufficient information for a solution, in 1969.<a class="footnote-ref" id="fnref:36" href="#fn:36"><sup>36</sup></a> He also designed a <a href="/facts/Constructed_language/x4Ec5trY">constructed language</a>, <a href="/facts/Lincos_(artificial_language)/ACTQCRbT">Lincos</a>, to make possible <a href="/facts/Communication_with_extraterrestrial_intelligence/SR1FUWxU">communication with extraterrestrial intelligence</a>.<a class="footnote-ref" id="fnref:37" href="#fn:37"><sup>37</sup></a><a class="footnote-ref" id="fnref:38" href="#fn:38"><sup>38</sup></a> </p> <h2 id="selected-publications">Selected publications</h2> <ul><li>Freudenthal, Hans (1931), "Über die Enden topologischer Räume und Gruppen", <i><a href="/facts/Mathematische_Zeitschrift/8JqT7561">Mathematische Zeitschrift</a></i>, 33: 692–713, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF01174375">10.1007/BF01174375</a>, <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:120965216">120965216</a>, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0002.05603">0002.05603</a></li> <li>Freudenthal, Hans (1936), <a href="http://www.dwc.knaw.nl/DL/publications/PU00016905.pdf">"Teilweise geordnete Moduln"</a> (PDF), <i>Proc. Akad. Wet. Amsterdam</i> (in German), 39: 641–651, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0014.31302">0014.31302</a>.</li> <li>Freudenthal, Hans (1937), <a href="http://www.numdam.org/item?id=CM_1938__5__299_0">"Über die Klassen der Sphärenabbildungen. I. Große Dimensionen"</a>, <i><a href="/facts/Compositio_Mathematica/Igc7zupB">Compositio Mathematica</a></i> (in German), 5: 299–314, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0018.17705">0018.17705</a>.</li> <li>Freudenthal, Hans (1960), <a href="https://www.sciencedirect.com/bookseries/studies-in-logic-and-the-foundations-of-mathematics/vol/28/suppl/C"><i>Lincos: design of a language for cosmic intercourse</i></a>, Studies in logic and the foundations of mathematics, North-Holland Pub. Co..</li> <li>Freudenthal, Hans; de Vries, H. (1969), <i>Linear Lie Groups</i>, Pure and Applied Mathematics, vol. 35, New York: Academic Press, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0260926">0260926</a>.</li> <li>Freudenthal, Hans (1972), <i>Mathematics as an Educational Task</i>, Springer, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9789027702357.</li> <li>Freudenthal, Hans (1986), <i>Didactical Phenomenology of Mathematical Structures</i>, Mathematics Education Library, vol. 1, Springer, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9789027722614.</li> <li>Freudenthal, Hans (1991), <i>Revisiting Mathematics Education: China Lectures</i>, Kluwer Academic Publishers, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-7923-1299-6.</li> <li>Freudenthal, Hans; Freudenthal, Matías (2015), <i>El viaje de Ofantito</i> (in Spanish), Granada (Spain): Esdrújula Ediciones, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-84-164850-9-3 [Children's story left unfinished in 1943, completed and translated into Spanish by his son Matijs (Matías)].<a class="footnote-ref" id="fnref:39" href="#fn:39"><sup>39</sup></a></li></ul> <h2 id="awards-and-honors">Awards and honors</h2> <p>In 1951, Freudenthal became a member of the <a href="/facts/Royal_Netherlands_Academy_of_Arts_and_Sciences/3kMPbFAD">Royal Netherlands Academy of Arts and Sciences</a>.<a class="footnote-ref" id="fnref:40" href="#fn:40"><sup>40</sup></a> He was also an honorary member of the <a href="/facts/International_Academy_of_the_History_of_Science/KdS3L4j1">International Academy of the History of Science</a>.<a class="footnote-ref" id="fnref:41" href="#fn:41"><sup>41</sup></a> He was awarded the <a href="/facts/Gouden_Ganzenveer/UasppokL">Gouden Ganzenveer</a> award in 1984.<a class="footnote-ref" id="fnref:42" href="#fn:42"><sup>42</sup></a> </p><p>In 2000, the <a href="/facts/International_Commission_on_Mathematical_Instruction/T0LCUjam">International Commission on Mathematical Instruction</a> instituted an award named in honor of Freudenthal, the Hans Freudenthal Medal. It is given in odd-numbered years (beginning in 2003) for an "outstanding achievement in mathematics education research" in the form of "a major cumulative program of research". Recipients of the medal have included <a href="/facts/Celia_Hoyles/eNRjxFmg">Celia Hoyles</a>, Paul Cobb, <a href="/facts/Anna_Sfard/fvSIXJ0y">Anna Sfard</a>, Yves Chevallard, <a href="/facts/Luis_Radford/cbx9wuWq">Luis Radford</a>, Frederick Leung and <a href="/facts/Ole_Skovsmose/pgER2Pgw">Ole Skovsmose</a>.<a class="footnote-ref" id="fnref:43" href="#fn:43"><sup>43</sup></a> <a class="footnote-ref" id="fnref:44" href="#fn:44"><sup>44</sup></a> </p><p> The <a href="/facts/Asteroid/g7Ulr1VB">asteroid</a> <a href="/facts/9689_Freudenthal/3XDUaxt7">9689 Freudenthal</a> is named after him.<a class="footnote-ref" id="fnref:45" href="#fn:45"><sup>45</sup></a> </p> <h2 id="further-reading">Further reading</h2> Wikiquote has quotations related to <i>Hans Freudenthal</i>. Wikimedia Commons has media related to Hans Freudenthal (mathematician). <ul><li><a href="http://www.dbnl.org/tekst/freu002schr01_01/index.htm">Autobiography by Hans Freudenthal, Hans, schrijf dat op</a></li> <li>Strambach, Karl; Veldkamp, Ferdinand D. (1981), "A tribute to Hans Freudenthal", <i><a href="/facts/Geometriae_Dedicata/8sNcnkJs">Geometriae Dedicata</a></i>, 11 (1): 125, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF00183195">10.1007/BF00183195</a>, <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:121711425">121711425</a>.</li> <li>Howson, G. (1985), "Hans Freudenthal and the foundations of a discipline of mathematics education", <i>Nieuwe Wiskrant</i>, 5: 68–72.</li> <li>Van Est, W. T. (1993), "Hans Freudenthal (17 September 1905–13 October 1990)", <i>Educational Studies in Mathematics</i>, 25 (1–2): 59–69, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF01274102">10.1007/BF01274102</a>, <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:144711501">144711501</a>.</li> <li>Strambach, Karl; Veldkamp, Ferdinand D. (1991), "In memoriam Hans Freudenthal", <i>Geometriae Dedicata</i>, 37 (2): 119, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF00147407">10.1007/BF00147407</a>, <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:122967603">122967603</a>.</li> <li>Gravemeijer, K.; Terwel, J. (2000), <a href="https://research.vu.nl/en/publications/bd7f8341-860b-466d-8229-4833fdb27036">"Hans Freudenthal: A mathematician on didactics and curriculum theory"</a>, <i>Journal of Curriculum Studies</i>, 32 (6): 777–796, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1080%2F00220270050167170">10.1080/00220270050167170</a>, <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:55632373">55632373</a>.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Streefland, Leen, ed. (1994), The Legacy of Hans Freudenthal, Springer, ISBN 9780792326533. <a href="9780792326533" target="_blank">9780792326533</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Prof. Dr. Hans Freudenthal (1905 - 1990), Freudenthal institute for science and mathematics education, archived from the original on 2013-10-20, retrieved 2013-01-10. <a href="https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html" target="_blank">https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>O'Connor, John J.; Robertson, Edmund F., "Hans Freudenthal", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>O'Connor, John J.; Robertson, Edmund F., "Hans Freudenthal", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Bos, Henk J. M. (1992), "In memoriam Hans Freudenthal (1905–1990)", Historia Mathematica, 19 (1): 106–108, doi:10.1016/0315-0860(92)90070-R. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Prof. Dr. Hans Freudenthal (1905 - 1990), Freudenthal institute for science and mathematics education, archived from the original on 2013-10-20, retrieved 2013-01-10. <a href="https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html" target="_blank">https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>O'Connor, John J.; Robertson, Edmund F., "Hans Freudenthal", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Hans Freudenthal at the Mathematics Genealogy Project <a href="https://mathgenealogy.org/id.php?id=17394" target="_blank">https://mathgenealogy.org/id.php?id=17394</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Prof. Dr. Hans Freudenthal (1905 - 1990), Freudenthal institute for science and mathematics education, archived from the original on 2013-10-20, retrieved 2013-01-10. <a href="https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html" target="_blank">https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>O'Connor, John J.; Robertson, Edmund F., "Hans Freudenthal", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>O'Connor, John J.; Robertson, Edmund F., "Hans Freudenthal", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Bos, Henk J. M. (1992), "In memoriam Hans Freudenthal (1905–1990)", Historia Mathematica, 19 (1): 106–108, doi:10.1016/0315-0860(92)90070-R. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Prof. Dr. Hans Freudenthal (1905 - 1990), Freudenthal institute for science and mathematics education, archived from the original on 2013-10-20, retrieved 2013-01-10. <a href="https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html" target="_blank">https://web.archive.org/web/20131020201814/http://www.fi.uu.nl/en/freudenthal.html</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>O'Connor, John J.; Robertson, Edmund F., "Hans Freudenthal", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>O'Connor, John J.; Robertson, Edmund F., "Hans Freudenthal", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Bos, Henk J. M. 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