Biographies of past number theorists and various items of iistorical interest

Return to Menu page

Return to Number Theory Web page

Some biographies of past contributors to number theory

Some of the major sources of obituaries of mathematicians are:
  1. The Mactutor History of Mathematics (MacTutor)
  2. Russian Mathematical Surveys (RMS)
  3. Acta Arithmetica (AA)
  4. Notices of the Americal Mathematical Society (NAMS)
  5. Bulletin of the London Mathematical Society (BLMS)
  6. Journal of the London Mathematical Society (JLMS) (Pre BLMS)
  7. Proceedings of the London Mathematical Society (PLMS) (Pre JLMS)
  8. The Mathematical Intelligencer
  9. Journal of Number Theory
  10. Mathematicians of the Seventeenth and Eighteenth Centuries (David Wilkins' transcriptions from A Short Account of the History of Mathematics, by W.W. Rouse Ball)
  11. Historia Mathematica
A glance at Paulo Ribenboim's Fermat's Last Theorem for amateurs, Franz Lemmermeyer's Reciprocity Laws and L.E. Dickson's History of the Theory of Numbers, reveals the existence of many past number theorists about whom little is known.
Any corrections, extra information or links to additional online biographies should be passed on to Keith Matthews at webmaster@numbertheory.org


[ A | B | C | D | E | F | G | H | I | J | K | L | M ]
[ N | O | P | R | S | T | U | V | W | Z ]

  1. Rudolf Ahlswede
  2. Alexander Aigner
  3. Helen Popova Alderson
  4. William (Red) Alford
  5. William S. Anglin (1949-2004)
  6. Nesmith Ankeny
  7. Roger Apéry
  8. Tom Apostol died on May 8, 2016
  9. Peter Friedrich Arndt (Wikipedia)
  10. Cahit Arf (MacTutor)
  11. Emil Artin
    • Emil Artin (MacTutor)
    • Emil Artin, his life and his work, (by Hans Zassenhaus, Notre Dame Journal of Formal Logic V, No. 1, January 1964)
    • Creating a life: Emil Artin in America, Della Dumbaugh and Joachim Schwermer, Bull. Amer. Math. Soc 50 (2013), 321-330
  12. Robert Ash, 1935-2015
  13. Oliver Atkin
  14. Frederick Valentine Atkinson (Angelo B. Mingarelli)
  15. L. Aubry
  16. James Burton Ax (1937-2006)
  17. Raymond Ayoub (1923-2013)
  18. A. A. Krishnaswami Ayyangar
  19. Paul Gustav Heinrich Bachmann (MacTutor)
  20. Mark Borisovich Barban (RMS)
  21. Eric Stephen Barnes
  22. Paul Bateman
  23. Mihály Bauer (MacTutor)
  24. Felix Behrend
  25. Eric Temple Bell (MacTutor)
  26. Gennadii Vladimirovich Belyi (1951-2001) Russ. Math. Surv. 57 981 (2002)
  27. Anne-Marie Bergé
  28. Joseph Louis François Bertrand (MacTutor)
  29. William Edward Hodgson Berwick
  30. Arne Karl August Beurling
  31. Bhaskara (MacTutor)
  32. Jacques de Billy (MacTutor)
  33. Hans Frederick Blichfeldt (MacTutor)
  34. Fritz Blumer (1904-1988)
  35. Stjepan Bohniček (1872-1956)
  36. Alfred Theodore Brauer (MacTutor)
  37. Joel Lee Brenner (1912-1997)
  38. Robert Breusch (1907-1995)
  39. Béla Brindza (1958-2003)
  40. Jerzy Browkin (1934-2015) (Google translation)
  41. Viggo Brun
    • Viggo Brun (from an obituary by C. Scriba, Historia Mathematica 7 (1980), 1-6)
    • Viggo Brun (Christoph Scriba, Mitt. Math. Ges. Hamburg 11 (1985) 271-290)
    • Viggo Brun (Sigmund Selberg: Norske Vid. Selsk. Forh. (Trondheim) (1979) 57-61 - in Norwegian)
  42. Aleksandr Adol'fovich Bukhshtab (RMS)
  43. Viktor Yakovlevich Bunyakovsky (MacTutor)
  44. David G. Cantor passed away on November 19, 2012
  45. Leonard Carlitz
  46. Robert Daniel Carmichael (Wikipedia)
  47. John (Ian) William Scott Cassels
  48. Eugène Charles Catalan (MacTutor)
  49. Claude Chabauty
  50. John H. Chalk
  51. David Gawen Champernowne (ICGA Journal 23 December 2000)
  52. Albert Châtelet (MacTutor)
  53. François Châtelet (Wikipedia)
  54. Nikolai Grigorievich Chebotaryov (MacTutor)
  55. Pafnuty Lvovich Chebyshev (MacTutor)
  56. Thyagaraju Chelluri
  57. Chen Jingrun (Wikipedia)
  58. Claude Chevalley (MacTutor)
  59. Sarvadaman Chowla
  60. Nikolai Grigor'evich Chudakov
  61. Francisco Javier Cilleruelo (1961 - 2016), Fallece Javier Cilleruelo
  62. Paul Cohen biography (Wikipedia), Paul J. Cohen memorial web page
  63. Harvey Cohn died on May 16, 2014
  64. Robert Coleman
  65. George Erskine Cooke (21/5/1942-19/12/1976)
  66. Albert Everett Cooper
  67. Harald Cramér (MacTutor)
  68. Richard Crandall (1947-2012)
  69. Allan Joseph Champneys Cunningham (JLMS)
  70. Harold Davenport
  71. Clive Selwyn Davis (1916-2009)
  72. Nicolaas Govert de Bruijn (MacTutor)
  73. Julius Wilhelm Richard Dedekind (MacTutor)
  74. Hubert Delange (1913-2003)
  75. Boris Nikolaevich Delone
  76. Max Deuring
    • Max Deuring (from the Göttingen Collection - also see Martin Kneser, Jahresbericht der Deutschen Mathematiker Vereinigung 89 (1987) 135-143, Peter Roquette, ibid 91 (1989) 109-125)
    • Max Deuring (AA)
  77. Leonard Eugene Dickson (MacTutor)
  78. Diophantus of Alexandria (MacTutor)
  79. Johann Peter Gustav Lejeune Dirichlet
  80. Bohuslav Diviš (Also see J. Number Theory 9 1977, v-vii) and PhD tree
  81. Mary Dolciani
  82. Alain Durand (Lecture Notes in Mathematics 1415)
  83. Bernard Dwork
  84. Martin Eichler
    • Martin Eichler (AA)
    • Martin Eichler (MacTutor)
    • Leben und Werk von Martin Eichler, Elemente der Mathematik 49 (1994) 45-60 (by Jürg Kramer)
  85. Ferdinand Gotthold Max Eisenstein (MacTutor)
  86. Otto Endler (1929-1988)
  87. Veikko Ennola (1932-2013)
  88. Paul Epstein
  89. Eratosthenes of Cyrene (MacTutor)
  90. Paul Erdös
  91. Theodor Estermann
  92. Dennis Estes (June 18, 1941- Feb. 1, 1999)
  93. Euclid of Alexandria (MacTutor)
  94. Leonhard Euler
  95. Graham Everest
  96. Dmitrii Konstantinovich Faddeev
  97. Naum Il'ich Feldman
  98. Pierre de Fermat
  99. Nathan Fine (NAMS)
  100. Ernests Fogels
  101. Jérôme Franel (MacTutor)
  102. Giovanni Frattini (MacTutor)
  103. Ferdinand Georg Frobenius (MacTutor)
  104. Albrecht Fröhlich
  105. Wolfgang Fuchs (NAMS)
  106. Karl Rudolf Fueter
  107. Philipp Furtwängler (1869-1940)
  108. Steve Galovich
  109. Johann Carl Friedrich Gauss
  110. Leopold Bernhard Gegenbauer (MacTutor)
  111. Aleksandr Osipovich Gelfond
  112. Angelo Genocchi (MacTutor)
  113. André Gérardin
  114. Marie-Sophie Germain (MacTutor)
  115. Frank Emmett Gerth III
  116. James Whitbread Lee Glaisher (MacTutor)
  117. Herbert James Godwin (1922-2005)
  118. Christian Goldbach (MacTutor)
  119. Irving John (Jack) Good (1916-2009) (Virginia Tech)
  120. Basil Gordon Also see On the work of Basil Gordon
  121. William Sealey Gosset (MacTutor)
  122. Jorgen Pedersen Gram (MacTutor)
  123. George Greaves (BLMS 43, (2011) 203-205)
  124. Emil Grosswald
  125. Alexander Grothendieck - obituary (The Telegraph)
  126. Fritz Grunewald (MacTutor)
  127. Andrew Paul Guinand (MacTutor)
  128. Stan Gurak
  129. Jacques Salomon Hadamard (MacTutor)
  130. Heini Halberstam
  131. Marshall Hall Jr. (MacTutor)
  132. Harris Hancock
  133. Godfrey Harold Hardy
  134. Colin Brian Haselgrove (MacTutor)
  135. Helmut Hasse
  136. David Ryan Hayes (MacTutor)
  137. Erich Hecke
  138. Kurt Heegner
  139. Hans Arnold Heilbronn (MacTutor)
  140. Kurt Hensel (MacTutor)
  141. Jacques Herbrand (MacTutor)
  142. Charles Hermite (MacTutor)
  143. Gustav Herglotz (MacTutor)
  144. David Hilbert
  145. Edmund Hlawka (Robert Tichy)
  146. Ludwig Holzer (1891-1968) (Rudolf Einhorn: Rostock. Math. Kolloq. No. 27, (1985) 23-30)
  147. Loo-keng Hua
  148. Richard Hudson (1945-2016) (ColaDaily.com)
  149. Adolf Hurwitz
  150. Jun-ichi Igusa
  151. Masatoshi Gündüz Ikeda (MacTutor)
  152. Albert Edward Ingham
  153. Kustaa Inkeri
  154. Kenkichi Iwasawa
  155. Shokichi Iyanaga
  156. Carl Gustav Jacob Jacobi
  157. Ernst Jacobsthal
  158. Timothy Paul Jameson (Lancaster Guardian)
  159. Vojtěch Jarník
    • Vojtěch Jarník (MacTutor)
    • Life and work of Vojtěch Jarník, Břetislav Novák, Published by the Union of Czech Mathematicians and Physicists, Zitna 25, Praha 1, Czech Republik
    • Vojtěch Jarník (AA)
  160. Michał Kalecki (Wikipedia)
  161. Pierre Kaplan
  162. Irving Kaplansky
  163. Erich Kamke
  164. Shri Dattathreya Ramachandra Kaprekar
  165. Anatolii Alexeevich Karatsuba (1937-2008) (photo)
  166. Aubrey J. Kempner
  167. Aleksandr Yakovlevich Khinchin (MacTutor)
  168. Péter Kiss (Wikipedia)
  169. Hendrik Douwe Kloosterman
  170. Stanislaw Knapowski (MacTutor)
  171. John Knopfmacher
  172. Marvin Knopp (1933-2011)
  173. Chao Ko (Wikipedia)
  174. Niels Fabian Helge von Koch (MacTutor)
  175. Jurjen Ferdinand Koksma (MacTutor)
  176. Kjell Kolden
  177. Ivan Korec
  178. Alexander Nikolaevich Korkine (in Russian) (english translation by Bob Burns)
  179. Miloš Kössler
  180. Marc Krasner (Wikipedia)
  181. Leopold Kronecker (MacTutor)
  182. Jonas Petrovich Kubilius
  183. Robert Maruo Kubota (1942-1973)
  184. Ernst Eduard Kummer (MacTutor)
  185. Sigekatu Kuroda
    • Sigekatu Kuroda (MacTutor)
    • Sigekatu Kuroda (J. Number Theory 7 1975, 1-4)
  186. József Kürschák
  187. Rodion Osievich Kuz'min (Wikipedia)
  188. Nikolai Vasil'evitch Kuznetsov (1939-2010)
  189. Joseph-Louis Lagrange
  190. Gabriel Lamé (MacTutor)
  191. Edmund Georg Hermann Landau
  192. Serge Lang
  193. Bob Laxton (1933-2002)
  194. Victor Amédée Lebesgue (1791-1875) (Les-mathematiques.net)
  195. Adrien-Marie Legendre
  196. Derrick Henry Lehmer (AA)
  197. Emma Lehmer
  198. Joseph Lehner
  199. Cornelis Gerrit Lekkerkerker (Nieuw Archief voor Wiskunde)
  200. Heinrich-Wolfgang Leopoldt
  201. Mathias Lerch (MacTutor)
  202. William Judson LeVeque (NAMS)
  203. Norman Levinson (MacTutor)
  204. Donald J. Lewis died on February 25, 2015
  205. Richard P. Lewis died on 26th July 2007 Pierre Liardet died on August 29, 2014
  206. Carl Louis Ferdinand von Lindemann (MacTutor)
  207. Frederick Lindemann - Lord Cherwell (1886-1957) (Wikipedia), Number Theory and Other Reminiscences of Viscount Cherwell (Notes and Records of the Royal Society of Londoni, E.M. Wright)
  208. Edward Hubert Linfoot
    • Edward Hubert Linfoot (J.H. Bell: BLMS 16 (1984) 52-58); J. Linfoot: Math. Intelligencer 15 (1993) 39-43
    • Edward Hubert Linfoot (Wikipedia)
  209. Yuri Vladimirovich Linnik
  210. Joseph Liouville (MacTutor)
  211. John Edensor Littlewood
  212. Wilhelm Ljunggren (MacTutor)
    • The Collected Papers of Wilhelm Ljunggren, Ed. Paulo Ribenboim, Queen's papers in pure and applied mathematics 115, 2003
  213. Robert Landis Long
  214. Salomon Lubelski (AA)
  215. François Edouard Anatole Lucas (MacTutor)
  216. Hans Maass (Wikipedia)
  217. Alexander Murray Macbeath
  218. Manohar Lal Madan died on April 3, 2011
  219. Kurt Mahler
  220. Wilhelm Maier (1896-1990)
  221. Edmond Maillet
  222. Henry Mann (Ohio collection)
  223. Alla Lavrik-Männlin (March 2nd, 1964-February 14th, 2003)
  224. Andrei Andreyevich Markov (MacTutor)
  225. George Ballard Mathews
  226. Emile Léonard Mathieu (MacTutor)
  227. Daniel Friedrich Ernst Meissel (MacTutor)
  228. Puliyakot Kesava Menon (1917-1979) (Bull. Math. Assoc. India 18 (1986), no. 1-4, 21-24)
  229. Franz Mertens (MacTutor)
  230. William H. Mills (November 9, 1921- March 7, 2007) (See A prime-representing function, Bull. Amer. Math. Soc., Volume 53, Number 12 (1947), 1196-1196, also Wikipedia article
  231. Hermann Minkowski
  232. Dimitry Mirimanoff
  233. Leon Mirsky (BLMS 18 (1986) 195-206)
  234. Richar Anthony Mollin
  235. August Ferdinand Möbius (MacTutor)
  236. Louis Joel Mordell
  237. Taro Morishima
  238. Leo Moser
  239. Theodore Samuel Motzkin
  240. Thomas Muir (MacTutor)
  241. Trygve Nagell (AA)
    • The Collected Papers of Trygve Nagell, Ed. Paulo Ribenboim, Queen's papers in pure and applied mathematics 121, 2003
  242. Christopher Eastick Nelson (?-1973)
  243. Jürgen Neukirch, (1937-1997) in memoriam by Theodor Bröcker
  244. Donald J. Newman (Wikipedia)
  245. Morris Newman
  246. Ivan Niven (obituary by Kenneth Ross)
  247. Břetislav Novák
  248. Robert Winston Keith Odoni (Sept 2003 issue, Glasgow Math. Journal)
  249. Carl Douglas Olds
  250. Vyacheslav Alekseevich Oleinikov (RMS)
  251. Kathleen Timpson Ollerenshaw (MacTutor)
  252. Alexander Oppenheim
  253. Hans-Heinrich Ostmann (Wikipedia), also (Obituary JDMV 86, 1984, 31-35)
  254. Oystein Ore (MacTutor)
  255. Alexander Markowich Ostrowski
  256. Ali Özlük 1952-2012
  257. Gordon Pall (no biography)
  258. Pan Chengdong
  259. William Parry Royal Society Memoirs
  260. Wilhelm Patz (no biography)
  261. William Barry Pennington (BLMS)
  262. Oskar Perron
  263. Hans Petersson (MacTutor)
  264. Walter Philipp
  265. Ilya Piatetski-Shapiro (1929-2009)
  266. Joachim Piehler
  267. Jean François Théophile Pépin (Wikipedia)
  268. Subbayya Sivasankaranarayana Pillai
  269. Nils Pipping (1890-1982)
  270. Charles Pisot
  271. Peter Arthur Barry Pleasants (24th August 1939- 20th April 2008)
  272. Henry Cabourn Pocklington Obituary Notices of Fellows of the Royal Society, Vol. 8, No. 22 (Nov. 1953) 555-565 (JSTOR)
  273. Felix Pollaczek
  274. George Pólya (MacTutor)
  275. Alf van der Poorten (1942-2010)
  276. J. Popken (1905-1970) (H. Jager, C.G.Lekkerkerker: Nieuw Archief voor Wiskunde 19 (1971) 1-9)
  277. Aleksei Georgievich Postnikov (RMS)
  278. Ralph Earnest Powers (Wikipedia)
  279. Karl Prachar (1924-1994) (E. Hlawka: Monatshefte für Math. 121 (1996) 1-9)
  280. Hans Rademacher
  281. S. Raghavan
  282. Steve Rallis (AMS Notices)
  283. Kanakanahalli Ramachandra
  284. Kollagunta Gopalaiyer Ramanathan
  285. Chidambaram Padmanabhan Ramanujam (MacTutor)
  286. Srinivasa Ramanujan
  287. George Neal Raney (1922-2015)
  288. Robert Alexander Rankin (MacTutor)
  289. Ramanujan website (Prof. K. Srinivasa Rao)
  290. László Rédei
  291. Hans Reichardt
  292. Robert Remak (MacTutor)
  293. Alfréd Rényi
  294. Giovanni Ricci (AA)
  295. Hans-Egon Richert
  296. Georg Friedrich Bernhard Riemann
  297. Hans Riesel (Wikipedia biography)
  298. Phillipe Robba (Wikipedia biography)
  299. Raphael Robinson (MacTutor)
  300. Kirill Andreevich Rodosskii (1913-2004)
  301. Claude Ambrose Rogers
  302. Jonathan Rogawski (1955-2011)
  303. Nikolai Pavlovich Romanov
  304. David Rosen
  305. Arnold Ross (NAMS)
  306. John Barkley Rosser (Wikipedia)
  307. Klaus Friedrich Roth
  308. Louis Saalschütz (Wikipedia)
  309. Raphaël Salem
  310. Pierre Samuel (Wikipedia)
  311. Giovanii Sansone
  312. Peter Scherk (1910-1985)
  313. Theodor Schneider (MacTutor)
  314. Lev Genrikhovich Schnirel'mann (translation by Vladimir Drobot)
  315. Arnold Scholz
  316. Lowell Schoenfeld (John Ewing's tribute)
  317. Theodor Schönemann (Wikipedia)
  318. Issai Schur (MacTutor)
  319. Jack Schwartz died on March 2, 2009 (author of Algebraic Number Theory, 1961, NYU Institute of Mathematical Sciences) Also see Jack Schwartz Memorial Blog and Wikipedia article
  320. Stefan Schwarz (MacTutor)
  321. Wolfgang Schwarz
  322. Sanford (Sandy) Segal (1937-2010)
  323. Beniamino Segre (AA)
  324. Atle Selberg
  325. Sigmund Selberg (Wikipedia)
  326. Clas-Olaf Selenius
  327. John Selfridge (1927-2010)
  328. Joseph Alfred Serret (MacTutor)
  329. Joseph Shalika
  330. Daniel Shanks
  331. Harold Nathaniel Shapiro
  332. Andrei Borisovich Shidlovsky (RMS)
  333. Takuro Shintani (J. Fac. Sci. Tokyo 28 (1981) iii-vi)
  334. Lev Genrikhovich Shnirelman (MacTutor)
  335. Carl Ludwig Siegel
  336. Waclaw Sierpinski
  337. Václav Šimerka (Franz Lemmermeyer, LMS J. Computing and Mathematics, 16 (2013) 118-129) Also see Wikipedia article
  338. Stanley Skewes (Wikipedia)
  339. Albert Thoralf Skolem
  340. Boris Fadeevich Skubenko (1929-1993) (see Zap. Nauchn. Semin. POMI 212 5-14 (1994) and Boris F. Skubenko. An essay on his life and scientific work, Volume 83, Number 5/February, 1997, 689-693)
  341. Henry John Stephen Smith
  342. Robert Arnold Smith (1937-1983) (E. Kani: Rocky Mountain J. 15 (1985) 413-415)
  343. Julius Sommer (Wikipedia)
  344. Robert Samuel Spira (1927-2013)
  345. Vladimir Gennadievich Sprindzuk
  346. Paul Gustav Stäckel (MacTutor)
  347. Gertrude Katherine Stanley
  348. Sergei Borisovich Stechkin (RMS)
  349. Ray Steiner (1942-2014) (The Blade)
  350. Rosemarie Stemmler (July 27, 1930-July 18, 2011)
  351. Moritz Abraham Stern (MacTutor)
  352. Ludwig Stickelberger (Wikipedia)
  353. Thomas Jan Stieltjes (MacTutor)
  354. Richard G. Stoneham (1920-1996)
  355. Carl Størmer (1874-1957)
    • Carl Størmer in memoriam, by Viggo Brun, Acta Math. 100, 1958, i-vii
    • Carl Størmer (Wikipedia)
  356. Walter Wilson Stothers
  357. Reinhold Straßmann (Wikipedia)
  358. Ernst Gabor Strauss
  359. Erik Stridsberg (1871-1950)
  360. Matukumalli Venkata Subbarao, 1921-2006 (R. Balasubramanian)
  361. Zyoiti Suetuna (MacTutor)
  362. George Szekeres(1911-2005)
  363. Kazimierz Szymiczek (1939-2015)
  364. Teiji Takagi (MacTutor)
  365. Ralph Tambs-Lyche (Obituary by Ernst S. Selmer, Normat 39 (1991))
  366. Yutaka Taniyama
  367. Olga Taussky-Todd (MacTutor)
  368. Paul Emery Thomas (Berkeley memorial)
  369. Axel Thue
  370. Heinrich Franz Friedrich Tietze (MacTutor)
  371. Nikolai Mikhailovich Timofeev (RMS)
  372. Edward Charles Titchmarsh
  373. Paul Turán
  374. Jerzy Urbanowicz
  375. James Victor Uspensky (1883-1947)
  376. Charles-Joseph de la Vallée Poussin
  377. Johannes Gualtherus van der Corput (AA)
  378. Harry Schultz Vandiver (MacTutor)
  379. Joost van Hamel
  380. Jacobus Hendricus van Lint (MacTutor)
  381. Boris Alekseevich Venkov (Wikipedia)
  382. Boris Borisovich Venkov died in Aachen on November 10th, 2011
  383. Tirukkannapuram Vijayaraghavan (JLMS 33 (1958) 252-255)
  384. Askol'd Ivanovich Vinogradov (1929-2005)
  385. Ivan Matveevich Vinogradov
  386. Niels Fabian Helge von Koch (MacTutor)
  387. Karl Georg Christian von Staudt (MacTutor)
  388. Sergei Mikhailovich Voronin (RMS)
  389. Georgy Fedoseevich Voronoi (MacTutor)
  390. Arnold Zel'manovich Walfisz
  391. Donald Dines Wall (Wikipedia)
  392. Edward Waring (MacTutor)
  393. Morgan Ward
  394. Jack Warga
  395. George Neville Watson (MacTutor)
  396. George Leo Watson
  397. Heinrich Martin Weber (MacTutor)
  398. André Weil
  399. Alfred Edward Western (JLMS)
  400. Hermann Weyl
  401. Albert Leon Whiteman (NAMS)
  402. Arthur Wieferich
  403. Carl Severin Wigert (Wikipedia)
  404. Herbert Wilf
  405. John Raymond Wilton (Australian dictionary of Biography)
  406. Anders Wiman (Trygve Nagell, Acta Math. 103 (1960) I-VI)
  407. Aurel Friedrich Wintner (MacTutor)
  408. Jan Wójcik (1936-1994) (A. Schinzel, Wiadom. Math. 33 (1997), 199-203)
  409. Dieter Wolke (1942-2015)
  410. Joseph Wolstenholme (MacTutor)
  411. Rod Worley died on 24th July 2011
  412. John Wrench Jr.
  413. Sir Edward Maitland Wright
  414. Yoshihiko Yamamoto (died in 2004)
  415. Hans Zassenhaus
  416. Egor Ivanovich Zolotarev

Top of page

Last modified 12th July 2016