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Royal Society (1981–) American Academy of Arts and Sciences (1992–)[10]
Utmerkelser
Fellow of the Royal Society (1981) Pólya Prize (1987) Berwick Prize (1971) Nemmers Prize in Mathematics (1998) Steele Prize for Mathematical Exposition (2000)[11]
Conway ble hyllet for sin pedagogiske evne til å forklare komplekse matematiske teoremer på et tydelig og underholdende vis.[trenger referanse] For dette fikk han Steeleprisen i 2000.[trenger referanse]
Siobhan Roberts: Genius At Play: The Curious Mind of John Horton Conway. Bloomsbury Publishing USA, 2015, ISBN 978-1-62040-594-9.
T. M. Thompson: From error-correcting codes through sphere packings to simple groups. Washington 1983 (historische Darstellung, die aber auch mathematisch ausführlich ist).
Donald J. Albers, G. L. Alexanderson (utg.): Mathematical People: Profiles and Interviews. Cambridge/MA 1985, S. 43–50.
Heinz-Dieter Ebbinghaus, Friedrich Hirzebruch (utg.): Zahlen. Springer Verlag, 1993 (mit einem Kapitel über surreale Zahlen).
Donald Knuth: Insel der Zahlen – eine zahlentheoretische Genesis im Dialog. Vieweg, 1979. (Original: Surreal numbers. 1974).
Marcus du Sautoy: Die Mondscheinsucher. Mathematiker entschlüsseln das Geheimnis der Symmetrie. C.H. Beck, 2008, ISBN 978-3-406-57670-6 (du Sautoy gehörte als Doktorand zu Conways Arbeitsgruppe in Cambridge).
Siobhan Roberts: Genius at Play. Bloomsbury Publishing, 2015, ISBN 978-1-62040-593-2 (Biographie von Conway).
John Conway – mathematician of symmetry and everything else. In: Mathematical Intelligencer. Bind 23, 2001, Nr. 2 (Interview med István Hargittai).