Editing Max Newman (section)

===Early academic career===
On 5 November 1923, Newman was elected a [[Research fellow|Fellow]] of St John's.<ref name="frs"/> He worked on the foundations of [[combinatorial topology]], and proposed that a notion of equivalence be defined using only three elementary "moves".<ref name="odnb"/> Newman's definition avoided difficulties that had arisen from previous definitions of the concept.<ref name="odnb"/> Publishing over twenty papers established his reputation as an "expert in modern topology".<ref name="colossus.newman" /> Newman wrote ''Elements of the topology of plane sets of points'',<ref name="topology"/> a work on [[general topology]] and undergraduate text.<ref>{{cite journal|author=Smith, P. A.|author-link=Paul Althaus Smith|title=Review of ''Elements of the Topology of Plane Sets of Points'' by M. H. A. Newman|journal=Bull. Am. Math. Soc.|volume=45|issue=11|year=1939|pages=822–824|doi=10.1090/S0002-9904-1939-07087-0|url=https://www.ams.org/journals/bull/1939-45-11/S0002-9904-1939-07087-0/S0002-9904-1939-07087-0.pdf|doi-access=free}}</ref> He also published papers on [[mathematical logic]], and solved a special case of [[Hilbert's fifth problem]].<ref name="frs"/>

He was appointed a lecturer in mathematics at Cambridge in 1927.<ref name="odnb"/> His 1935 lectures on the Foundations of Mathematics and [[Gödel's incompleteness theorems|Gödel's theorem]] inspired [[Alan Turing]] to embark on his work on the ''[[Entscheidungsproblem]]'' (decision problem) that had been posed by [[David Hilbert|Hilbert]] and [[Wilhelm Ackermann|Ackermann]] in 1928.<ref>David Hilbert and Wilhlem Ackermann. Grundzüge der Theoretischen Logik. Springer, Berlin, Germany, 1928. English translation: David Hilbert and Wilhelm Ackermann. Principles of Mathematical Logic. AMS Chelsea Publishing, Providence, Rhode Island, USA, 1950.</ref> Turing's solution involved proposing a hypothetical [[Computer program|programmable]] [[computer|computing machine]].<ref>{{Cite journal | first1 = A. M. | title = On Computable Numbers, with an Application to the Entscheidungsproblem | journal = Proceedings of the London Mathematical Society | last1 = Turing | volume = 42 | series = 2 | issue = 1 | pages = 230–265 | year = 1936 | publication-date = 1937 | doi = 10.1112/plms/s2-42.1.230 | s2cid = 73712 | url = https://turingarchive.kings.cam.ac.uk/publications-lectures-and-talks-amtb/amt-b-12 }}</ref> In spring 1936, Newman was presented by Turing with a draft of "On Computable Numbers with an Application to the Entscheidungsproblem". He realised the paper's importance and helped ensure swift publication.<ref name="colossus.newman" /> Newman subsequently arranged for Turing to visit [[Princeton University|Princeton]] where [[Alonzo Church]] was working on the same problem but using his [[Lambda calculus]].<ref name="n176"/> During this period, Newman started to share Turing's dream of building a [[Stored-program computer|stored-program computing machine]].<ref name="colossus.rise">{{cite book |last=Copeland |first=Jack |editor-first=B. Jack |editor-last=Copeland |title=Colossus The Secrets of Bletchley Park's Codebreaking Computers |publisher=Oxford University Press |year=2010 |pages=91–100 |chapter=9. Colossus and the Rise of the Modern Computer |  isbn=978-0-19-957814-6 }}</ref>

During this time at Cambridge, he developed close friendships with [[Patrick Blackett]], [[J. H. C. Whitehead|Henry Whitehead]] and [[Lionel Penrose]].<ref name="colossus.newman" />

In September 1937, Newman and his family accepted an invitation to work for six months at Princeton. At Princeton, he worked on the [[Poincaré Conjecture]] and, in his final weeks there, presented a proof. However, in July 1938, after he returned to Cambridge, Newman discovered that his proof was fatally flawed.<ref name="colossus.newman" />

In 1939, Newman was elected a [[Fellow of the Royal Society]].<ref name="colossus.newman" />