Mathematical  practice,  crowdsourcing,  and  social  machines  

 Ursula  Martin  

University  of  Oxford    

supported  by  a  UK  EPSRC    Senior  Fellowship  2014-­‐2017,    invesBgaBng  the  collaboraBve    

producBon    of    mathemaBcs              

 Formal  proofs  and  crowdsourcing  are  changing  MATHEMATICAL  PRACTICE.  This  project  uses  SOCIAL  SCIENCE  methods  to  analyse  CROWDSOURCED  MATHEMATICS,  with  the  long  term    goal  of  developing  a  MODEL  of  the  process  and  building  be@er  tools  to  support  it  

Polymath  8                      towards  twin  primes    Live  now!!!                      hSp://Bnyurl.com/k6cuclt    Polymath  -­‐  deep  interdisciplinary  collabora4ons  

Nature  461,15  Octob

er  2009  

What  next?  

Polymath  8            http://tinyurl.com/ktdjgkb

Improve  the  bound  on  the  least  gap  between  consecu4ve  primes  that  is  aDained  infinitely  oFen,  by  developing  the  techniques  of  Zhang.      Bound  from  70,000,000  (4/6/13)  to  246  (14/4/14)  ….  a  kinda  dead  end                                        (11/6/13-­‐18/6/14)        hDp://4nyurl.com/lqfwowc  …  4dy  up  loose  ends      (14/4/14-­‐17/5/14)  hDp://4nyurl.com/k6cuclt  ….  Now  wriDen  up  as  two  papers  on  arxiv  

Computer  proof    

 

Russell and Whitehead, Principia Mathematica, Vol II p79

NASA  Formal  Methods,  Lecture  Notes  in  Computer  Science  Volume  7226,  2012,  pp  85-­‐99  

 Formal  proofs  and  crowdsourcing  are  changing  MATHEMATICAL  PRACTICE.  This  project  uses  SOCIAL  SCIENCE  methods  to  analyse  CROWDSOURCED  MATHEMATICS,  with  the  long  term    goal  of  developing  a  MODEL  of  the  process  and  building  be@er  tools  to  support  it  

Face  to  face  collaboraBon    Ethnographic  study  at  a  research  ins4tute  • Variety  of  collabora4ons  and  outcomes  • What  makes  it  work  (or  not)  • Role  of  shared  and  private  spaces  • Nature  of  informa4on  flows  • Use  of  physical  and  virtual  space  • Measures  of  success  

   

Next  steps  

• Con4nuing  study  of  collabora4on    • Philosophy  •  Ethnography  • HCI  • Cogni4ve  science  • AI/computer  science  

• Model  using  argumenta4on  theory/LCC  • Real-­‐4me  tracking  of  polymath  

Mathematical  production  2050??