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SUMMARY:After Math: Reasoning\, Computing\, and Proof in the Postwar Unite
 d States (via Skype) - Stephanie Dick (Harvard University)
DTSTART:20170714T123000Z
DTEND:20170714T133000Z
UID:TALK73279@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Computers ought to produce in the long run some fundamental ch
 ange in the nature of all mathematical activity.&rdquo\; These words\, pen
 ned in 1958\, capture the motivation behind an early field of computing re
 search called Automated Theorem-Proving or Automated Reasoning. Practition
 ers of this field sought to program computers to prove mathematical theore
 ms or to assist human users in doing so. Everyone working in the field agr
 eed that computers had the potential to make novel contributions to the pr
 oduction of mathematical knowledge. They disagreed about almost everything
  else. Automated theorem-proving practitioners subscribed to complicated a
 nd conflicting visions of what ought to count and not count as a mathemati
 cal proof. There was also disagreement about the character of human mathem
 atical faculties - like intuition\, understanding\, and reasoning - and ho
 w much the computer could be made to possess them\, if at all. Different p
 ractitioners also subscribed to quite different imaginations of the comput
 er itself\, its limitations and possibilities. Some imagined computers as 
 mere plodding &ldquo\;slaves&rdquo\; who would take over tedious and mecha
 nical elements of mathematical research. Others imagined them more generou
 sly as &ldquo\;mentors&rdquo\; or &ldquo\;collaborators&rdquo\; that could
  offer novel insight and direction to human mathematicians. Still others b
 elieved that computers would eventually become autonomous agents of mathem
 atical research. Automated theorem-proving practitioners took their vision
 s of mathematicians\, minds\, computers\, and proof\, and built them right
  in to their theorem-proving programs. Their efforts did indeed precipitat
 e transformations in the character of mathematical activity but in varied 
 and often surprising ways. They crafted new formal and material tools and 
 practices for wielding them that reshaped the work of proof. They also rei
 magined what &ldquo\;reasoning&rdquo\; itself might be and what logics cap
 ture or prescribe it. With a focus on communities based in the United Stat
 es in the second half of the twentieth century\, this talk will introduce 
 different visions &nbsp\;the novel practices and materialities of mathemat
 ical knowledge-making that emerged in tandem.
LOCATION:Seminar Room 1\, Newton Institute
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