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UID:30ea85e073890de1e682409e3956aec4
CATEGORIES:Lean Seminar
CREATED:20260323T112150
SUMMARY:Towards Learning a Metric for Mathematical Interestingness
LOCATION:Hill 705
DESCRIPTION:<div data-olk-copy-source="MessageBody" style="border: 0px; font-style: nor
 mal; font-weight: 400; font-size: 12pt; line-height: inherit; font-family: 
 Aptos, Arial, Helvetica, sans-serif; margin: 0px; padding: 0px; vertical-al
 ign: baseline; letter-spacing: normal; orphans: 2; text-align: start; text-
 indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-spac
 e: normal; background-color: #ffffff;">Mathematics has been shaped as much 
 by its open questions as its proofs, famously some of Hilbert's 23 problems
  are still influencing research more than a century after they were conject
 ured. Despite the recent advancements in AI-assisted math, there is limited
  progress in machines generating consequential conjectures. We present ongo
 ing work on a reinforcement learning framework for automated hypothesis gen
 eration, centered on discovering interestingness as a learnable reward sign
 al.&nbsp;</div><div style="border: 0px; font-style: normal; font-weight: 40
 0; font-size: 12pt; line-height: inherit; font-family: Aptos, Arial, Helvet
 ica, sans-serif; margin: 0px; padding: 0px; vertical-align: baseline; lette
 r-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-tr
 ansform: none; widows: 2; word-spacing: 0px; white-space: normal; backgroun
 d-color: #ffffff;">Our metric draws on the graph structure embedded in Proo
 fWiki, a repository of theorems, definitions, and their dependencies. Conje
 ctures that closely mirror densely connected, well-trodden regions of the g
 raph score low, while those that forge links between distant or sparsely co
 nnected nodes score higher, capturing the intuition that interesting mathem
 atics bridges unexpected concepts. Together with measures of a conjecture's
  structural non-triviality, these signals operationalize the middle ground 
 between the obvious and the intractable. We discuss open challenges in quan
 tifying interestingness, and the gap between formal metrics and mathematica
 l taste.</div>
CONTACT:Abhinav Verma
DTSTAMP:20260828T114633
DTSTART;TZID=America/New_York:20260325T100000
DTEND;TZID=America/New_York:20260325T110000
SEQUENCE:0
TRANSP:OPAQUE
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