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UID:30ea85e073890de1e682409e3956aec4
CATEGORIES:Lean Seminar
CREATED:20260323T112150
SUMMARY:Towards Learning a Metric for Mathematical Interestingness
LOCATION:Hill 705
DESCRIPTION:Mathematics has been shaped as much by its open questions as its proofs, fa
 mously some of Hilbert's 23 problems are still influencing research more th
 an a century after they were conjectured. Despite the recent advancements i
 n AI-assisted math, there is limited progress in machines generating conseq
 uential conjectures. We present ongoing work on a reinforcement learning fr
 amework for automated hypothesis generation, centered on discovering intere
 stingness as a learnable reward signal. Our metric draws on the graph struc
 ture embedded in ProofWiki, a repository of theorems, definitions, and thei
 r dependencies. Conjectures that closely mirror densely connected, well-tro
 dden regions of the graph score low, while those that forge links between d
 istant or sparsely connected nodes score higher, capturing the intuition th
 at interesting mathematics bridges unexpected concepts. Together with measu
 res of a conjecture's structural non-triviality, these signals operationali
 ze the middle ground between the obvious and the intractable. We discuss op
 en challenges in quantifying interestingness, and the gap between formal me
 trics and mathematical taste.
X-ALT-DESC;FMTTYPE=text/html:<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:20260828T003000
DTSTART;TZID=America/New_York:20260325T100000
DTEND;TZID=America/New_York:20260325T110000
SEQUENCE:0
TRANSP:OPAQUE
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