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Dashboard of Human Progress in Formal Fields

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Zach Dexter

on 5 November 2013

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Transcript of Dashboard of Human Progress in Formal Fields

Dashboard of Human Progress in Formal Fields
Is Factoring in P?
Getting people involved in science
Get students excited with visuals and context on important open problems
Communicate to policymakers why basic research matters - just pull up problems' connections on ProblemMuncher
What do we know, and what do we not know?
Why build ProblemMuncher?
Instant access to the research frontier
Get stuff done and Don't Repeat Yourself
Show policymakers why basic research matters to the frontier
Coordinate Productive Directions
Tag approaches with recent papers from arxiv.org and coordinate productive directions

Speaking of cooperation...
Grants can be collaboratively planned to tackle certain potentially-fruitful directions in a distributed way
Helps turn increasing specialization in research into a positive
... instead of a context-management problem.
Want to help us build the ultimate open-source problem library?
We are looking for researchers, teachers, coders, designers, philosophers of science etc to help. This is a massive open source project and we need you.

Start date: Early to mid 2014

Building a Context Acquisition Tool for Research
What's the state of the art?
Clever algorithms
Automated or human-generated proofs
Isomorphisms and reductions
Maybe graph-theoretical
Maybe field-theoretical
Maybe number-theoretical
Which directions have been tried?
How have they turned out?
Tried and failed
Tried and succeeded
Trying as we speak
Which untried directions might be fruitful?
Right now we guess and use intuition
We should be employing statistical AI systematically
Also, we should be collaboratively attacking problems. Researchers should be able to visit a dashboard and coordinate with others on open problems.
Research Direction Coordination and Suggestion
Socially coordinate productive research directions (and have hooks for AI to find directions where possible)
Systematically use automated reduction and isomorphism finding, and automated theorem proving, to test out new directions where intuition that an efficient solution exists is strong.
Difference from current approach: It's systematic. Entire research community can coordinate research directions and split up effort.
Reduce wasted effort
Use specialists' intuition, and statistical AI where possible, to trim search tree branches
Do this for the literal search tree for provers & reduction finders
Do it for the 'my lab is going to try this direction' search tree
(Background) Example of finding reductions automatically by transforming problems to SAT: http://people.cs.umass.edu/~mcc/pub/reductions.pdf
Similar techniques use QBF instead of CNF and are more powerful
What's related to this problem?
Implications (represented by edges on a graph) if answer is "yes" or "no"
Isomorphic representations
Relevant reductions
Better Problem-Solving
Computers and professional humans around the world are all monitoring progress on open problems from a 'Star Trek'-style dashboard.
Beaming you up is known to be NP-Complete ;-) but getting context quickly with a nice dashboard can:
Save time
Utilize specialization more effectively
Increase collaboration between research groups and amongst individual researchers
Special cases aside, can a computer find the prime factors of large integers efficiently?
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