Research Scientist at the @MIT @ProbCompProj studying interactions of randomness and computation
Cambridge, MA
Joined September 2009
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A counterexample to Vaught’s conjecture for infinitary logic has been verified in Lean!
In joint work with Nate Ackerman and Robin Knight, we developed and formalized a construction based on Knight’s unpublished manuscript.
A Comparator-checked version is registered on Palomar: palomar-registry.org/entry?i…
Streamlined Lean development: github.com/cameronfreer/vaug…
Discussion on Lean Zulip: leanprover.zulipchat.com/#na…
The formal proof builds on mathlib and our infinitary-logic library, with reusable developments of infinitary model theory and descriptive set theory: github.com/cameronfreer/infi…
Cameron Freer retweeted
Excited to share the launch of Tau Ceti, a new library of AI-formalized mathematics in Lean, with human-curated roadmaps and adversarial review against open rubrics.
Tau Ceti: github.com/TauCetiProject/Ta…
Review rubrics: github.com/TauCetiProject/Ta…
Roadmaps: github.com/TauCetiProject/Ta…
Zulip discussion: leanprover.zulipchat.com/#na…
Tau Ceti sits downstream of Mathlib, the gold standard for human-curated mathematics in Lean. It aims for reusable code others can build on, not the "perfection of knowledge" role Mathlib plays.
Mathematicians contribute roadmaps; AIs implement the formal mathematics and review each other's work against evolving rubrics. Contributors can use the project's tools or their own.
We're glad to co-incubate Tau Ceti alongside Kim Morrison and the Mathlib Initiative. New roadmaps, roadmap review, and AI contributors are all welcome.
#LeanLang #LeanProver #Mathlib #AI #Mathematics
The world is on the cusp of abundant autoformalization. This will empower anyone to verify their mathematical ideas more quickly and engage in co-discovery with computers backed by a large, growing foundation of formalized mathematics.
Excited to share that we’re doubling down on @mathematics_inc.
AI is generating more code than ever, but correctness isn’t guaranteed and failures can be catastrophic.
Their agent Gauss delivers a missing primitive for AI: provably correct code and knowledge.
Thrilled to keep working with @jessemhan, @jdlichtman, and the @mathematics_inc team!
Cameron Freer retweeted
It gives the maintainers of the Sphere Packing Project great pleasure to announce a major milestone in the formalization effort: we now have a sorry-free Lean proof of the theorem that the optimal sphere packing in ℝ⁸ is the E₈ lattice packing. (1/9)
I'm excited to share de Finetti's theorem formalized in Lean: three different proofs that infinite exchangeable sequences are conditionally IID.
43k lines across 113 files with 600+ lemmas.
💻 code: github.com/cameronfreer/exch…
📊 blueprint: cameronfreer.github.io/excha…
(1/3)
All three proofs from Kallenberg (2005), each filling different mathlib gaps:
• Reverse martingales
• Mean ergodic theorem machinery
• Elementary L² bounds
Built over 3 months with Claude + GPT with my Skill for Lean 4: github.com/cameronfreer/lean…
(2/3)
Currently coordinating with mathlib to upstream parts of the formalization.
Discussion: leanprover.zulipchat.com/#na…
(3/3)
Cameron Freer retweeted
Computer scientists often look to natural phenomena like the cosmic background radiation in order to obtain truly random sequences — but randomness can only take you so far. Many real-world situations depend on weighted outcomes. quantamagazine.org/how-and-w…
Cameron Freer retweeted
Neuer #Algorithmus wirft effizient gezinkte Würfel. Klimaforschung, Epidemiologie, Finanzen:... pressetext.com/news/20200529…
Our work on near-optimal exact samplers, to appear at #AISTATS2020: arxiv.org/abs/2003.03830
The fast and efficient generation of random numbers has long been an important challenge. For centuries, games of chance have relied on the roll of a die, the flip of a coin, or the shuffling of cards to bring some randomness into the proceedings @MITEECS news.mit.edu/2020/algorithm-…
Cameron Freer retweeted
One week to Oct 18 deadline for your 2-pager on Probabilistic Programming to popl18.sigplan.org/track/pps… part of #POPL2018
Cameron Freer retweeted
How life (and death) spring from disorder bit.ly/2kEU15q
Cameron Freer retweeted
Living organisms feed on "negative entropy" by capturing and storing information, Schrödinger said: quantamagazine.org/20170126-…
Cameron Freer retweeted
New preprint “Priors on directed exchangeable graphs" out - On what's missing in many digraph models arxiv.org/abs/1510.08440 @cameronfreer
Cameron Freer retweeted
I don't always observe a zero-probability event, but when I do, I specify the observed variable, not just a Boolean predicate.
Cameron Freer retweeted
Workshop on probabilistic programming semantics, colocated with POPL 2016, call for extended abstracts conf.researchr.org/track/POP…