Emil Elakehal

Mathematics undergraduate at ETH Zürich and organizer at Zurich AI Safety

"We can only see a short distance ahead, but we can see plenty there that needs to be done." Alan Turing

I'm shaping my degree around logic, computability, cryptography and formal verification, with the aim of working on theoretical AI safety. Here are some of the questions I am interested in and the topics I hope to study in order to understand them better:

Emil Elakehal

Foundations of mathematics and the limits of formal systems

  • What exactly are the limitations of formal systems? (Gödel's theorems, Tarski's undefinability of truth, the Entscheidungsproblem)
  • What do these limitations mean in practice? (independence results / forcing, Rice's theorem)
  • What are the ultimate limits of computation? ((Extended) Church-Turing thesis, computational complexity, quantum computing)
  • What do different philosophies of mathematics entail for mathematical truth? (platonism, formalism, intuitionism)
  • How do we answer the skeptic when every justification, in mathematics and in the systems we trust, has to bottom out somewhere? (Münchhausen trilemma, foundationalism vs coherentism, trusted computing base)

Formal methods and cryptography

  • How can we capture the intended specification and prove that a system satisfies it? (formal verification, faithful formalization)
  • How will AI and proof assistants transform mathematical research? (automated theorem proving, Lean)
  • How can cryptography be used to protect privacy and redistribute trust? (cryptographic primitives, zero-knowledge proofs, cryptographic obfuscation, post-quantum cryptography, privacy-enhancing technologies)

Mathematical guarantees for AI safety

  • What does it take to describe an agent that is part of the world it reasons about? (embedded agency, logical induction, decision theory)
  • When agents can inspect and reason about one another, which outcomes become reachable and which are ruled out? (open-source game theory)
  • Which properties of a model can be hidden from someone with full access to it? (obfuscated backdoors, undetectable watermarks)
  • Still exploring!

Language, logic and reasoning

  • Does symbolic logic describe how we actually think, or point at something platonic? (non-classical logics, logicism)
  • How does language shape the way we reason? (linguistic relativity, Wittgenstein)

Connect

If any of this interests you, I would be grateful to hear from you. If you are in Zürich I am always glad to meet for lunch. If not, an email is welcome :)

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