Emil Elakehal

Mathematics undergraduate at ETH Zürich.

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

I am currently focused on learning the fundamentals of mathematics and theoretical computer science. Here are some of the questions I am interested in and the topics I hope to study in order to understand them better:

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, cryptography and AI safety

  • How can we prove correctness and security? (formal specification / verification)
  • How can cryptography be used to protect privacy and redistribute trust? (cryptographic primitives, zero-knowledge proofs, cryptographic obfuscation, post-quantum cryptography, privacy-enhancing technologies)
  • How will AI and formal verification transform mathematical research? (automated theorem proving, proof assistants / Lean)
  • How can mathematics and theoretical computer science contribute towards the safe adoption of AI? (verified control and containment, game theory, d/acc)

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)

Determinism and the physical world

  • Does true randomness exist, or is the universe deterministic? (Bell's theorem, interpretations of quantum mechanics)
  • How does order emerge from randomness? (classical limit of QM, thermodynamic irreversibility)

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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