Frontiers

There are too many open problems to list. Some are too broad to pursue, and others are too small to matter much. A few combine three qualities: they are important, tractable, and close to the edge of what we understand or can do. We call these frontiers. This site is an attempt to collect them.

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Requests for theories

Phenomena observed in nature or experiment, but not yet understood well enough to reproduce or control.

Why do copper oxides superconduct at high temperatures?

Why can some animals regenerate body parts or entire bodies?

  • Some animals can regenerate complex structures after injury. Salamanders can regrow entire limbs, zebrafish can regrow fins and parts of the heart, and planarian flatworms can regenerate whole bodies from small fragments.
  • Animal regeneration has been documented since antiquity.
  • Existing theories do not fully explain how animals know what is missing, rebuild the right tissues in the right places, and stop once the missing structure has been restored.
  • A theory of regeneration would need to explain where the target shape is stored, how large-scale outcomes like regrowing limbs or organs could be controlled, and how regeneration relates to morphogenesis.

Requests for cures

Common conditions with major quality-of-life effects and no general cure.

Tinnitus

Chronic pain

  • Chronic pain is pain that persists or recurs for more than three months. In many cases, the nervous system becomes sensitized, so pain continues even after the original injury or illness has healed.
  • Current options are limited and carry serious tradeoffs: opioids can cause dependence and overdose, while NSAIDs can cause gastrointestinal, kidney, and cardiovascular problems.
  • Nature offers a clue that generalized non-opioid pain relief is possible: loss-of-function mutations in SCN9A, the gene encoding Nav1.7, can eliminate pain while leaving other forms of sensation relatively intact.

For a broader map of unmet medical needs, including rare conditions, see Convoke's Unmet Needs Index.

Requests for step changes

Technologies that already work, but still have room for order-of-magnitude improvement.

Verifiable computation

  • Reduce the cost and time required to generate proofs that a computation was performed correctly.
  • The premise is simple: given a known input, a known program, and a claimed output, produce a proof that the output is correct. Where homomorphic encryption and zero-knowledge proofs are about hiding information from some party, verifiable computation is simply about proving correctness.
  • We can judge how valuable a computational proof is by the asymmetry it creates between doing a computation and checking it: how much overhead is required to generate the proof, how large the proof is, and how much cheaper verification is than reproducing the underlying computation.
  • Note that NP does not fully capture what makes a computational proof practical:
    1. NP guarantees only that a polynomial-size certificate exists and can be verified in polynomial time in the size of the input. It does not require that the certificate be easy to find.
    2. Even when a certificate exists, checking it may not be meaningfully cheaper than recomputing the answer.
    3. Computational proofs can exist for arbitrary programs, not only for NP decision problems.
  • State-of-the-art proof systems can already make proofs succinct and verification cheap. The remaining bottleneck is that generating proofs for general-purpose computations is still substantially more expensive than simply running the computation.
  • If proof generation became cheap enough, computational outputs could become independently trustworthy objects: they could be outsourced, traded, reused, and stored for decades without requiring the verifier to trust the machine that originally produced them or rerun the computation.
  • Trusted execution environments are a practical stand-in today, but they move the trust assumption into the hardware rather than eliminating it.
  • For more frontiers related to computation and cryptography, see 0xPARC.