Is the S combinator computation-universal by itself?

Prove or disprove Stephen Wolfram’s conjecture that the S combinator alone—without K or other primitive combinators—is computation-universal.

combinatory logicuniversalitymodels of computation

The problem

Prove or disprove Stephen Wolfram’s conjecture that the S combinator alone—without K or other primitive combinators—is computation-universal.

Open since2020conjecture and prize launch

Last checked2026.07.27Catalog verification

Reward offers

Offer 01$20,000Wolfram Foundation

Documented

The first individual or group to submit a correct full proof to the committee wins. Work must be original, nonanonymous and presented as a technical research paper suitable for publication. Submissions remain open until a satisfactory solution is achieved.

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Sources & reading

1 unique reference linksOfficial Wolfram S Combinator Challenge

Is the S combinator computation-universal by itself?

The problem

Reward offers

Sources & reading

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