In the area of mathematics known as differential topology, the disc theorem of Palais (1960) states that two embeddings of a closed k-disc into a connected n-manifold are ambient isotopic provided that if k = n the two embeddings are equioriented.

The disc theorem implies that the connected sum of smooth oriented manifolds is well defined.

A different although related and similar named result is the disc embedding theorem proved by Freedman in 1982.^[1][2]