# How do I synthesize 3-hydroxydihydrofuran-2-one from formaldehyde?

I want to synthesize 3-hydroxydihydrofuran-2-one from formaldehyde but I do not know of a method. I tried a Mannich reaction and lactonization after dehydration.

Starting from pyruvic acid which is readily available and not very expensive: react pyruvic acid (only one enolizable side) with a Mannich base, then react the resulting amide with $\ce{MeI}$ and base to obtain the exo-methylene product. Brominate the exo-methylene. Now cyclization will prefer the five-membered ring over the strained four-membered ring. Reduce the ketone with a reletively mild reducing agent like $\ce{NaBH4}$ and then eliminate $\ce{HBr}$ in a E1cB type reaction, yielding 3-hydroxydihydrofuran-2-one.