As an undergraduate student at Harvard University, Hutchings did an REU project with Frank Morgan at Williams College that began his interest in the mathematics of soap bubbles.

[3] He finished his undergraduate studies in 1993, and stayed at Harvard for graduate school, earning his Ph.D. in 1998 under the supervision of Clifford Taubes.

His work on circle-valued Morse theory (partly in collaboration with Yi-Jen Lee) studies torsion invariants that arise from circle-valued Morse theory and, more generally, closed 1-forms, and relates them to the three-dimensional Seiberg–Witten invariants and the Meng–Taubes theorem, in analogy with Taubes' Gromov–Seiberg–Witten theorem in four dimensions.

ECH is a holomorphic curve model for the Seiberg–Witten Floer homology of a three-manifold, and is thus a version of Taubes's Gromov invariant for certain four-manifolds with boundary.

[5] He gave an invited talk at the International Congress of Mathematicians in 2010, entitled "Embedded contact homology and its applications".