He continued the work of Carl Friedrich Gauss concerning differential geometry of surfaces, especially its intrinsic aspects.

He attended lectures in the University of Halle and eventually graduated with a thesis "De valore intergralium duplicium quam proxime inveniendo" (1829).

However, his 1842 bid for election to Berlin Academy, supported by Peter Gustav Lejeune Dirichlet, failed and in 1843 he relocated to the University of Dorpat, where he was a professor of mathematics for the next 40 years.

In Dorpat he taught Karl Peterson and supervised his doctoral thesis that established the Gauss–Bonnet theorem and derived Gauss–Codazzi equations.

Minding also worked on differential equations (Demidov prize of the St Petersburg Academy in 1861), algebraic functions, continued fractions and analytical mechanics.