He made a fundamental contribution to the n-body problem in celestial mechanics by proving that using a third degree approximation for the disturbing forces implies instability of the major axes of the orbits, and by introducing the concept of secular perturbations in relation to this.

In 1870, while a student in his second term, he became teacher of mathematics at the Nifon Seminary in Bucharest, but quit the following year in order to continue his studies.

After graduation, Haret won a scholarship competition organized by Titu Maiorescu and went to Paris in order to study mathematics at the Sorbonne.

After his return to Romania in 1878, Haret largely abandoned scientific research and dedicated the rest of his life to improving Romanian education, which was heavily underdeveloped at the time, both as professor and as politician.

The folk song "Cântă cucu-n Bucovina" ("Sings the Cuckoo in Bukovina") was composed in 1904 by Constantin Mandicevschi [de; ru; uk] at Haret's request for commemorating the 400th anniversary of the death of Prince of Moldavia Stephen the Great.

Pierre Laplace (in 1773) and Joseph Louis Lagrange (in 1776) had already studied the problem, both of them showing that the major axes of the orbits are stable, by using a first degree approximation of the perturbing forces.

In his thesis, Haret proved by using third degree approximations that the axes are not stable as previously believed, but instead feature a time variability, which he called secular perturbations.

Henri Poincaré considered this result a great surprise and continued Haret’s research, which eventually led him to the creation of chaos theory.