Wulff was born in Nizhyn, Chernigov province where his mother Lydia was daughter of teacher E. V. Gudim.
His father Viktor Konstantinovich Vulf was a literature teacher at the 6th Warsaw Gymnasium.
In the third year, he studied the electrical properties of quartz for which he received a gold medal.
He began to study the relationship of crystal structure and optical properties and in 1888 he published a paper on the "theory of rotatory polarization".
[1] Wulff studied crystal growth processes and modified Curie's principle on the minimization of surface energy.
He developed a relationship in X-ray diffraction (nλ = 2d sin θ) which was also found independently by the Bragg father and son duo in 1913 and sometimes called the Bragg–Wulff equation.