After his dissertation, Determination de la latitude du nouvel observatoire d'Upsala (1856), Schultz worked during the years 1857-1859 at the observatories in Vienna, Munich and Berlin.
He was appointed Observator at the Uppsala observatory in 1859 and started observing with the new Steinheil refractor in late 1860. The results of his first years of observations were published in 1864, Refractorsbeobachtungen der K. Universitätssternwarte in Upsala (UU,1864), containing observations of Mars, asteroids, comets and nebulae.
In 1872 he published Micrometric determinations of 104 stars in the stellar group 20 Vulpecula (KVA,1872).
His most extensive and important work was Micrometrical observations of 500 nebulae. (Nova Acta RSS,1875) which contributed to the famous NGC catalogue; the New General Catalogue of nebulae and clusters of stars (1888).
Schultz also published two text-books in Swedish: Astronomiska observationskonsten (1878) and Sferiska astronomiens grundbegrepp (1879).