His dissertation in 1752, "Mercurii Theoria", contained theory and calculations of the orbit of Mercury.

In 1754 he made a scientific journey to England and France, and during his period in London he worked as a link between the the famous telescope manufacturer John Dollond and professor Samuel Klingenstierna, who at that time worked with the problem of how to achieve achromatical lenses. At his return, after three years abroad, he was appointed "Observator" at the Uppsala observatory.

Mallet carried out many astronomical observations. Of particular value is his observations of the Venus transits in the years 1761 and 1769.

His published works comprize mathematical and astronomical articles in the publications of the Royal Academy of Sciences in Stockholm, the Royal Society of Sciences in Uppsala and also in "Philosophical transactions" of the Royal Society in London. He also presided at many dissertations in mathematics and later research has valued his contributions to mathematics high.

In 1795 he donated his large library and many instruments to the Uppsala observatory, now known as "Mallet's donation", still in the posession of the astronomical institute.