Three years later Craig returned to Scotland, and Liddel, on his advice, moved to Breslau in Silesia, where he studied mathematics under Paulus Wittichius, and encountered Andreas Dudith.
Having received an education in languages and philosophy at the school and university there, he went abroad at age 18. After a few months he arrived at Frankfort-on-Oder, where a Scot, John Craig was teaching logic and mathematics. Craig superintended his studies.
In 1584 he returned to Frankfort, took pupils in mathematics and philosophy, and took up the study of physic.
With the help of his new contacts, he visited Tycho Brahe in 1587 and again the following year. Shortly after his return to Frankfort in 1590 Liddel joined the new university of Helmstadt, established by Duke Julius of Brunswick.
Caselius had already been appointed to the chair of philosophy there. Next year Liddel obtained the lower mathematical chair vacated by Parcovius, and in 1594 he succeeded Erhardus Hoffmann in the higher mathematical chairman
In 1596 he became Doctor of Medicine of the university, and began publicly to teach physic and to act as præses at the recitation of medical dissertations.
In 1599 he was dean of the faculty of philosophy. In 1603 he resigned his mathematical professorship, and in 1604 became pro-rector of the university. Liddel returned to Scotland in 1607, financially secure.
In 1612 he endowed the university of Aberdeen with lands for the education and support of six poor scholars.
And in 1613 he endowed a professorship of mathematics in Marischal College. He died on 17 December 1613, at age 51.
His funeral sermon was given by Gilbert Gray of Marischal College. Liddel bequeathed his books and instruments to Marischal College.
A brass memorial figure of him was later set up in the Kirk of Street Nicholas, Aberdeen.
Liddel was reputed as a mathematician in Germany, where he was said to have been the first to teach the astronomy of Copernicus and of Tycho Brahe side by side with the Ptolemaic system. In theology, also, Liddel built a reputation. He found arguments against the Lutheran theologian Daniel Hofmann, who had deployed the doctrine of double truth at Helmstedt in a divisive fashion.