SCIENTISTS OF THE NORTH-EAST OF SCOTLAND 115 
greater advances were made than in mathematics. Until the end of the 
sixteenth century Scotland contributed nothing to the progress of the 
science, and the history of mathematics is entirely wanting in the name of 
even one man born north of the Borders before the middle of that century. 
Indeed, Britain as a whole lagged far behind other European countries, 
like France, Germany, and Italy, in her attachment to mathematical 
learning. It is therefore all the more surprising to find that in the period 
immediately succeeding the Reformation Scotland produced several 
mathematicians who won a European reputation. ‘The name of John 
Napier of Merchiston, the discoverer of logarithms, comes readily to one’s 
mind in this connection. The rudiments of the subject, a little arithmetic, 
Euclid’s Elements, conic sections and astronomy on the Ptolemaic system 
were taught in the universities in a mild fashion, but those who wished 
to take up the study of the subject with some earnestness found it necessary 
to attend centres of learning on the Continent, mainly in France,Germany, 
and Holland. 
LippEL, DuNncan.—One of the earliest of such scholars was Duncan 
Liddel, a native of Aberdeen, who was born in 1561. At the age of 
eighteen he went abroad to Danzig, but on learning that Dr. John Craig 
taught mathematics at Frankfurt-on-the-Oder he went there, and a close 
friendship was thereafter formed between the two Scotsmen, which had 
a determining influence on Liddel’s career. Craig, it may be remem- 
bered, figures in the controversy over the priority of discovery of loga- 
rithms. He was personally acquainted with Tycho Brahe and Kepler, 
and also with John Napier, and it is generally accepted that it was through 
Craig that Kepler first learned of Napier’s achievement. Liddel took up 
the study of mathematics and astronomy at Breslau under Wittichius, 
one of the ablest of Tycho’s pupils ; and later he went to Rostock as a 
teacher of mathematics. It is claimed for Liddel that he was the first 
man in Germany to teach Copernican astronomy. He visited Tycho 
at Hveen in June 1587, but, as was the case with Kepler and others, the 
Danish astronomer conceived the idea that Liddel was taking credit to 
himself for some of his discoveries, a charge indignantly denied by Liddel. 
About 1590, attracted by the reputation of the newly established University 
of Helmstadt in Brunswick, Liddel took up his residence in that town, 
where he was appointed to the Chair of Mathematics. At this period 
it was by no means unusual for men to combine the teaching of mathe- 
matics with the practice of medicine. Liddel took the degree of Doctor 
of Medicine in Helmstadt in 1596, and for several years he carried on both 
professions. But in the course of a few years he acquired a large and 
lucrative practice among the principal families in Brunswick, and by his 
teaching and his writings he became the chief support of the Medical 
School at Helmstadt. In 1603 he resigned the Chair of Mathematics, 
and confined himself entirely to the teaching and practice of medicine. 
At this time the German universities, like our own, were passing through 
a very troubled period, and Liddel, advised it is thought by Dr. John 
Craig, determined to return to Scotland. He settled in Aberdeen and 
died there in 1613. 
