After studying ancient languages in his hometown, van Roomen studied mathematics and philosophy at the Jesuit College in Cologne. He studied medicine, first at Cologne and then at Leuven. He then spent some time in Italy in April 1585, when he met Christopher Clavius in Rome. Seven years later, he referred to his meeting with Clavius in a letter he wrote to him:-
Greetings. Reverend Father, though now I might look unfamiliar to you, yet when the papal seat was vacant because of the death of Gregory XIII, being in Rome, your reverence usually met me. At that time we treated the subjects of arithmetic and mainly algebra.Van Roomen was professor of mathematics and medicine at Leuven from 1586 to 1592 and, for six months during 1592, he was rector of the University. During this time he planned to publish an overview of the whole of mathematics :-
As a first part of this project, he worked on a 'theoria polygonorum', a theory of the regular polygons. This should result in tables of sines, tangents and secants, and in a solution of the circle squaring problem, which for him meant the calculation of the proportion between the circumference and the diameter of a circle. The work was intended to have 12 chapters, of which the first four would treat the regular 3-, 4-, 5- and 15-gon, and the related polygons produced by a repeated doubling of the number of sides. Sections 5-9 would treat all other regular polygons. In Chapters 10 and 11 van Roomen would study the circle. Section 10 would teach how to compute its circumference and area. Section 11 would examine the many faulty or simply wrong solutions to the problem of squaring of the circle. Finally, Section 12 would show how the necessary arithmetical operations can be carried out with the least difficulty.In 1591, van Roomen published Ouranographia. This was his first work and it was essentially a work on astronomy, in particular on the number and nature of the heavenly spheres of Ptolemy. In 1593 the first part of his overview of mathematics appeared, namely Ideae mathematicae pars prima, sive Methodus Polygonorum. This contained the first four chapters from the total of twelve that he had planned. Although some of his later publications contained sections that might have been intended as part of the remaining eight chapters, he never completed his grand plan.
After these years in Leuven, van Roomen went to Würzburg where again he was appointed professor of medicine giving his first lecture on 17 May 1593. Although there was an earlier attempt to found this university, the Julius-Maximilians University of Würzburg was permanently endowed and established in 1582 on the initiative of Prince Bishop Julius Echter von Mespelbrunn (1545-1617). Van Roomen's appointment by Prince Bishop Julius Echter von Mespelbrunn was officially confirmed on the last day of August 1593. It is likely that van Roomen was glad to have an opportunity to leave the Netherlands since there was much unrest and fighting over the Spanish held territory. It was around the end of 1593 that van Roomen married Anna Steeg, the niece of Godefrid Steeg who was the doctor to Prince Bishop Julius Echter von Mespelbrunn. Although he was employed as a professor of medicine, it was mathematics that was van Roomen's real love. However, at Würzburg he did not have as much time to devote to mathematics as he would have liked. Partly this was because his health was poorly and partly it was because of his duties - he was dean of the medical school in 1596, in 1599 and for a third time in 1602. However, he did get involved in some mathematical work.
Van Roomen had proposed a problem which involved solving an equation of degree 45 in Ideae mathematicae (1593). The problem, which was given in the form of a challenge to "mathematicians all over the world", was solved by François Viète who realised that there was an underlying trigonometric relation. Viète's solution was published in 1595 and, at the end of his booklet, he proposed the Apollonian Problem of drawing a circle to touch three given circles. Van Roomen solved it using two hyperbolas, publishing the result in 1596. Viète published a ruler and compass solution to the Apollonian Problem in 1600 which greatly impressed van Roomen :-
Van Roomen was so impressed by Viète's mathematical talent that he visited France to recover his health and personally met his French rival in the summer of 1601. On his arrival in Paris, he was told that Viète was in Poitou and travelled there to talk with him. It is said they spent a month together and were very friendly.A dispute with the French scholar Josephus Justus Scaliger (1540-1609) prompted van Roomen to publish further works. Scaliger announced in 1590 that had solved the three classic problems of squaring the circle, trisecting an angle and duplicating the cube. He published his 'proofs' of the first two of these in pamphlets in 1594 and in these he also claimed that Archimedes' method of computing the area of a circle is worthless. Van Roomen bought Scaliger's pamphlet on squaring the circle from a book fair in Frankfurt in the autumn of 1594. In November of that year he wrote to Clavius saying he was astonished that Scaliger had dared to publish such a work. He wrote to Scaliger pointing out errors in his work and eventually Scaliger wrote an appendix 'correcting' the errors. He sent a copy to van Roomen in March 1595. Van Roomen decided to publish a work defending Archimedes from Scaliger's attacks. Scaliger had stated that Archimedes' method of calculating the area of a circle was useless since he was using an arithmetical method to solve a geometrical problem. Van Roomen's response was the three-part book In Archimedis Circuli Dimensionem Expositio et Analysis (1597). The first part contains a Latin translation by van Roomen of the Greek text of Archimedes' On the measurement of the circle. In the second part he defends Archimedes from Scaliger's attack introducing a concept he calls 'mathesis universalis'. Van Roomen claims:-
There is a science common to geometry and arithmetic which considers quantity generally as measurable.In more detail he states:-
Surely there is a certain science common to arithmetic and geometry to which properties common to all quantities pertain: since a proportion is common to all quantities, not only abstract ones such as numbers and magnitudes, but also concrete ones such as times, sounds, voices, places, motions, and forces (for all these and many others are said to have a proportion if their relation is considered from the viewpoint of quantity).Van Roomen proposes unifying geometry and arithmetic under his concept of 'mathesis universalis'. The importance of these ideas must be their influence on Descartes' use of algebra for geometric problems. The third part of van Roomen's 1597 work, consisting of ten dialogues, points out the errors in Scaliger's attempt to square the circle and also points out the errors in the works of several other mathematicians including Oronce Fine who had made similar claims.
During the ten years 1593-1603 that van Roomen spent in Würzburg he supervised the dissertations of twenty students which were printed by the local printer Georgius Fleischmann. Most treat medical or anatomical subjects, but there is one on astronomy and one on meteorology. From 1596 to 1603 he was also "mathematician" of the chapter in Würzburg, his main duty being to annually draw up the calendar. It appears that his wife Anna died during these years; they had no children. In 1603 van Roomen gave up his duties as professor at Würzburg, requesting permission from Prince Bishop Julius to travel to Leuven on 19 March 1603. From 1603 to 1610 he lived frequently in both Leuven and Würzburg although he did not officially resign his Würzburg professorship until 1607. He was ordained a priest in Leuven in 1604 or 1605. He was made a canon at the church of Saint John of Würzburg on 1 October 1605 but, due to the many travels he undertook, he seems to have failed to fulfil all his obligations as a canon and he was reprimanded in November 1609. In September 1610 he requested that he be given leave from his duties as a canon for two years, but that he might continue to be paid. His request for continued payment was refused. The reason for this request was that van Roomen had been invited to the Zamoyski Academy in Zamosc, Poland. This academy had been founded in 1594 by the Polish Crown Chancellor Jan Zamoyski (1542-1605).
We have accurate details of van Roomen's travels from Würzburg to Zamosc preserved in the diary of the Polish mathematician Jan Brozek (1585-1652), also known as Ioannes Broscius or Johannes Broscius, who worked at Kraków Academy (now the Jagiellonian University). He noted the days that van Roomen spent in Kraków in his travels between Würzburg and Zamosc. Van Roomen arrived in Kraków on 24 August 1611 after spending about a year in Zamosc. He spent time studying in Kraków University library before returning on 1 September to Würzburg. Two months later he was back in Kraków, travelling on to Zamosc on 29 October. After teaching for ten months at the Zamoyski Academy in Zamosc, he stayed in Kraków from 12 to 18 August 1612 on his way back to Würzburg. It is clear that by this time van Roomen was sufficiently concerned about his health that, in 1613, he travelled to Leuven where he made a will. After returning to Würzburg in April 1613, he added a codicil detailing his wishes about his property in Würzburg. Some of his possessions were left to Prince Bishop Julius Echter while his property was left to his sister Maria van den Brouck. Returning to Leuven later in the same month, he visited a Spa in an attempt to improve his health.
Although van Roomen had no children with his wife Anna, nevertheless he had two sons Jacob and Koenraad with Catharina Trauthmann. Jacob became a medical doctor in Leuven and died there in 1635 while Koenraad was born in Nuremberg and became an apothecary in Leuven, dying there in 1668. Van Roomen died in Mainz while on a journey from Leuven to Würzburg. He was travelling with his son Jacob and died in Jacob's arms.
Van Roomen also wrote a commentary on al-Khwarizmi's Algebra but the only two known copies were destroyed in 1914 and 1944 (as a result of World War I and World War II). However, before they were destroyed, copies of large parts of this work were made and these copies have survived. Here is a short extract from  where Paul Bockstaele gives a full and fascinating account of this work by van Roomen:-
In the Prolegomena to the edition of al-Khwarizmi's 'Algebra', van Roomen says that his intention is to examine what kind of science the algebra or 'ars analyticais', by looking at its origin and history. First of all he gives a summary of the different names which have been proposed for this science. Then he examines the place of the 'ars analytica' among the other sciences. It deals with quantities, their equality or inequality, their proportion and proportionality. For this reason it belongs to mathematics. Those who have written about algebra considered it to be a part of arithmetic, although it might as well be considered to be part of geometry. Algebraic propositions usually are demonstrated by geometrical constructions, so that algebra should perhaps better be considered as a part of geometry. Van Roomen ... prefers to classify the algebra or analytical science as belonging to the 'Mathesin prima', which deals with quantity in general. The material object of the 'ars analytica' or algebra is indeed quantity. The formal object, however, is the equality (aequalitas) of quantities, since only those problems, in which some equation is either explicitly given or can be deduced from the data of the problem, are analytic.One of van Roomen's most impressive results was finding π to 16 decimal places. He did this in 1593 using 230 sided polygons. Van Roomen's interest in π was almost certainly as a result of his friendship with Ludolph van Ceulen. Van Roomen worked on trigonometry and the calculation of chords in a circle. In 1596 Rheticus's trigonometric tables Opus palatinum de triangulis were published, many years after Rheticus died. Van Roomen was critical of the accuracy of these tables and wrote to Clavius at the Collegio Romano in Rome pointing out that, to calculate tangent and secant tables correctly to ten decimal places, it was necessary to work to 20 decimal places for small values of sine, see . In 1600 van Roomen visited Prague where he met Johannes Kepler and told him of his worries about the methods employed in Rheticus's trigonometric tables.
Among other contributions made by van Roomen was one to figures of equal perimeter. Pappus had proved a number of results concerning the maximum area of polygons of equal perimeter. For example regular n-sided polygons have the maximum area among all n-sided polygons of fixed perimeter. Van Roomen generalised the results of Pappus and, again showing his precise thinking, realised that 'regular' had not been properly defined. His work in this area is discussed in detail in .
Article by: J J O'Connor and E F Robertson