In my opinion, this dissertation is one of the best in mathematics to have appeared in the Netherlands in this century. If, after exactly 36 years, I read it again, and delve into the subject again, I am struck not only by the results achieved and by the deep reasoning used, reasoning different from that usually used in the rest of mathematics, but also by the graceful form in which he has cast his work. Although many eminent mathematicians had devoted their energies to this difficult area, only a few general propositions were known, while it was the intention of the author to derive a number of comprehensive propositions. To this end, he divides his thesis consisting of 121 pages into six parts. In the introduction, he discusses the old results obtained by others and the new ones from the author himself. Five parts follow. Parts I and II are devoted to the solutions of Hurwitz differential equations; part III deals with algebraic functions, part IV with functions that satisfy algebraic equations and finally part V with certain functions that he calls elementary.

The dissertation is written in the well-known Edmund Landau style, nowhere a word too much, but nowhere a word too little. With regard to the propositions, people sometimes wonder what the point of a particular proposition is, but nowhere is there given any information on this, because that connection appears later in the proof of a major proposition where the earlier proposition is applied. In an oral presentation, when dealing with such an assertion, it will as a rule be indicated with a few vague words how it fits into the direction of the requested theorem, but that indication does not fit into the aforementioned style, where no vagueness is allowed.

In Popken's dissertation there are fifteen major propositions with almost twice as many, most elaborate, minor propositions, which, all artfully and ingeniously combined, yield exactly the intended results. Many mathematics practitioners can read the dissertation without difficulty, because the entire argument is divided into so many small steps that each result follows from a single carefully worded statement. But a reading, step by step, takes weeks and even though the reader can then guarantee the correctness of the results achieved, he does not yet oversee the series of thoughts that led the author when writing the work.

The period after his dissertation until the end of World War II was bleak for this scholar. His dissertation, however important, was actually read, understood and appreciated by only a few in the Netherlands. After all, mathematicians do not easily have the opportunity to take a period of one month away from the time available to them, solely for the purpose of studying a piece of writing that is outside of their interest. I have the impression that he has received a shock during that period, of which he never fully recovered, but he never spoke about it.

The danger is not inconceivable that mathematical lectures are difficult to digest for some listeners due to their technical nature and are therefore only slightly appreciated by these listeners. The Amsterdam inaugural lecture of Prof dr Popken, also addresses the non-mathematicians in his audience in a richly documented argument. The work of the mathematician is to discover new paths in mathematics, paths that are sometimes decisive for the course of humanity, even though the mathematician may have been far ahead of his time. This statement is illustrated by compelling examples. The inaugural lecture also sketches how the tragic isolation and unpopularity of mathematics grew especially in the 19th century, at a time when many influential outsiders often identified mathematics with totally petrified school mathematics. A turn comes in the twentieth century; an understanding arises for the meaning of mathematics in philosophy. In the second industrial revolution we now live in, enthusiastic and successful searches are being made for new ways to which mathematics can be applied. Nobody left this lecture uninformed.