... one branch of the old Ruthenian Prince family of the Puzyna had settled down in the district of Upyté. During the 17th century, this branch of the family converted to Calvinism and assimilated with its ethnically non-Slavic neighbours. Another branch of the Puzyna, which settled among the Ruthenians, resisted polonization and preserved its East Slavic identity. In mid-17th century, the head of this branch, Afanasiusz Puzyna, became Orthodox bishop of Lutsk. Later, members of the Puzyna family would take part in three different national movements (Lithuanian, Belarusian and Ukrainian). Jonas Puzinas became a prominent Lithuanian archaeologist.

In the winter semester, his main attention was given to familiarising himself with Weierstrass's theory of functions, and in the summer semester he studied new directions in geometry. At the same time, throughout the whole year, he participated in the mathematics seminar, which was led in the first half of the year by Professor L Kronecker, and in the second half by Professors K Weierstrass and L Kronecker.

Puzyna worked mostly in complex analysis. His monograph on the theory of analytic functions in two volumes was the first Polish mathematical book that used the language of set theory.

Famous mathematicians Stanisław Saks and Antony Zygmund highly praised Puzyna's monograph, considering it a real encyclopaedia of analysis, which, in addition to the contemporary exposition of the theory of analytic functions, contained information from the field of set theory and set-theoretic topology, group theory, algebra, differential equations, and harmonic functions.

Actually, Puzyna's book was the first attempt to teach a course in the theory of analytic functions based on set theory. One of the initial chapters of the book was devoted to the foundations of this theory, as well as some fundamental concepts of set-theoretic topology (accumulation point, derivative, compactness, connectedness, etc.). Examples of subsets of the set of real numbers with predetermined properties of the transfinite derivative (necessary for countable ordinal numbers) were presented.

However, later in the book, Puzyna changes the style of exposition of the material: the chapters on the topology of surfaces are actually written without the use of language of set theory. The author mostly relies on an intuitive-visual argument.

In fact, in Puzyna's book we observe a certain eclecticism, a combination of both the set-theoretical and the visual-intuitive approach. The latter corresponds to Poincaré's philosophical views: the basis of mathematics is intuition, and not everything in mathematics lends itself to formalisation and analytical exposition. When explaining the theory of surfaces, Puzyna appeals to the reader's geometric intuition and uses rich illustrative material. Note that a systematic presentation of the theory of surfaces based on set-theoretic topology would hardly be possible at that time, as it needed systematic development of the necessary topological apparatus, primarily homeomorphisms and deformations (homotopies).

As a professor, Puzyna always encouraged his students to work independently but was happy to support them with advice and guidance. His approachability, kindness and other personal qualities made students fell as if they were in the presence of a senior colleague, not a professor or a superior. It was only in closer contact with Puzyna that the richness of his nature was revealed. The simplicity and helpfulness characteristic of profound minds made him closer to his listeners, but much more than that. His lectures, always prepared in detail, attracted many students.

The beginning of the theory of integral equations as an own discipline started in the late 19th and early 20th century with the work of Volterra, Fredholm and Hilbert. The lectures of Puzyna demonstrate the ideas of these pioneers. Puzyna's goal was to present, in a transparent way, the complete theory of the integral equations which was known at that time. With this aim he mixed different methods to solve integral equations.
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Comparing the framework of Puzyna's lecture on integral equations with any modern lectures, we can notice, that his lecture was an introduction to the theory of integral equations mainly based on work of Fredholm. From the historical point of view the Fredholm's method was many years ahead of its time and had one of the most famous follower who was D Hilbert. We can notice Hilbert's influence in Puzyna's lecture and in the concept of the modern theory of integral equations as well.

He had broad musical interests, was a great pianist and admirer of Wagner's music, and it is worth emphasising both his broad interests in the humanities and in the field of management and in running a farm. His estate in Stańków in Stryi district was known for its excellence in Galicia.