He told me that his university study was delayed by his army service and that, to make up for lost time, he had read Hausdorff's book "Grundzüge der Mengenlehre" Ⓣ from cover to cover during the summer preceding his enrolment at the university. He had also read Goursat's "Cours d'Analyse" Ⓣ and worked out all the problems in it early in his study years.

Juliusz Schauder attended lectures on mathematics and physics. He never took notes, only listened and read a lot in the early years. He worked non-stop. He did not recognise either holidays or vacations. He spent all his vacations at home, lying on the couch, with a book in his hand. ... Juliusz Schauder devoted all his thoughts to mathematics, he discussed with his colleagues very willingly, he was interested not only in his own problems, but also in those of others. There were quite a few breaks of an hour or more between lectures, the place of discussions was the corridor in front of the lecture hall. There, leaning against the stove, he stood for hours, formed problems, specified their titles, developed proofs, in a word, he began his independent scientific start early. A little later, these discussions from the corridor moved a few hundred metres away from there to the Roma or Szkocka cafes, located opposite each other, where Stefan Banach initiated broad mathematical discussions. There were always several people sitting at one table, and among them very often was Juliusz Schauder.

Not only could I do no Mathematics during this period, but also the entire year after.

I received the result of the test I took, which shows that I am not suitable for any job.

Although Lwów was a remarkable centre for mathematics, the number of professors both at the Institute and at the University was extremely limited and their salaries were very small. ... Schauder had to teach in high school in order to supplement a meagre income as lecturer ...

Schauder was one of the teachers full of dedication. He spared no effort and work for his students, not only during lessons at school, but also during numerous free additional hours, some of which started as early as 6 a.m. His thoughts were constantly absorbed in scientific issues, he often gave the impression of being absent-minded, which on the one hand gave the students many opportunities for pranks and jokes, but on the other hand they highly valued their professor because of his knowledge and the work he put into teaching.

His approach to important matters of life was unusual. Once when we were taking a walk in a park he told me: "I am now approaching the age of thirty. This is a serious age, it is time for me to marry and to settle down. I would like to marry a girl studying Mathematics, preferably one knowing some foreign languages, so that she can help me to prepare my results for publication. Among your classmates I like the looks of only two girls: Miss X and Miss Y, but I have not met either of them. Tell me, which one of them do you think I should marry". I replied: "Marry Miss X". This he did, after first confirming my recommendation with Stefan Banach.

... was a dark-haired girl, of medium height, with delicate facial features. ...She had no academic ambitions, although she was a very talented student. In 1931, she wrote her master's thesis "Picard's Theorem" under Banach's supervision. She later worked as a teacher. She was very devoted to Juliusz, cared for him and helped him as much as she could.

Schauder has a daughter (who is currently a few weeks old). Poor Schauder complains that he cannot sleep at night because his daughter screams.

Schauder and his wife met Hans Lewy in the spring of 1933 in Paris. Banach also came to Paris. Banach, Lewy, Schauder and others spent many evenings together in Paris. All the mathematicians met at Hadamard's seminar - any other would have been considered un-French.

One beautiful spring day, Hans Lewy introduced us to each other in a modest restaurant on the Rue Soufflot. I immediately said to Schauder: "I have read your paper on the relationship between existence and uniqueness of the solution of a nonlinear equation. I know now that existence is independent of uniqueness. I admire your topological methods. In my opinion they ought to be useful for establishing an existence theorem independent of any uniqueness and assuming only some a priori estimates." To this he replied (in German) - "Now that would be a theorem!" Forty-eight hours later the theorem existed; it had been formulated and meticulously proved in the beautiful Jardin du Luxembourg. A day or two later, in the same park, Jules Schauder proposed to enrich our work with a result which is the most beautiful of his applications: the proof of the existence, in the whole plane and convex domain, of a solution of the Dirichlet problem for an elliptic equation of a particular form ... After 15 days of strenuous but joyful work - it was carried out in the Jardin du Luxembourg or in Meudon, where I lived, or in the surrounding woods - our article "Topologie et équations fonctionnelles" Ⓣ was finally written.

In this paper what is now known as Leray-Schauder degree (a homotopy invariant) is defined. This degree is then used in an ingenious method to prove the existence of solutions to complicated partial differential equations.

Schauder's main achievement consists in transferring some topological notions and theorems to Banach spaces (the fixed point theorem, invariance of domain, the concept of index). In particular, Schauder's formulation of a fixed point theorem originated a new, extremely fruitful method in the theory of differential equations, known as Schauder's method ...

Schauder's fixed point theorem and his skilful use of function space techniques to analyse elliptic and hyperbolic partial differential equations are contributions of lasting quality. Existence proofs for complicated nonlinear problems using his fixed point theorem have become standard. The topological method developed in the 1934 Leray-Schauder paper ... is now utilised not only to obtain qualitative results but also to solve problems numerically on computers.

Even for docents of great scientific renown the chances of obtaining a professorship in a reasonable length of time were extremely small. They were nil for docents who were Jewish (the name of the mathematician Juliusz Schauder, an internationally famous Lwów docent, who never became a professor, comes to mind). Steinhaus used to say in jest that the United States is a poorer country than Poland because Poland educates superb mathematicians and then finds no use for them, while the States could not afford such waste.

As long as I can earn a living in my own country - even if in a way that is inappropriate for me - I will not agree to this offer.

I met Schauder in the evening in a quiet, empty street near the Lviv citadel, where I lived at the time. We walked up to each other, almost face to face. He was without an armband, walking with his head down. When I said, "Good evening, Professor," I saw terrified eyes, like those of a hunted animal. He stopped for a moment and without raising his head immediately disappeared into the darkness. A terrified, hiding man who suddenly realised that someone knew him. I think he didn't have time to look at me, he didn't recognise me, although I was one of his closest students.

Leray wanted to have a photograph of [Schauder] for himself and for Schauder's daughter who survived the war and lives in Italy. But he could not find any in Poland or anywhere and he wrote to me asking whether I might have a snapshot. Some months after Johnny von Neumann's death I was looking at some of the books in his library and a group photo of the participants in the [1935] Moscow conference fell out. Schauder was there, as were Aleksandrov, Lefschetz, Borsuk, and some dozen other topologists. I sent this photograph to Leray.