He had a lively mind and broad horizons, and he liked to give his children mathematical problems to solve. Otton's uncles told him years later that his mother Marianna excelled at the solutions.

... during one of the lessons, the teacher gave the following definition of division: to divide one number by another means to find the third, which, when multiplied by the second, gives the first. The teacher repeated this definition very quickly, without supplementing it with any examples or explanations, and then began to call the students by the alphabet and demand that they recite it correctly. In this way, he reached the letter N and Otto began to pray for the bell to end the lesson, because none of his classmates had repeated this definition correctly so far. Fortunately, the bell rang just in time. After returning home, Otto began to think about the definition, recall it and try to understand its meaning. In the next lesson, he was able to formulate it correctly and support it with his own example. He received a very good grade, and at the same time, pondering this problem and understanding the need for precision in formulations gave rise to a deep passion for mathematics.

Otto Nikodym is present in my consciousness as a rather unusual individual. ... In my memory, I see him as a slim, dark-haired man with a beard. He was only twenty-something, but different from others of that age, almost impersonal, as if not changing with age. Alienated and distant. ... Ascetically indifferent, with a frail physique, he did not raise his voice, but spoke constantly in a dispassionate, yet clear voice. ... The lecture was interesting due to the consistency of the content, which would seem dry, but aroused some curiosity about what would happen next. This mood was contagious, although the content was accessible only to a relatively small number of students.

Otto Nikodym gave a presentation of knowledge, such as it is, without including his own personality, which somehow disappeared from the plan. ... Stanisław Ruziewicz was similar in type to Otto Nikodym, as a university lecturer. Both also taught in a secondary school and both probably had similar results. They educated mathematical individuals, they did not find mass recipients.

A feature of his teaching was an extraordinary ability to engage students in discussion. In these discussions, he tried to convince us that he was not always right. He led the discussion in such a way that he created several possibilities to reach the goal. He often led the student to discovering a new law. He had a great sense of humour and called this law, for example, the law of Kosiński, our colleague. He gave the impression that he was pleased when a student proved him wrong. Maybe he created such situations on purpose. ... At that time, there was no differential calculus in the high school mathematics programme. But Otton Nikodym taught us elements of "higher mathematics" in a very original and accessible way, so that we could understand physics. He taught it beautifully, using mathematical concepts. He was able to arouse appreciation in his students, and in some, delight and enthusiasm, for the perfection and elegance of expressing the laws of physics in a strict mathematical form. Thanks to Nikodym, 16-17-year-old boys could feel the perfection of describing all electromagnetic phenomena using Maxwell's equations, which he considered one of the greatest achievements of the human intellect.

Even though Kraków was formally a fortress, one could take walks in Planty in the evenings. During such a walk I heard a conversation, or rather just a few words; the words "Lebesgue integral" were so unexpected that I approached the bench and introduced myself to the two young adherents of mathematics. They told me that they had another companion, Witold Wilkosz, whom they highly praised. They were Stefan Banach and Otton Nikodym. The three were united not only by mathematics, but also by the hopelessness of the situation of young people in the fortress that was Kraków at that time, the uncertainty of tomorrow, the lack of opportunities for gainful employment, and the lack of contact not only with foreign scholars, but even with Polish ones - such was the atmosphere in Kraków in 1916. But that did not prevent the three from sitting in a café and solving problems in the crowds and the hustle and bustle. Since then, we met regularly ...

Am I going to be any wiser because of that?

It is commonly believed that it was Sierpiński who encouraged Otton to start publishing his results, but I am certain that is not the truth. The correspondence of the newly married couple with Stanisława's family presents the story in a different way. In my opinion, Stanisława and some friends from Kraków had far more impact on Otton than Sierpiński did.

[Otton] said that he senses all the happiness coming to us together, including good health and his doctorate. It seems that his scientific success is constantly growing. Sierpiński wrote that he communicated one of Otton's results to Professor Aleksandrov (in Moscow), who really admired it. ... Sierpiński wrote that Professor Fréchet, a very well-known French mathematician, asked him for Otton's address, because he wanted to send him an article in which his name is cited many times. Otton obtained many results that were later achieved by Professor Fréchet, but he hid them in a drawer and communicated only some of them to Tadeusz Ważewski, who cited Otton in an article published in 'Comptes Rendus'. In this way, Fréchet was able to base his work on one of Otton's nice ideas.

If we consider the case of real variables in classical analysis, we find two kinds of problems, theorems, definitions and reasonings: these are integral problems, theorems etc., and local problems, theorems etc. Here is an example:

If we are given a differential equation

$\Large\frac{dy}{dx}\normalsize = f(x, y)$

and a domain D in the (x, y)-plane and we propose to find integrals of this equation, as extended in D as possible, we are dealing with an integral problem.

But if we only suppose the existence of a neighbourhood of a given point $x^{0}, y^{0}$ in which the function $f(x, y)$ satisfies certain conditions of regularity and we seek functions for which there exists a neighbourhood of $x^{0}$ in which this function satisfies the given equation, we are dealing with a local problem.

Integral problems, theorems, and reasonings are related to a domain given in advance and considered in its entire extent, while local problems are related only to the neighbourhood of a point given in advance and it is in the nature of things that we do not need to know either the size or the precise form of this neighbourhood and it is only the pure existence of the neighbourhood that is the object of the problem. The same is true for theorems, definitions, and reasonings that can be integral or local. Differential calculus provides us at first sight with local theorems and, to obtain integral theorems, we need additional reasonings borrowed especially from topology. Now, I will only speak of local problems, theorems, definitions, and reasonings in the case of real variables.

During the war, of course, the German Nazis were fairly efficient at exterminating the Polish intelligentsia.  Nikodym and his wife escaped into the countryside, disguised as peasants. They were sheltered for the duration of the war in a small village, hidden and fed by the peasants. In exchange for being taken care of, they tutored the village children in arithmetic, and sometimes in other subjects, generally at the primary level.

Let $\mu$ be a $\sigma$-finite measure on a $\sigma$-algebra $\Sigma$ of subsets of $\Omega$ and $\nu$ a countably additive set function on $\Omega$. If $\nu$ is absolutely continuous with respect to $\mu$: that is, $\mu(A) = 0$ implies $\nu(A) = 0$, then $\nu(A) = \int _{A}f d\mu$ for any $A \in \Sigma$, where $f$ is locally integrable on $\Omega$.

In the early days [at Kenyon College] the Nikodyms went to class together; he lectured from a prepared text and she helped field the questions.  They were a dramatic contrast to the usual inhabitants of central Ohio, moving together through this strange culture and language.  The small college town was a big help: there was usually someone who could translate, by way of French or German, if there was difficulty communicating in the butcher shop or at the barber, and the shopkeepers knew the college would straighten out any problems By a few years later, his English had improved enough to manage questions himself and his wife no longer needed to attend his classes.

By the time I was a student at Kenyon and took a course from Nikodym (an introduction to Hilbert Space, using the text by Halmos) in the early 1960's, he was in his eighties.  A small man, somewhat stooped over, he was driven to work every morning by his wife. She followed two paces behind as he walked to his office, removed his coat for him and hung it up, then went home until she returned for him in the evening.  A sweet, soft spoken man, he still lectured from a prepared text but his English was limited and we often had to phrase our questions in French and German, a good experience for us students but it generally restricted his enrolment to senior maths majors planning to attend graduate school, not a large number of people in this small college which then had about 800 students.  A high point of our undergraduate education was being invited home for dinner at the Nikodym home. It was a small but elegant apartment carved from a large house on a  hilltop owned by the college, built well over a century ago as the palace of the then Episcopal Bishop of Ohio. Mrs Nikodym served what seemed to us a very European dinner, and with some prompting from her husband told of their earlier lives and especially their hiding out during the Second World War.

In that case I will not have to correct the galley-proofs.

There are so many new problems that I cannot spend more time on those that I have already finished.

Nikodym was a very demanding man - both towards himself and others. Perhaps that is why not everyone liked him. ... He always set himself ambitious scientific goals, liked to struggle with difficult problems and persistently worked for years to solve them.

He despised what he called careerism: he despised fame-hungry scientists who, in order to advance, play politics in universities and in government. He also despised what he called sham - any pretence of greatness not based on honest truth. ... I remember vividly some of his sayings, for example: - An honest shopkeeper is worth much more than a pretend scientist; - Beware of the "happy-makers." They are usually unhappy themselves and bring misfortune to others; - Work is a reward and pleasure for those few who understand it, all the rest are careerists. And yet a person is quite happy with family, home, friends, a few beautiful things around him, creative work at his desk and health. Applause is unnecessary.

We should invite lecturer-enthusiasts since enthusiasm is infectious.

Otton was, and always will be, a great man. I am happy that I knew him. His discoveries were very deep and will live for ever as long as Pythagoras's theorem, which has survived for centuries.