## Vojtěch Jarník on teaching

 The quotes below are taken from a number of sources, in particular: [1] V Jarník, Poznámky k otázkám vysokoškolské vyuky, Pokroky MFA 16 (1971), 5-8; [2] B Novak, In Memoriam Prof Vojtech Jarník, Pokroky Mat. Fyz. Astronom. 16 (1971), 1-5; [3] J Vesely, Pedagogical activities of Vojtěch Jarník, in B Novák (ed), Life and work of Vojtěch Jarník (Society of Czech Mathematicians and Physicists, Prague, 1999), 83-94. All the quotes are by Jarník himself except Quote 6:

Quote 1.

This quote is from [3] and was made by Jarník in 1952:

I am extremely fond of lecturing. Especially formerly, when I did not have so many offices and duties, I was a huge nuisance to the students. When one of my lectures was cancelled, whether it was for a holiday or for some other reason, I always tried hard to compensate by delivering it at some other time.

Quote 2.

This quote is from [3] and was made by Jarník in an unfinished text:

A mathematical lecture possesses one characteristic property: A correctly and purposefully performed chain of inferences leads with absolute reliability from the statement a theorem to its proof. But conversely, if we make a single mistake or if we do not maintain reasonable continuation of the chain of thoughts at any moment, the whole proof of a theorem or the solution of a problem collapses.

Quote 3.

This quote is from [1]:

To lecture from notes or without notes: for an introductory lecture I write down at most some points so that I do not forget anything, and also the data for the examples. For advanced lectures I have the text always with me, of course I "extemporize" but I check myself from time to time to make sure I haven't forgotten something I will need later. I also sometimes check the statements of theorems - for example, I formulate an auxiliary result including a complicated auxiliary formula which I will only prove later on. It is of course quite unnecessary to learn the formula by heart - apart from the possibility of a lapse of memory. Moreover, it would be incorrect also from a pedagogical point of view - I recommend to students that they should not memorize such things but first of all that they should understand the connections so that they know which results or arguments are to be used in a particular case, to be able to find it in the literature or, as the case may be, to be able to derive it independently by themselves. Trivial but lengthy transformations of complex expressions occur frequently, too. Such a routine procedure should be run through in the lecture as quickly as possible, and it is also important to check the result by comparing it with the prepared text in order not to be forced some moments later to look for an accidental mistake which occurred somewhere.

Quote 4.

This quote is from [1]:

I cannot help speaking when writing on the blackboard. Naturally, the sketches are rather primitive - I sketch a line and say ten words, I plot a point and say another ten or twenty words. I cannot imagine explaining, for example, the continuity of a function first and then to sketch a figure, or to sketch a figure first and then discuss it. Here it is important that the figure develops in accordance with my developing the thoughts related to it. Mathematics has the advantage that a figure only illustrates certain mathematical relations which could be explained without it - in this respect it is different from many other subjects. The advantage as compared with a book is precisely in the fact that the student sees the genesis of the figure (simultaneously with the genesis of notions or proofs) while the figure in a book is static and the reader must analyze it by themselves to find the procedure by which it has arisen.

Quote 5.

This quote is from [1]: