Zbigniew Semadeni

• Ph. D, professor
• University of Warsaw

Efforts to modernize Polish mathematics education began in the first half of the twentieth century. After 1957, the moving spirit of the Polish reforms was Zofia Krygowska; a description of her role in Poland and in international fora is augmented with explicit quotations from her books and articles. In 1967, under a strong influence of the French...

Category theory is symmetric in the sense that all definitions, theorems and proofs have uniquely defined duals, obtained by formal reversing of arrows. In contrast, the products and coproducts in typical categories whose objects are sets endowed with basic algebraic, topological etc. structures of Cantorian Mathematics show a specific lack of symm...

To explicate certain phenomena, e.g., the possibility of deduction without definition, we hypothesize that an individual is able to understand and appreciate reasoning with a due feeling of its necessity when the concept image of each concept involved in the reasoning has reached a certain level of development; we then speak of deep intuition. This...

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Without Abstract

The celebrated principle of the permanence of the rules of calculation is contrasted here with another principle, called concretization permanence principle (c.p.p.). Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended so as to include further numbers (these numbers are alread...

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Without Abstract

Introduction At ICME-2 in Exeter, in 1972, I listened to the plenary lecture delivered by René Thom (1972). His apt analysis clearly demonstrated the untenability of the basic assumptions (mathematical and philosophical) of the "modern mathematics" movement (i.e., "new math"), which had just reached its zenith before the strong criticism expressed...

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W: Roczniki Polskiego Towarzystwa Matematycznego, Ser. 2, 11(2):344-350, 1970. (in Polish).