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We describe in dialogue form a possible way of discovering and investigating10-adic numbers starting from the naive question about a `largest naturalnumber'. Among the topics we pursue are possibilities of extensions totransfinite 10-adic numbers, 10-adic representations of rational numbers, zerodivisors, square roots and 10-adic roots of higher degree of natural numbers,and applications of 10-adic number representation in computer arithmetic. Theparticipants of the dialogue are idealized embodiments of differentphilosophical attitudes towards mathematics. The article aims at illustratinghow these attitudes interact, in both jarring and stimulating ways, and howthey impact mathematical development.

What is worthy of investigation? Philosophical attitudes and their impact on mathematical development by the example of discovering 10-adic numbers