The János Bolyai Mathematical Society has its beginnings in the Mathematical Society (Mathematikai Társaság), an informal private society for the mathematicians in Budapest in 1885. Lóránd Eötvös, Hunyadi, König, and others set up these meetings but there was no formal statutes, officers of the Society and the meetings are reported to have looked like dinner parties except for the blackboard.
Although initially only a mathematical society, physicists were encouraged to join and in June 1891 the first issue of their journal Mathematikai és Physikai Lapok was published. Work was now going on to formalise the Society and statutes were being drawn up. On 5 November 1891 the Mathematical and Physical Society was founded. König stressed the fact that:-
... all who work and teach in the fields of mathematics can be chosen members.
The groundwork had been done well for the Society had 298 members when it was founded. By 1893 over 400 people had joined the Society which today is called the János Bolyai Mathematical Society.
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