The Teleki-Bolyai is a large working library, used by scholars from all over the world, but a casual visitor is more likely to be interested in the historical side.
This means essentially two rooms. First, the core of Count Teleki and his wife's library, where the books are kept in their original shelves, with chicken wire to protect them whilst allowing the air to circulate. Many of the books are open, on display, so you can see, for example, vividly-illustrated volumes of the Description de l'Égypte (compiled by the French scholars who accompanied Napoleon), the very first Tibetan dictionary, a work by Manutius, the Encyclopédie, an extraordinary diagram of a proposed mechanical carriage horse... In many different languages. Teleki was the Chancellor of Transylvania under the Austro-Hungarian Empire, and he collected from all over Europe.
The other room is devoted to Farkas and Janos Bolyai, two of the greatest mathematicians ever, especially Janos, the son, who was one of the discovers of non-Euclidean geometry. (A crater on the moon is named after him.) This section is more a small museum, and it's fascinating. It's also very well explained. Even a non-mathematician can feel some of the excitement that Janos Bolyai felt on contemplating a world in which Euclid's fifth postulate doesn't hold.
There's a small entrance fee. The staff are exceptionally helpful and understanding. If you want a postcard, just ask - they've got them in the desk in the office.
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