What is the meaning of "interesting" in a mathematical context? Does it have an abstract mathematical model?

Question

I, from time to time, see the word "interesting" in a mathematical context when models are explained, and I realized that there is actually a philosophical depth to that.

• Is there a philosophical definition of what makes a mathematical model or mathematical finding interesting?
• Does "interesting" have an abstract mathematical model? (in category theory perhaps?)

Answer 1

Terence Tao wrote an article entitled "What is Good Mathematics?" that may provide you with some food for thought. Whether it answers your question or not is hard to say. Personally, I think that something being interesting is highly subjective. In any case, here are the opening sentences from Tao's article. Please see the link above for the whole piece.

We all agree that mathematicians should strive to produce good mathematics. But how does one define “good mathematics”, and should one even dare to try at all? Let us first consider the former question. Almost immediately one realises that there are many different types of mathematics which could be designated “good”. For instance, “good mathematics” could refer (in no particular order) to

(i) Good mathematical problem-solving (e.g. a major breakthrough on an important mathematical problem);

(ii) Good mathematical technique (e.g. a masterful use of existing methods, or the development of new tools);

Another thought on interesting mathematics comes from Richard Brown's TEDx talk Why mathematics?, in which he defines "interesting" roughly as "hard, but worthy of study".