In mathematics, a conjecture is a statement believed to be true but not yet proved. In this sense, every mathematician, great or small, makes conjectures when faced with a problem. For example, arranging the points as shown in the following figure might lead us to conjecture that the parallelogram ABCD is a rectangle and that the three points E, G and H are collinear.
The first conjecture is easily proved by applying Pythagoras' theorem to triangle ABC, while the second can be refuted by calculating the angle at G (which is 89°, not 90°). Of course, conjectures of this kind are more like exercises; they are of little mathematical interest…
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What makes a good conjecture
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