Mostly the significance of a conjecture is that we don't know the answer. A conjecture is successfully resolved if it proven or disproven. (In fact, of the three big conjectures to be resolved in the past couple of weeks, one was proven and two were disproven.) The Jacobian conjecture, which is the one that was resolved this week, was largely thought to be false. It was only the fact that no one could disprove that raised the tantalizing possibility that it was true.

The reason the author is upset is not that the conjectures were false, but that an AI settled them. That's why so much of his post is about the loss of the human element.