This "mathematical head" sounds to me like they'd be an extraordinary person... maybe even an extraordinary man!

Having further context for the novel here helps but it's so interesting seeing the ideas of the extraordinary man being fleshed out slowly before getting to the conversation we know and love. It seems like this is the hook for an analytical essay about saving mankind. Even though the conversation is yet to happen about Rasko's ideas regarding the extraordinary man, it's easy to see how Dostoevsky it guiding the reader by planting the seed. In a funny way, it's his way of highlighting the absurd aspects of the idea before Rasko offers his own commentary on the issues. It's also key to note how right after there is a mention of a "instinctive dislike of history." This sounds like commentary from the author about the controversial views that many have on whether historical figures are truly "extraordinary" or not. When there is a later mention of Napoleon and others like Muhammad, it's clear that he is nodding towards figures that not all audiences would agree on, just not Rasko makes claims that not everyone is quick to concur with.

This portion in which the omen is ignored by Hektor even after being advised to pay mind to it seems to be the turning point in where Hektor's decline in glory truly begins. Up until this point, Hektor had been a glorious warrior fueled by successful battles, and more importantly, the Gods. Now it seems that these two attributes that brought him about his military success are starting to become his ruin. He believes that the Gods are completely and utterly on his side as well as that he can stand up to the Achians as the God-like warrior he has become. Whether this is his own doing or the work of the God's leading him to his fate is up for debate but this is the pinnacle that changes Hektor's character from a noble soldier with a loving family to a blind war-addicted warrior thirsty for nothing else but blood.