This is the 14349th most frequent Russian word.
открытию
"Opening" or "discovery" (dative case of "открытие").
In this sentence, 'открытию' is in dative case to define the purpose or objective (the discovery) related to the subsequent activities.
Это изобретение стало важным шагом к открытию новых технологий.
This invention became an important step towards the discovery of new technologies.
Here, 'открытию' is used in the dative case, describing the result or endpoint (the discovery of the truth) the subject is moving towards. The context shows the abstract concept of understanding.
Я шел к открытию истины постепенно, размышляя о случившемся.
I approached the discovery of the truth gradually, pondering what had happened.
Here, 'открытию' is used to denote the event (the opening) to which the speech action refers, demonstrating a dative case usage to connect it to the action.