There are many types of knowledge, and erudition is one of them. Erudition is a thorough, formal, and profound sort of knowledge obtained by extensive research. The term is often used to discuss knowledge in fields other than those of mathematics and the physical sciences—so you're more likely to encounter it in discussion of philosophy or literature than in discussion of biology. Erudition is not a high-frequency word in English, but when it is used, it's likely to be in a context of glowing appreciation, as something that inspires respect or awe.

To call something consequential is to say that it's significant or important, with special attention to the consequences, or effects and outcomes, it brings. The primary meaning of consequential is "following as an effect, result, or outcome." The term ultimately comes from the Latin verb sequī meaning "to follow," which is also the source of the word sequence. A consequential decision is one that will significantly shape what follows. An event that is politically consequential is one that might alter the course of politics in some significant way, and something that proves consequential is revealed over time to have been an important or determining factor in the course of events.

To ensure something is to guarantee or make certain that it will happen. For instance, someone heading to a job interview might leave their house an hour early to ensure that they arrive on time. The verb secure is used with a very similar meaning, but often implies bringing something about, or getting ahold of something. A critically acclaimed book might secure an author's reputation, or an impressive play in a championship game might secure a victory. Additionally, secure is often used to talk about safety, both as a verb and an adjective, e.g. "The townspeople used sandbags to secure the town during the flood; as a result they all felt more secure."