Two moments of growing in mathematical maturity I remember vividly:

Realizing that equations are claims that are therefore either true or false. Everything asserted with symbols… could just as well be asserted in English. I could start chunking up arbitrarily long and complicated equations between the equals signs, because those equals signs were just the English word “is”!

Learning about the objects that mathematical claims are about. Going from having to look up “Wait, what’s a real number again?” to knowing how Z, Q, and R interrelate told me what we’re making claims about. Of course, there are plenty of other mathematical objects—but getting to know these objects taught me the general pattern.

Two moments of growing in mathematical maturity I remember vividly:

Realizing that equations are

claimsthat are therefore either true or false. Everything asserted with symbols… could just as well be asserted in English. I could start chunking up arbitrarily long and complicated equations between the equals signs, because those equals signs were just the English word “is”!Learning about the

objectsthat mathematical claims are about. Going from having to look up “Wait, what’s a real number again?” to knowing how Z, Q, and R interrelate told mewhat we’re making claims about.Of course, there are plenty of other mathematical objects—but getting to knowtheseobjects taught me the general pattern.