Hi. One of the quickest ways to become frustrated
with mathematics is to believe that making mistakes
means you are bad at math. It doesn't. It simply
means you are doing math. Mathematics is difficult,
and if it weren't, we would not be spending years
studying it. The problems become more complex,
the ideas become more abstract, and the connections
become less obvious. Mistakes are not an exception.
They're simply a part of the process. In fact,
one of the biggest differences that I see between
students who continue to grow and those who get
stuck is not intelligence, but it is humility.
The humble student assumes they might have made
a mistake, so they check their algebra. They
revisit their assumptions. they ask, where could
I have gone wrong? While the prideful student
assumes the answer must be right because they
got it. If something does not match the solution,
they're more likely to think the book is wrong,
the calculator is wrong, or the problem is simply
unfair, before ever considering that maybe they
made a mistake. Of course, we've all been there.
I cannot tell you how many times I've stared
at a solution, convinced it had to be incorrect,
only to discover that I had dropped a negative
sign 20 minutes before. And those experiences
are quite humbling. But they're also healthy.
So one habit I've developed is to expect mistakes.
Not because I lack confidence, but because I
know I'm shooing. So when I finish a problem,
I don't just ask, did I get the answer? I ask,
does this answer make sense? So if I'm calculating
the probability of an event, is the answer between
0 and 1? Or if I'm finding someone's age, did
I somehow end up with a negative number? Or if
an insurance company should collect about $500
in premiums, why did my calculation produce $50
,000? Those simple reasonableness checks have
saved me countless times. Now, they do not prove
the answer is correct, but they often reveal
when something has gone terribly wrong. And that
mindset changes everything. Rather than viewing
checking your work as a chore, it simply becomes
part of doing mathematics well. Professional
mathematics do this all the time. They share
their papers with colleagues before they publish
them. They ask others to look for mistakes. And
they know that no matter how experienced they
are, they can still be overlooking something.
And that's not weakness. I would consider that
wisdom. And there's a subtle difference between
confidence and humility. Confidence says, I think
this is correct. And humility says, let's make
sure. And those two ideas are not enemies. In
fact, they often work better together. So do
not be discouraged by mistakes and do not let
them become a judgment on your ability. Instead,
let them become reminders that mathematics is
not about protecting your ego. It is about pursuing
the truth.