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Blast into Math! Afterword

8 Afterword

The first time we read mathematics, we often feel like we haven’t understood it very well. It is healthy
to take a break and return again later. When you do this, you’ll find that you understand things better,
because even though you’re not thinking about math, your brain will keep working on on it without you
noticing it. It’s like there is a mathematical cow in the back of your brain, and when you feed her some
math she’ll keep chewing and chewing on it, while you think about other things. When you look at the

same math later, your math cow will have digested it for you, and it will be easier for you to understand
and digest.

The last chapter of this book delves into some pretty deep topics. The first time I learned about limits,
sequences and series, I didn’t understand them very well. They were spooky! But now, I work comfortably
with them. So, if you’ve found parts of this book challenging, remember that most mathematicians
probably found the same parts challenging when we first learned them. However, if you take breaks and
keep coming back to the difficult parts, you will eventually understand them. I don’t promise you’ll be

able to prove the Riemann Hypothesis, or any of the other unsolved problems in this book, but if you
began the book with the requisite background, then you can understand all the material and almost all
the problems, if you spend enough time and take breaks in between.

As for the unsolved problems in this book, it’s a general rule that all famous unsolved math problems are
extremely difficult. Don’t give up hope, but don’t waste your time either. You should spend most of your
time on problems which you have a good reason to think you can solve and spend only a little time on
famous unsolved problems. This general principle is true both in math courses and math research. For
example, in an exam you should always do the easier problems first. Research mathematicians should
prioritize the problems which they expect they are most likely to solve. Because mathematics research

involves solving problems which have never been solved before, we can’t be completely sure we’ll solve
any particular problem. Nevertheless, if it’s similar to a problem we have solved in the past, and if
we have experience working on similar problems, then it’s likely we can solve it. You are nonetheless
encouraged to be hopeful that you might solve a famous problem, but even if you don’t, you have made
a great accomplishment if you have read this book and worked on every problem.

If you continue returning to the difficult “monster-under-the-bed” problems, re-reading and re-working
through the book, you will eventually understand all the mathematics in this book. The mathematical-

monster-under-the-bed will eventually become your snuggly mathematical pal. So, this is not goodbye,
but until we meet again. Please give yourself some time and re-read this book after a few months or so.
Whether you felt like you understood everything the first time or found this book a challenging struggle,
it will become easier and easier, and you’ll understand more and more each time we meet again…♥

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