Essay of How Not To Be Wrong, The Power of Mathematical Thinking

HOW NOT TO BE WRONG, The Power of Mathematical Thinking is a book written
by Jordan Ellenberg, a Mathematician and a child prodigy, this book focuses on
mathematics, but he approaches it on such a way for everyone to understand even if
they don’t have much mathematical background, while still letting people with
knowledge about mathematics to learn more things without being too easy or too
boring.

“The armor, said Wald, doesn’t go where the bullet holes are. It goes where the
bullet holes aren’t: on the engines.” This is from the second story the author opens the
book with, which is a great example on the purpose of the book and how it develops.
Ellenberg does an excellent job at telling us different stories –that involve mathematics
in one way or another– and teaching us –the readers– some valuable insights.
This second story is about Wald, a member from the Statistical Research Group, he was
considered a mathematician eminence, and he was approached to find the optimum way
to shield planes so they’re not too heavy but they’re protected enough, and his way of
thinking let him realize there was no use on analyzing the bullet holes from the planes
that did come back, and if they didn’t have many holes on the engine, it was simply
because the ones that did get hit, didn’t come back.

There are many stories that Ellenberg gives us to show us precisely what he
showed above, that sometimes we are stuck with some problem or there’s something
going on in the world, and mathematics let us think and analyze things in such a way
that we can solve problems in an unexpected way.

Ellenberg is successful in collecting real life situations, from every possible
field, that mathematics had a big impact in them. To write about every single one of
them would be pointless, I encourage you to read the whole book. The subjects that he
goes through go from war, to personal anecdotes, economics, politics, lotteries,
parabolas, calculus, infinity, science, social studies, etc. showing us that no matter the
field, no matter where we are looking at or trying to do, we can always make informed
decisions and “not be wrong” if we have mathematical knowledge and we take them
into consideration.

Going through a lot of real life examples through a wide variety of subjects is to
convince us –the readers– that no matter what you do, what you like, what your future
plans are, you will face certain situations, certain problems, that require a way of
thinking that mathematics provides and can solve the problem.

By reading this book and changing the way we think, the way we approach
problems and the way we accept or decline ideas –Ellenberg’s objective with his book
is met by this– we can change the way we live and the way others live, by not being
fooled so easy, by making good decisions, by demanding ourselves to think critically
and analytically.

He closes the book with the following:

“Every time you observe that more of a good thing is not always better, or you
remember that improbable things happen a lot, given enough chances, and resist the
lure of the Baltimore stockbroker, or you make a decision based not just on the most
likely future, but on the cloud of all possible futures, with attention to which ones are
likely and which ones are not, or you let go of the idea that belief of groups should be
subject to the same rules as beliefs of individuals or simply you find that cognitive sweet
spot where you can let your intuition run wild on the network of tracks formal reasoning
makes for it, without writing down an equation or drawing a graph, you are doing
mathematics.

When are you going to use it? You've been using mathematics since you were born and
you'll probably never stop. Use it well.”

I really enjoyed this book, I have always loved mathematics and many of the
things he talked about, I had lived a similar story. I have friends that are mathematicians
(or will be) and we have talked about this, about how crucial it is for everyone to grasp
concepts about mathematics, it doesn’t matter what they want to be professionally;
listening to people say things like “I hate maths” or “I can’t wait to study [INSERT
COLLEGE CAREER WITHOUT MATHS] so I don’t encounter maths for the rest of
my life” is really sad, because they will use maths for the rest of their lives, and they’re
truly beautiful, and if they were taught mathematics in a different way, they wouldn’t
hate it.

My conclusion would be, if you like knowledge, if you want to challenge your
ideas and want to be amazed by all the applications that mathematics has, give this book
a try, it will not disappoint you.