Kids ask the best
questions. Unburdened by prior knowledge or assumptions, their questions are
driven by pure curiosity and a deep desire to learn something new. As adults we
can learn a lot from how kids ask questions and seek knowledge. And we can also
learn or strengthen our understanding of a particular topic by answering kids
questions.

For example, my son
asked me a question about even and odd numbers, and why we get an even number when
we add two even numbers or two odd numbers, and an odd number when we add an
even and an odd number. Because this knowledge is drilled into us since our
younger years, we stop wondering why.

Intuitively we
know the proposition is true, and we can cite a couple of examples to prove it
to ourselves. For example, adding 2 and 4--both even numbers, gives us 6, also
an even number. When we add 3 and 5--both odd numbers, we get 8, which is an
even number. If we choose a mix of an even number and an odd number and add
them, we got an odd number. For example, adding 2 and 3, we get 5, which is an
odd number. It seems that our intuition is onto something. Sometimes intuition leads
us astray, and reality is reflected by something non-intuitive. The theory of
relativity—both special and general, and quantum mechanics for example offer
non-intuitive description of reality and how things work.

The addition
examples above are not enough to gain confidence that we answered the original
question. Since there is an infinite number of natural numbers (1,2,3, …etc),
we have to find a different way of establishing or refuting the statement
without listing an infinite number of examples. The clue is in how we write
even and odd numbers.

An even number is
a number divisible by $2$. We can write an even number as the product of two
numbers, $2$, and another natural number $k>0$ in the form of $n_1=2k$. This
number is even, because it is divisible by $2$. An odd number is one that is
not divisible by $2$, or one where if divided by $2$ would have a remainder of $1$.
Thus, we can express an odd number as $n_2=2m+1$, where $m>0$ is a natural
number greater than zero.

Now we can see
what happens when we add two even numbers, two odd numbers, and a mixture of
numbers. Let’s add two even numbers first $n_1=2k$ and $n_2=2m$. The sum is $n_1+n_2=2k+2m=2(k+m)$
which is an even number.

How about adding two
odd numbers $n_1=2k+1$ and $n_2=2m+1$? The sum is $n_1+n_2=2k+1+2m+1=2(k+m)+2=2(k+m+1)$
which is an even number.

Finally, how
about adding mixed numbers one even $n_1=2k$, and one odd $n_2=2m+1$. Their sum
is $n_1+n_2=2k+2m+1=2(k+m)+1$ which is an odd number.

By working
through this simple math, we have gained insight into something drilled into us
long time ago. Indeed, kids ask the smartest questions;
don’t dismiss them, but use them to learn something new, or understand
something you already know better.