Hi, what if there were numbers smaller than zero?
Now, today that question seems ordinary. We talk
about temperatures below zero, bank accounts
with negative balances, and elevations below
sea level. But there was a time when negative
numbers seemed absurd. How could you possibly
have less than nothing? Yet, someone was curious
enough to ask the question. And mathematics?
Then another question appeared. What if we could
undo the squaring process? If 3 squared equals
9, could we find a number whose square is 2?
And that question led mathematicians to discover
irrational numbers, numbers that cannot be written
as fractions. Well, then came an even stranger
question. What if the square root of negative
1 existed? Now, at first, this seemed completely
impossible. After all, no positive number multiplied
by itself gives a negative result. And yet, mathematicians
explored the idea anyway. And that curiosity
eventually led to complex numbers, which today
helps to describe electricity and sound waves
in modern physics. So again and again, mathematics
has grown because someone asked a question. What
if? What if there is another kind of number?
What if this pattern continues? What if geometry
worked differently? What if infinity behaves
different than we expect? It is easy to think
about mathematics as being about certainty. And
in some ways it can be. But before there was
certainty, there was curiosity. Before there
were theorems, there were questions. And before
there were answers, there were people willing
to explore. I've come to believe that curiosity
is one of the most powerful forces in human history.
It expands mathematics, it expands science, and
it expands us. Because every new discovery begins
the same way. someone becomes curious enough
to ask, what if? And maybe the curiosity you
need today is not about discovering a new kind
of number. Maybe it's simply asking, is there
a different way to solve my algebra problem?
Is there another perspective I have not considered?
Could there be more here than I currently see?
Because every meaningful discovery begins with
those same two words. What if?