All rise. This week, mathematics is going on
trial. The charges are a bit unusual. Mathematics
stands accused of being difficult, abstract,
beautiful, practical, mind -boggling, and remarkably
consistent. It has even predicted things about
the universe before anyone knew they existed.
So what does the evidence reveal? Is mathematics
simply a useful invention of our human mind,
or are we discovering patterns already living
into reality? And if mathematics can lead us
toward the hidden structure of the universe,
can it also tell us anything about how to live?
Mathematics, please take the stand. Okay, here
we go. Our first issue in any trial is the burden
of proof. The person making the claim must provide
enough evidence to support it. but different
kinds of cases require different levels of evidence.
A civil court may decide according to a preponderance
of the evidence what is more likely than not.
A criminal conviction requires the stronger standard
of beyond a reasonable doubt. However, math demands
something stronger still. Testing thousands or
even millions of examples cannot establish that
a mathematical statement is always true. Examples
do provide evidence, but math requires proof,
a logical argument showing that the conclusion
must follow from the starting assumptions. For
example, the Pythagorean theorem does not become
more true each time someone measures a right
triangle. But once it is proved, it applies to
every right triangle in Euclidean geometry, including
those that no one has ever drawn and those that
no one ever will. This is an extraordinary claim
that math makes. Not merely this seems to work,
but this must be so. That kind of certainty is
powerful, at least to me. But in life, we rarely
meet this standard. My most important decisions
do not come with mathematical proof. We cannot
prove that a friendship will last or that a new
direction will succeed. or that someone will
always remain faithful. Instead, we look for
another kind of evidence, perhaps consistency
or character, maybe experience. How about a trustworthy
pattern over time? The evidence may not eliminate
every doubt, but it can give us reasonable grounds
for taking our next step. So, on the charge of
demanding proof, mathematics is found guilty.
Of course, rarely does life offer proof. More
often, it offers enough evidence to make trust
reasonable. So our question to kick off our week
is, is there a decision where we are demanding
certainty when the evidence has already given
us enough reason to take one hopeful step?