Some Thoughts About Mathematics And Life

The one thing that comes to mind when I think about mathematics and life is:  You can’t solve any mathematical problem with a confused or unfocused mind.  So, to do a math problem your mind needs to be clear and directed to the problem at hand.  The same could be said about any problem that arises in a life situation.  We are more likely to achieve a better solution if our mind is tranquil and rational.  In other words,  unsettling, spoiling emotions must be kept at bay.  For, a great disturbance in many life events is the spilling over of emotions that cause us to act in an irrational manner and to reach sometimes distorted and even absurd “solutions”

In the realm of life problem solving, mathematical problems form only a tiny subset of all the problems we must deal with.  Mathematicians have established clearly defined rules for solving mathematical problems.  In their special province they serve as architects, beginning with the simple counting numbers or natural numbers, and then including 0 and the rational numbers and stretching out to the irrational numbers to form the set of real numbers.  The real number line is created where all these numerical sets have their home.  And mathematicians begin with axioms and postulates(assumed truths) and from them derive theorems and corollaries to theorems.  Theorems and their corollaries must be subjected to the rigor of mathematical proof before they can be accepted as truths.  What can we use to prove a particular theorem?  Any definition(a definition is an agreement to use words, phrases or symbols as substitutes for other words, phrases, or symbols.), postulate or axiom, or previously proved theorem may be used in a proof.  The use of precedent is also essential to legal, medical and some forms of scientific problem solving.  And mathematics teaches us that to disprove a theorem it is sufficient to find only one example where the statement does not hold.  This latter statement applies to all life problems as well.  For, when we toss around generalizations, it is important to realize that it takes only one counterexample to destroy our generalization.

Mathematics also teaches us to think twice; to be careful before reaching a conclusion.  When graphing functions on the Cartesian plane, it’s not uncommon to have restricted domains, meaning the functions are defined on a certain interval.  And sometimes separate cases must be considered, for example, what does the graph look like when x is greater than zero and how does the graph change when x is less than zero.  Arguments in life may also have restricted domains and statements that may be true for an adult are utter nonsense when applied to a child.  So, we must be cognizant of our audience and know where to apply our argument.  Thus, the study of mathematics can and does help us to cope better and to grasp better the multitude of problems we encounter in life.