ARE MATHEMATICIANS DISCOVERERS OR INVENTORS

DOES ANYONE CARE?

Are mathematicians discoverers or inventors? This question has been in my mind for a long while and the answer still has not been revealed to me. I suspect this question has been asked by many people, many times, over many years and remains unanswered to this day. So, why trouble myself with it if I believe there is little hope for an answer within my lifetime? Because, I answer, I am enamored with issues such as this which are related to the larger subject: The Nature of Reality. I find it impossible to cease wondering.

Humans, being capable of cognition, use their ability to observe what is around them to construct their perceived “reality”. For instance, most people when asked to describe the rock they have been handed would reply: it is a heavy red solid object with a hard surface. That is their “reality” as constructed from their sensory inputs. However, the rock is composed of atoms and the empty space between the atoms. Atoms are very small, in fact, so small that the rock is mostly empty space. This constitutes a different “reality” for the rock. Taking this example a step further, one wonders what the rock’s “reality” is when there are no living things to construct a “reality” for the rock.

As an aside, the “heaviness” of the rock is due to the mutual gravitational attraction between the mass of the rock and the mass of our planet, Earth. The rock looks “red” because the atoms of the rock absorb the non-red part of the incident light and reflects the red part. The rock is “hard and solid” due to the interaction between the electromagnetic forces that hold the atoms of the hand, and rock, in place.

Using the example of the rock’s “reality” as a kind of template, let us return to the mathematics question. Sir Issac Newton is remembered both for his insight-full motion and gravity equations as well as the mathematics required to understand the equations. It is noted that today Newton’s equations have been observed to apply everywhere in the visible Universe. We ask this question: Does “The Universe” operate according to its own “rules”, the effects of which Newton observed and then invented equations which provided much needed insight into these “rules”of the Universe, or, does “The Universe” operate without “rules” at all and thus any hope of for discovery of the “rules” is just another Human folly? It seems to me to be the latter. I believe any hope expressed of finding the “rules” that govern the operation of “The Universe” is the product of collective human hubris and any effort to do so is doomed to failure. However, I believe also that humankind is well served in many ways by the collective effort to better understand the “rules” of “The Universe” and we must keep trying in spite of it being thought folly. Is there a better way to have fun? Oh, by the way, I believe the whole body of mathematics enjoyed by Humankind was invented by Humans and the Universe just “IS”.