Wrong Views Of Mathematics
Peter Oye Sagay
May 29, 2023
The word mathematics invokes various emotional responses in accordance to the responders views of mathematics. Many of the views are negative and wrong. Many years ago, I was a participant in a mentorship program for youths. The objective was to elicit mathematical enthusiasm. There were three primary reasons most of the youths disliked mathematics: it is difficult, it is boring, it is not financially rewarding. These were youths but many adults and even great thinkers support their disinterest in mathematics.
St Augustine, Bishop of Hippo (A.D. 354 - 430) was a great thinker, philosopher, theologian and one of the great fathers of Christianity. I am particularly in awe of his treatment of Time in his book The Confession. This book contains other philosophical and theological beauties. However, St Augustine did not like the mathematicians of his time. About 400 A.D, St Augustine viewed mathematicians as follows:
"The good christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell".
I am sure that after many centuries in heaven St Augustine knows that mathematicians made no covenant with the devil. In fact several catholic monks became great mathematicians and influencers of other great mathematicians.
There were other thinkers who hated mathematics: poet Johann Wolfgang Goethe, historian Edward Gibbon and philosopher Arthur Schopenhauer, to name a few. In fact, one of the many negative statements Schopenhauer made about mathematics was that arithmetic is the lowest activity of the spirit because machines can perform it.
There is no true mathematician or student of mathematics of current time who has not heard of the great mathematician Blaise Pascal (he gave the world several mathematical gifts). However, even Pascal doubted the relevance of mathematics. Pascal wrote the following in a letter to his friend, the great mathematician Fermat, in August 16, 1660:
"To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession; and I have often said that it is good to make the attempt [to study mathematics], but not to use our forces:so that I will not take two steps for mathematics, and I am confident that you are strongly of my opinion."
Youths, great men and many others with the wrong views of mathematics. Why? Simply put, wrong definitions over the centuries as humans became linguistically sophisticated and fanciful in their definitions. The great mathematician Pythagoras coined the word mathematics. He defined mathematics as consisting of two groups: the discrete and the continued in the context of problem categorization. He further classified the discrete into the absolute and the relative; to the absolute, he assigned arithmetic; to the relative, he assigned music ( note that he considered music as mathematics). He classified the continued into the stable and the moving; to the stable, he assigned geometry; to the moving, he assigned astronomy. In essence, everything is mathematics and to the Pythagoreans, numbers grant the access to the everythingness of mathematics. This was TECTechnics Theory in its infancy. I formulated TECTechnics Theory. Over the years, I have systematically shown that, base on the Pj Problems Axioms, everything reduces to numbers in the final analysis.
So, here is the simple and proper definition of mathematics: mathematics is posing and solving Pj Problems (there are only seven types). This is all Nature and cognitive beings do. They pose and solve Pj Problems. This is what even God was doing in Genesis chapter 1. In fact, all religious books are compilations of Pj Problems and their solutions. The ultimate solution being oneness with the Spirit of God (an equilibrium problem). Over the years, mathematics have over-emphasized the methods used to arrive at solutions at the expense of the fundamentals. A student will be more at ease if at first he or she knows that only seven types of problems exist. The fancy mathematical symbolism can be presented thereafter. The unawareness that all problems posed by Nature and humans are Pj Problems is a roadblock to mathematical enthusiasm. In other words, when people know that they have been posing and solving only Pj Problems all their lives and that that is all mathematics is, they will come to realize that Nature and all cognitive beings are mathematicians. Being mathematicians, they will be more kind to mathematics and wrong views of mathematics will be few.