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Saturday, March 17, 2012
Euclid: Father of Catholic Mathematics
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If any of you are homeschoolers, you may be familiar with Khan Academy, a website in which high quality and free video content from a wide variety of subjects (earth sciences, mathematics, physics, business taxation, art, etc) is distributed.  In the above video from the Khan Academy, you can listen to a basic overview of Euclid, the Father of Geometry.

Yet, I suggest that Euclid, who lived nearly 300 years before the advent of Christ, is to be considered the Father of Catholic Mathematics.

Some anti-Catholics may think that I am choosing a pagan mathematician to be the "Father of Catholic Mathematics" because there simply are no successful Catholic mathematicians. After all, don't all Catholics reject science and empirical study in order to blindly follow the teachings of the Pope and factual inaccuracies (e.g. orbit of the Earth)? To this group of depressed and ill-informed individuals, I'd like to direct you to "How the Catholic Church Built Western Civilization," in which Dr. Woods expounds upon the varied, significant, and priceless contributions of Catholics to mathematics, science, industrial production, art, charity, and a whole host of other worthy endeavors.

My choosing of Euclid to be the Father of Catholic Mathematics, albeit an informal title, is not in the least because there are few Catholic mathematicians. I believe that Euclid is the true precursor to the Catholic mathematician.

Euclid's systemic demonstrations of geometry - including planar geometry, three-dimensional geometry, and number theory - expressed in his Elements is one of the greatest collection of mathematics (if not the greatest) ever produced. By some estimates, Euclid's Elements is second only to the Sacred Scriptures as the most printed book in human history.

Lincoln himself toward the end of the video at the beginning of this post expressed his admiration for Euclid. In fact, it was held, up until the modern era, that a man was not educated if he had not read, studied, and memorized some of the proofs of Euclid!

But what is it that makes Euclid the "Father of Catholic Mathematics"?  It is a two-fold comparison that I would like to illustrate.  First, I wish to illustrate that the very foundations of Euclidean geometry parallel the foundations for Catholic theology. 

Now you might be surprised by this assertion.  After all, how does geometry compare to Theology?  Well, let's take a step back.  What is the underpinning of Theology?  Well for anyone that has studied it, we would recognize Philosophy as the underpinning of Theology.  One does not study Theology without first studying Philosophy. 

Axioms & First Principles

But how is geometry and philosophy both connected?  Euclidean geometry consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.  In Euclid's method, the most basic of axioms include:
  1. Things that are equal to the same thing are also equal to one another.
  2. If equals are added to equals, then the wholes are equal.
  3. If equals are subtracted from equals, then the remainders are equal.
  4. Things that coincide with one another equal one another.
  5. The whole is greater than the part.
In a similar manner, philosophy is based upon "first principles."  What are "first principles"?   According to Collins English Dictionary – Complete and Unabridged, first principles are "one of the fundamental assumptions on which a particular theory or procedure is thought to be based, also called axioms".

Both in Euclidean geometry and philosophy are based on the notion of using a small set of axioms to come to knowledge of a larger body of knowledge!  In philosophy, we have the following axioms as first principles:
  • The principle of noncontradiction: the same thing cannot both be and not be at the same time and in the same respect. The same proposition cannot be both true and false.
  • The principle of excluded middle: Either a thing is or it is not, there is no third possibility. (Tertium non datur: a third is not provided.)
  • The principle of the reason of being (the principle of intelligibility): being is intelligible to the human intellect and as an object of intellection it can be explained ontically only through being, and so it cannot be identified with non-being. Every being has a reason of its existence either in itself or in something else.
  • The principle of finality: Every agent acts for an end.
  • The principle of causality: Every effect has a cause.
  • The principle of identity: Every being is that which it is. Each being is separated in its existence from other beings.
Both Euclid and St. Thomas can be said to use the same thought process in their respective disciplines to come to greater knowledge.  Yet, while this is certainly interesting, is it possible to observe Euclidean geometry actually affecting Catholic practices and thought, rather than merely sharing a common method?  Absolutely, and to that we now turn.

Euclidean Geometry in Cathedrals

Hugh McCague of York University in "A Mathematical Look at a Medieval Cathedral" explains the importance of geometry in the building of Cathedrals.  Rather than simply re-writing what has already been written, I'd like to direct you to that link.  In the article, you will note that Euclid's Elements is cited as the important precursor to the practical geometry that was of central importance in the building of some of the greatest Cathedrals ever made for the honor of God.

Simply put, every Catholic, whether he is a mathematician, artist, architect, student, or average layperson should be familiar with the works of Euclid.  Euclid's theories truly impacted the construction of Catholic architecture for centuries.

Conclusion

The website Much More About Math (Editor Note: website no longer exists) does a good job at summarizing the importance of Euclidean geometry:
Geometry holds great importance in the forever-expanding world of mathematics. It enables us to picture what is happening in problems we may encounter in the study of mathematics. The study of geometry helps us develop the ability to visualize shapes, volume, area, and so on. Geometric proofs play an important role in the expansion and understanding of many branches of mathematics, from Venn diagrams in set theory to area under the graph in calculus.

One must realize that probably the most important reason a mathematician and/or non-mathematician should understand geometry is the use of deductive thinking and logic. For the mathematician, the use of logic and deductive thinking is important especially in such courses as finite mathematics. For the non-mathematician, logic and deductive reasoning could play a role in doing such courses as Philosophy.

Geometry holds great importance in the forever-expanding world of mathematics. It enables us to picture what is happening in problems we may encounter in the study of mathematics. The study of geometry helps us develop the ability to visualize shapes, volume, area, and so on. Geometric proofs play an important role in the expansion and understanding of many branches of mathematics, from Venn diagrams in set theory to area under the graph in calculus.

One must realize that probably the most important reason a mathematician and/or non-mathematician should understand geometry is the use of deductive thinking and logic. For the mathematician, the use of logic and deductive thinking is important especially in such courses as finite mathematics. For the non-mathematician, logic and deductive reasoning could play a role in doing such courses as Philosophy.
Below you can find through Amazon.com all of the contents of the Elements in English.  This set of three books is also added to my Wishlist so if any reader would be so kind as to purchase these three for me, know that I would be extremely grateful.


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