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Disclaimer: I wanted to write about mathematics, but the more I read, the less I know where to begin and how to end.

This is a postulate of mine: mathematics is divine.

“Mathematics is the language with which God has written the universe” – Galileo Galilei

The mathematician and philosopher of epic proportions, Bertrand Russell , wrote this on the beauty of mathematics in his The Study of Mathematics (1919):

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.”

Poetry in the Pythagorean Theorem

I can only speak of my personal experience with numbers. The mystery allures me so. Mathematics is a system of describing the universe, real and imagined. A system that technically, we humans created. Isn’t it a happy coinsidence that what we devised to describe and explain the universe as we knew it 3000 years ago (to pick an arbitrary birth of modern mathematics) just happens to be excellently fit for describing phenomena that we are just now, thirty millenia later, encountering, discovering. Like I said before , I don’t believe in coincidences.

Galileo loved truth and would not recant his findings and conclusions on the nature of the world around us. This only adds to the conviction with which he says that mathematics is God’s language…an infinitely complex yet arrestingly simple system which is inherent to God’s creation. We did not create it. We just stumbled upon it. And does it not reflect God well, himself both intricate and direct, complex and yet very accessible.

In a burst of delight Paul proclaims:
“O the depth of the riches both of the wisdom and knowledge of God! How unsearchable are his judgments, and his ways past finding out! For who hath known the mind of the Lord? Or who hath been his counselor?” – Romans 11:33-34

While Jesus promises us brotherhood with Him, and knowledge of Him.

Bringing this down to Earth, a while ago I was reading the press release issued by the Clay Mathematics Institute about awarding the first millennium prize to Dr.Grigogiy Perelman for proving the Poincare Conjecture. (If you are not in the loop on this man, you can learn about him here and here . His story is much more fascinating than anything you’ll read here 🙂

Anyway, in the press release I came to this phrase in the description on his resolution: “These shapes are hard to visualize, since they naturally are contained in four-dimensional space, five-dimensional space, and so on, whereas we live in three-dimensional space. Nonetheless, with mathematical training, shapes in higher dimensional spaces can be studied just as well as shapes in dimensions two and three.” Pardon my dullness and pedestrianism , but how can anything exist naturally in five-dimensional space?! So somewhere out there is a world, or space, or non-space, or non-matter or something in n-dimensions? Existing naturally? What I think, maybe, happened is that mathematicians created these nth dimensions, and then imagined shapes existing in them, and then created a mathematical system for describing these imaginary shapes in imagined dimensions, and got so carried away that they forgot that all of this was just in their brilliant, luminary heads. Just saying.

I cannot purport to speak authoritatively on any of this, so I shall just say that the example above is exactly why I find mathematics divine. Was it created? Discovered? By God? By man? It’s a mystery.

To end, I will quote the same press release again: “Perelman deployed his new ideas and methods with great technical mastery and described the results he obtained with elegant brevity. Mathematics has been deeply enriched.”

*Garf*

M.C. Escher's mathematics

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I created a “Postulates” category because I believe that most every person on Earth has a set of postulates that they base their world view on. According to this article, a postulate is a “proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.”

Great definition. Even the most pragmatic and “rational” among us hold several postulates near and dear, although they may be unwilling to acknowledge that at the very core of their rationalized world view lies something that is not proved, is subject to necessary decision, and whose truth is taken for granted. Recall that the term “postulate” in its traditional use was and continues to be used in mathematics and logic (and nothing can be more logical than logic, right?). At the very heart of the geometry that engineers and architects use every day to build real, complex, and sustainable structures lies the belief that, say, “A straight line may be drawn from any given point to any other” (Postulate #1 of Euclidean Geometry).

Here you can read all about the other postulates...


A similar paradox lies at the heart of even the most robust system of understanding and viewing the world to date: the system of scientific inquiry based on reason and observation.

What are the postulates of the scientific-minded thinker?
1. The scientific inquiry approach will work every time.
2. Nature is not random – it works according to discoverable laws and patterns.
3. There are answers to be found.

My father, a hard-core scientist, has openly admitted that behind his ardent, ferocious research and inquiry into the way nature works (he is a biochemist) lies the conviction (ie. stong belief) that there are patterns in nature, there are answers to his questions, and he is using the best tool to get to them. These are beliefs because they have not been proven conclusively. Note: for a postulate to become a law, it has to be proven for all cases, no exceptions. That’s why even in science, most of the “laws” people take for granted are actually termed “hypotheses”.

So there goes the whole “reason vs. faith” confrontation. It’s more like “concealed faith vs. open, self-confessed faith”.

Faith is fundamental to the human experience. So, returning to my initial point, I started a Postulates category to create a special place for entries on my own postulates, and on the postulates of others: the backbone of my system of beliefs, and of yours.

Image credits: Clay Mathematics Institute, http://www.claymath.org/library/historical/euclid/images/euclid_3_31.jpg

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