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“God’s Equation”

“God’s Equation”

Last updated on: April 30, 2026 at 2:56 pm by Dan Peterson

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“God’s Equation” 2026-04-30T14:56:20-06:00 Dan Peterson

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A NASA/NOAA photo of the Nile River and the Nile Delta — the ORIGINAL “delta” — from approximately 512 miles above the surface of the planet. The exceptionally bright glow of Cairo at the southern end of the Delta is plainly visible, as is the long narrow strip along the Mediterranean coast on western side of the Delta that is Alexandria. Moving westward, after the sparsely populated moonscape of the Sinai Peninsula, the very populous nations of Israel and Lebanon and coastal Syria are unmistakable. The Nile Valley and the Delta, taken together, resemble an Egyptian lotus flower and its stem. Far to the east of the Mediterranean, across a vast desert in the upper right corner of the photograph, you can see the populous centers of Mesopotamia (Iraq), that are watered by the Tigris and Euphrates rivers.

A new article of mine appeared early this morning in Meridian Magazine. Whether it does its job or not, my hope for it is that it might help at least a little bit in understanding some of the narratives of the Old Testament: “Why the Fertile Crescent Matters: A Map That Unlocks the Bible’s Geography and History”

And please don’t forget to watch and rewatch and recommend Becoming Brigham. All of its episodes are and will continue to be posted at becomingbrigham.com.

A 1753 portrait of Leonhard Euler (Wikimedia Commons public domain image)

On one of my bedroom bookshelves, I have

a small volume by the science writer David Stipp entitled A Most Elegant Equation: Euler’s Formula and the Beauty of Mathematics (New York: Basic Books, 2017)

Euler’s formula — the pronunciation of his surname is roughly the same as that of the English noun oiler — states that, for any real number x,

$e^{ix}=\cos x+i\sin x,$

When x = π, Euler’s formula can be rewritten as eiπ = −1 or eiπ + 1 = 0, which is then known as “Euler’s identity.”

I know, I know. Don’t worry. And don’t be frightened off. It’s not essential, it’s not even particularly important or relevant, that you or I really understand the equation or its implications. I readily admit that I don’t — which I deeply regret. (In the next life, I hope to devote serious attention to mathematics. Really, I do.) But my point is a different one. It’s not, as such, even really mathematical.

Nearly two and a half centuries after the death of the great Swiss mathematician Leonhard Euler (1707-1783) his formula shows up all over the place — not only in mathematics, but in physics (e.g., quantum theory, the analysis of waves and oscillations and alternating currents), chemistry, and engineering (e.g., signal analysis, communications theory, and control systems). The late great Nobel laureate physicist Richard Feynman, of the California Institute of Technology, called the equation “our jewel” and “the most remarkable formula in mathematics.” (See Richard Feynman. “Chapter 22: Algebra,” in The Feynman Lectures on Physics [1970] 1:10.)

“Euler’s identity,” which is sometimes labeled “God’s equation,” includes just five numbers. But these are five core constants and, thus, it represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity.

Permit me to share a few passages that I marked in just the first few pages of A Most Elegant Equation:

Who can resist lists of all the ten best this or that? Not me. So a few years ago when I ran across a ranking by math experts of the most beautiful theorems, I tuned in. I decided to treat it as a pop quiz: How many of them could I dredge up from my distant undergraduate days as a math major? Alas, I’m afraid I flunked. Still, I was consoled by being able to recall nine of the top 10 (of two dozen). But the No. 1 beauty, an equation known as Euler’s formula, bothered me — I’d seen it before, yet couldn’t remember going over it in school (1).

Stipp points out that Euler is sometimes called “the Mozart of mathematics” (1).

And as the formula started playing through my head like a tune whose provenance maddeningly eluded me, I discovered via Google that a number of authorities on math have considered it not only beautiful, but also one of the most remarkable results in the history of mathematics. (2)

In my limited experience with them, mathematicians (and those who are seriously involved with the use of higher mathematics) are prone to describe certain formulae as “elegant” and “beautiful.” I’m pretty sure that I don’t fully grasp their appreciation — my mastery of the discipline was never great and is, now, much less than it once was — but such sentiments do raise the question of why mathematics should ever be considered a matter of aesthetics. And, yet, it often is.

Also, the formula isn’t just a math version of abstract art. Long after Euler’s era, scientists and engineers realized that the general equation mentioned above (the conceptual parent of eiπ + 1 = 0) is immensely useful for mathematically modeling phenomena, such as the rhythmic flow of alternating current. Thus, Euler’s brilliant pure math discovery is now effectively embedded in electrical devices all around us. I’d call that scary cool, too, if I hadn’t already used up my weekly allotment of that epithet.

The formula’s timelessness also appealed to me. As electrical engineer Paul Nahin nicely put it in a book he wrote about the equation for people who’ve taken college math: “Unlike the physics or chemistry or engineering of today, which will almost surely appear archaic to technicians of the far future, Euler’s formula will still appear, to the arbitrarily advanced mathematicians ten thousand years hence, to be beautiful and stunning and untarnished by time.” (5)

But, for me (and, I know, for others) such comments raise other really important and difficult questions. Why is it that developments in pure mathematics have so often found application, down the line, to previously unforeseen areas in the empirical sciences? Are such developments discoveries, or are they inventions? And, especially if the universe is thought to be fundamentally mindless and ultimately pointless, why is the mathematics that describes it and makes sense of it (as in the case of Euler’s formula)so often regarded by those who understand it,as “beautiful” and “elegant”?

His book, Stipp writes,

isn’t intended to increase quantitative skills or impart a thorough grounding in the math that it covers — its sole mission is to bring home that great mathematics is as provocative, beautiful, and deep as great art or literature (5).

Bertrand Russell (1872-1970), third Earl Russell, the prominent and prolific English philosopher, logician, mathematician, public intellectual, and Nobel laureate in Literature, put it this way in his 1910 collection of philosophical writings Mysticism and Logic and Other Essays:

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.

I find that extremely interesting, and I’m not alone in doing so.

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