In a world carved into thousands of languages, adversarial customs, and diverse creeds, there is one silent, immovable constant: mathematics' language. While human societies talk with one another in lovely diversities of idiom, mathematics' underlying reason appears to be a global system, a shared substrate of intellect that pays no heed to borders, past, or ideology. From the pyramids of ancient Egypt to the binary propelling a computer today, the same mathematical facts are discovered and applied independently of what culture does so. Universality implied by that was mathematics not merely human invention, but a secret script upon which the universe is inscribed, a script all cultures, in their own way, learn to read.
The most powerful argument for universality is the spontaneous development of basic mathematical concepts by cultures that were not in communication with one another. The most popular example is geometry. The Egyptians, to reconstruct boundary lines after the yearly Nile flood, created practical survey methods that crystallized into geometric principles. Thousands of miles and centuries distant, the Greeks formalized these very same standards into the framework of Euclidean geometry based upon axioms and proof. But even more surprisingly, in the Americas, the Maya civilization developed an extremely sophisticated comprehension of geometry and astronomy, built pyramids and a calendar of nearly unimaginable precision, entirely independent of Old World presence. They were looking at the same sky, taking the same measurements, and drawing the same conclusions.
Basic arithmetic and the theory of numbers are another common foundation. The need to count inventories, keep moon phases in mind, and enable trade forced every new civilization to develop a system of numbers. The individual symbols fluctuated wildly—Roman numerals, Babylonian cuneiform, Chinese rod numbers, the Inca quipu—but the quantity theory they represented was identical. That two things and two things will always be four things is as true if you're a merchant in Sumer as it is if you're a first-grader. This isn't anything related to culture; this is a statement of bare fact. Different cultures built different "dialects" of mathematics—the base-10 system we use today is much more convenient than the Babylonian base-60 system, though we still use the latter in time and angle measurement—but the laws they represent are universal across all dialects.
This universality is pointing towards a profound philosophical idea: that mathematical truth is discovered, not invented. When a mathematician is bent upon proving a theorem, he is not building a novel truth but uncovering an association that was already there before that. The circumference of the circle divided by the diameter is the value π (pi). It was approximately 3.14159 even before the existence of the human soul that could assign it numerically. It was thus in the circle of the sun, the cross-section of the tree, and the planetary orbit. Past Babylonians and Egyptians approximated it. Archimedes provided a closer approximation as a Greek mathematician. Indian and Chinese mathematicians later worked it out to even more digits. They were all after the same basic property of our world. The constant was waiting to be found. This is why mathematics has such monumental power in modeling natural objects, from the galaxy spiral to tree branching. The universe has a mathematical blueprint.
Mathematics is mankind's most effective instrument of cooperation due to its universality. In science, it is science's lingua franca par excellence. The physics equation that a Japanese researcher created is transparent to another scientist in Brazil. Symbols are common. Mathematical terminology is the basis for unambiguity in the expression of complex objects that cannot be adequately described by voice. International scientific accomplishment rests on this shared terminology of the laws of thermodynamics based on the template of building a satellite. The same engineers from hundreds of countries can work on the International Space Station because they all have access to the same mathematics of structural integrity, orbital dynamics, and propulsion. Their shared language is not English but mathematics.
Nevertheless, to say that mathematics is totally culture-free is an exaggeration. The applications of mathematics and the roles played by various branches in society are very culture-dependent. The ancient Greeks, for instance, adored mathematics largely for its abstract beauty and logical nature. Geometry was a means to philosophical truth. The early Chinese, however, left impressive mathematics, particularly in algebra and the approximation of pi, but were generally more interested in practical issues such as calendar calculation, astronomy, and engineering. Their mathematics is full of land measurement, taxation, and building problems. This shows that while truths in themselves are general, human reason for pursuing them is influenced by cultural needs and interests.
The beauty of mathematics also creates a cultural image. Universal human experience is a beautiful theorem or in symmetric beauty, but metaphors used to describe such beauty are not universal; they are culturally specific. A proof may be "powerful" or "elegant" to a Westerner, but the idea of mathematical harmony will be interpreted differently in Eastern philosophic cultures, where more emphasis is laid on balance and flow. But the underlying appreciation of the logic and the order is the same, nevertheless. It bears witness to the fact that the human mind, however conditioned by culture, is blessed with the coding to notice and appreciate the patterns that lie in the mathematical order of the universe.
The universality of mathematics is more transparent than ever before in the present digital era. The whole computer world rests upon the rock of binary logic—ones and zeros, as simple a notion as it is universal. Boolean algebra, from which this binary tongue arises, can be translated into any form, any letter, any tone, any image. It is mathematics's best argument as a code of the universe. A China-built, California-designed smartphone operates because all of its functioning is governed by mathematical principles that apply everywhere.
Mathematics is a profound and chastening fact. It makes one remember that beneath the thick and variegated tapestry of human existence lies a substratum of shared, objective reality. Our traditions, our art, and our languages can divide us, but the prime number logic, the value of pi, and the Pythagorean theorem unite us. They are our common heritage, discovered and rediscovered by many human brains throughout the ages. Mathematics is the only story all cultures tell in the same way, for it is the story of the universe itself. It is not a man's language in the ordinary sense of the term, but it is the language into which man has developed so that he may hear the universe. In its mathematics, in its constants, we have something precious and something precious by its rarity: an absolute truth that is accessible to all men and unbiased, giving us a glimpse of a reality that lies independent of the oscillating flux of culture and creed.