Mathematics is the language that we have devised to study the laws of nature. The act of measuring, the beginning of all mathematical activities, was recorded as early as 3500 BCE by the Sumerian civilization in Mesopotamia, present-day Iraq. In 2334 BCE, the Akkadian King Sargon conquered the region and continued the Sumerian traditions. During this era, Mesopotamian mathematics evolved from a proto-mathematical stage of metrological numeration systems to the adoption of the sexagesimal place-value number system, and continued to flourish in the Babylonian period. The poetry written during this time, which came in the form of temple hymns, depicts how their cultural practices deeply intertwined with mathematical development. The temple hymn dedicated to Enheduanna, daughter to Sargon and high priestess of the moon god Nanna, and Nisaba, the Sumerian goddess of writing and mathematical calculations, reads:
“True woman, pure as the soapwort, sprout of the holy reed.
She measures the heavens above
and stretches the measuring cord on the earth.”
By the 6th century BC, the Greek polymath Pythagoras became known as the first man to to call himself a philosopher, having coined the word “philosophy” to mean the love of wisdom and mathematics – that which is learned. Having passed by blacksmiths at work one day and heard the sound of their hammers clanging against the anvils, Pythagoras discovered harmonic progressions of the musical scales – that the musical intervals and the pitch of the notes corresponded to the relative lengths of the vibrating strings. He observed that dividing a string by consecutive integers yielded harmonious and pleasing, or consonant, intervals. When two arbitrary musical notes are made to sound together, the resulting sound is usually harsh, or dissonant, to our ears. The combinations making pleasant sounds are obtained when the notes are produced by similar strings whose lengths are in ratios given by the first few natural numbers, such as 1:1 (unison), 1:2 (octave), 2:3 (the fifth), and 3:4 (the fourth).
But, wondered the Pythagoreans, the cult, the brotherhood of Pythagoras, if musical harmony can be expressed by numbers, why not the entire cosmos? For example, the motions of heavens were also extremely regular and subject to a specific order. They thus concluded that the universe owed its characteristics to the nature of numbers. This conclusion led to the concept of a beautiful “harmony of spheres” – the notion that in their regular motions, heavenly bodies also create harmonious music. Even though Pythagoras apparently wrote nothing, the philosopher Porphyry in Life of Pythagoras wrote that “Pythagoras affirmed that the Nine Muses were constituted by the sounds made by the seven planets, the sphere of the fixed stars, and that which is opposed to our earth, called the ‘counter-earth’.”
As the German mathematician Leopold Kronecker said, “God created the natural numbers, all else is the work of man,” a great effort in mathematics goes into discovering the outstanding properties within each natural number, among which the highest fascination goes toward prime numbers. Prime numbers have only two divisors, themselves and 1. What’s fascinating about prime numbers is that there does not seem to be any great degree of order to their distribution. Yet prime numbers are the building blocks of arithmetic. The most famous problem concerning primes is known as Goldbach’s Conjecture, in which the Russian mathematician Christian Goldbach asked the Swiss mathematician Leonard Euler in a letter in 1742 if every even number greater than number 2 can be expressed as the sum of two prime numbers. Neither Euler nor anyone else since then could prove this proposition, though it has been verified for all even numbers up to 2(1017) by computer so far. It has been proven, however, that any odd number greater than number 5 is the sum of three prime numbers. This is called Vinogradov’s Theorem, as it was first proven by the Russian mathematician Ivan Vinogradov in 1937. Additionally, every number is either a prime number or a product of primes.
More than two millennia ago, the Greek mathematician Euclid already proved that prime numbers go on indefinitely. Euclid prime numbers, called the primordial primes, can be generated by multiplying the first several prime numbers together and adding 1. In 1850, the Russian mathematician Pafnuty Chebyshev proved that there is always a prime between the number n and 2n. It is also discovered that the number π can be expressed as a sequence of arithmetic operations of prime numbers. That prime numbers are intimately related to the circumference of a circle is another remarkable observation.
Euler was quoted by the American mathematician George Simmons regarding primes, “Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate.” One thus takes the opportunity to recognize the two different points of view of mathematics: whether we have discovered it, or invented it. In this regard Albert Einstein put it, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably adapted to the objects of reality?” Clearly, Einstein himself believed that mathematics was invented.
Inspired by the primordial numbers, this dress is decorated with the primes of the first ten natural numbers. The number 2 is geometrically represented by a line or one dimension. It is the number to represent the female, the number of opinion and division. The number 2 is associated to this day in many languages with hypocrisy and unreliability, for example, “two-faced” or “double-tongued.”
The number 3 is geometrically represented by a triangle or two dimensions. It represents the male number and is phallic in appearance. It is the first real number, as it has a beginning, middle, and an end, unlike the number 2 which does not have a middle. As the saying goes, “three is a crowd,” the number 3 served as the mark of plurality in numerous ancient languages.
The number 5 is especially associated with the Golden Ratio, which is another very special number 𝜑. From a pentagram, or a five-point star, which contains within it a pentagon, if we are to connect and extend the extremities of this star into another five-point star, which then includes another larger pentagon and the largest pentagon connecting its five extremities, then the proportion of every segment to its next shorter segment is precisely equal to the Golden Ratio.
The number 7 is represented by the seven classical planets, which are associated with the seven metals known since ancient times: gold corresponding to the Sun, quicksilver to Mercury, copper to Venus, silver to the Moon, iron to Mars, tin to Jupiter, and lead to Saturn.
