Albert Einstein once said, "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science." Propose your own original theory to explain one of the 16 mysteries below. Your theory does not need to be testable or even probable; however, it should provide some laws, principles, and/or causes to explain the facts, phenomena, or existence of one of these mysteries. You can make your theory artistic, scientific, conspiracy-driven, quantum, fanciful, or otherwise ingenious—but be sure it is your own and gives us an impression of how you think about the world.] —Inspired by Akash Goel, a graduate of Saint Bede Academy, Peru, IL (2003–2004) The mystery out of the 16 that I picked: Numbers

*(Mathematicians are famous for being super creative in naming theories. I am following in their footsteps by using the obvious name - mine.)*

**Introduction:**

We use numbers to explain so many mysteries in our world from Fibonacci numbers accounting for nature’s patterns to statistical analysis that cracks the myth of the Bermuda Triangle, yet the mystery of numbers still remains an open-ended question.

What are numbers? Where did they come from? Do they even matter?

**Proof**:

According to the Fundamental Principle of Arithmetic, all real integers greater than 1 are either prime or can be written as the product of prime numbers. In other words, all numbers other than 0 and 1 can be traced back to prime numbers. Prime factorization tells us how a number is made up of prime numbers, so if we understand prime numbers and prime factorization, then in turn, we can understand numbers. However, prime factorization remains a mystery since there is no efficient way to factor a number that is the product of large primes (e.g. the number 180690037441, whose only factors are prime numbers 180811 and 999331).

I have found a unique and relatively simple equation for representing the series of ALL prime numbers, as explained below in the Wang Corollary. This oversteps the problem of prime factorization, because we can use that common component of representing a prime number as I have found to debrief a number, instead of trying to determine which primes constitute that number and using those primes to then debrief that number.

Wang Corollary: The series of all prime numbers can be represented with the following equation:

1NΦ-1, 2NΦ-2, 3NΦ-3, , 4NΦ-4, , ... xNΦ-x

where x = 1, 2, 3, 4, 5, ...

and N and Φ are both constants, where 1<N<Φ,

We know from the Euclidean Theorem that there are infinitely many primes. In 2013, Thomas Zhang from the University of New Hampshire proved the conjecture that there are infinitely many consecutive prime numbers that differ by no more than 70 million. This narrows our list down drastically, since we now can prove that N < 70,000,000. However, there is no cap on Φ. What, then, is Φ?

Φ is a constant, but that doesn’t mean it is a number constant. No, it is not a “universal constant” of some sort, either. In fact, Φ is the multiversal constant.

Einstein’s theory of relativity and idea of space-time dictate that there is an infinite amount of space out there. However, since there are a finite number of combinations of particles, there must be the same combination of particles that constitute a replica of our universe in space. In fact, there should be infinitely many universes in space that are exactly like ours, and infinitely many that are unlike ours. These universes could be worlds apart in their characteristics, but they are all shaped by the same mathematical structure defined by Φ.

Max Tegmark, who proposed the idea of mathematical structures defining the universe, explains a mathematical structure as “something that you can describe in a way that's completely independent of human baggage." The “human baggage” part comes from humans’ numerical interpretation of mathematics. In other universes that make up our multiverse, the same mathematical structure exists based on the constant Φ but without numbers. Numbers are only a small sub-branch to the overall understanding of Φ because all mathematical structures based on primes can be represented through the Φ constant. However, Φ is multiversal because it still rules in universes without humans...or numbers.

**Final Proposal**:

Numbers are an invention of the human mind, a way for humans to understand and interpret our universe in the realm of multiverses. Without humans, there are no numbers, but there is still Φ.

***Disclaimer: I recognize and understand that this theory does not meet the rigor of a full mathematical proof, but expanding that skill and exploring this topic more deeply is something I would like to do at UChicago.

Lucy Wang

University of Chicago

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