Finding Security and Beauty in Number Theory

Do you remember what prime numbers are? 2, 3, 5… numbers that are not divisible by anything other than themselves and 1. You might have memorized them up to 100, 500, or even 1000. Perhaps you have struggled to find any clear pattern. You are not alone in this.

The distribution of prime numbers, or how far apart one is from another, is famously unpredictable. Mathematicians have spent centuries studying them. Sometimes for practical use, but often for the challenge of simply understanding how they behave.

In our class, we might do prime factorization together. That means breaking down a number into its most basic building blocks, or its prime components. For example, 60 becomes 2 × 2 × 3 × 5. Every whole number greater than 1 is either a prime itself or can be expressed as a unique product of primes.

This might seem obvious now, but it is something that had to be discovered and proved. That simple truth is still taught at the university level. Just as DNA now feels fundamental to life, its structure was once completely unknown. The same is true with numbers. What feels intuitive in hindsight took centuries to uncover.

Prime factorization is easy when the number is small. But when we scale up, the problem shifts. If I give you a 617-digit number, how do you know whether it is prime? And if it is not, which primes were multiplied to create it?

Imagine a Rice Krispie bar. You can easily take a bowl of rice crisps and marshmallow and press it into a single block. That is like multiplying two prime numbers. But try taking that bar apart again, crisp by crisp. It becomes incredibly difficult. Factoring a massive number into its original primes is just as messy.

This idea underpins encryption. When you log into a password manager or send secure information online, the system relies on a kind of mathematical one-way street. It is easy to compute in one direction, but incredibly hard to reverse. That asymmetry is what keeps your data safe.

There is something quietly beautiful about this structure. A system that allows one path to be clean and fast, while making the reverse path nearly impossible. It is not only a mathematical principle. It is a design philosophy. You can see it in the flow of transistors in everyday electronics, in architecture that hides structural complexity within open space, or in interfaces that feel intuitive while running on deep and layered systems.

The beauty in applications that use asymmetrical features lies in the thoughtful alignment of intricate design and seamless user experience. This is the design philosophy I envision for learning design as well. By turning science-backed research and real-life-tested strategies into learning experiences shaped with care, we thoughtfully balance rigour and creativity, tuned to how each student learns best.

Movie Reference

The Man Who Knew Infinity (2015), directed by Matt Brown. Based on the biography by Robert Kanigel.