Co-authored by Kashvi Jhamnani and Rudra Limbachiya 1. What Does It Mean to Find the “Best” Design? Imagine designing a bridge. There is rarely one obvious answer because several things have to be balanced at the same time. The bridge should be strong and safe, but it should also use a reasonable amount of material and ideally have a low environmental impact. Improving one of these factors can sometimes make another one worse. This is where optimisation comes in. In simple te

A world that refused to change For nearly two thousand years, Euclidean geometry was treated as the only possible description of space. Since Euclid's Elements was written around 300 BCE, mathematicians built almost every geometric idea on five simple postulates. Four of these were straightforward. The fifth, known today as the parallel postulate, stood apart. It stated that through a point outside a given line, exactly one parallel line can be drawn. This single postulate wa

Introduction: What Is a Tissue Actually Made Of? Look at a tissue under a microscope and it can seem like a mess, thousands of cells squeezed together with no obvious plan. But that mess has structure. Cells don't sit randomly next to each other. They connect and arrange themselves in patterns that let a tissue grow, hold its shape, and function properly. When those patterns change, it's usually a sign that something else is changing too, like development progressing, or a di

The Architecture of Networks: We live in a world defined by connections. Whether it is the people you follow on social media or the proteins interacting inside your cells, everything is essentially a giant map of dots and lines. Scientists call these maps networks. For a long time, we knew these networks existed, but we really struggled to understand how they were organised. The mess was visible, but we could not easily see the order behind it. If you look closely at any lar

Introduction: A Blueprint for Our Lives Have you ever felt like your life goes through weird, predictable phases? One year you are learning how to talk, the next you are figuring out your identity, and a few decades later, you are hitting new biological milestones. We usually think of this as a messy, random adventure. But what if there was actually a hidden math pattern guiding it all? Mathematicians have been obsessed for ages with Pascal’s Triangle. It is just a simple pyr

Introduction: Can a Structure Build Itself? Imagine having thousands of tiny square tiles laid out on a flat surface. Each tile has coloured edges that determine how it can connect to other tiles. These tiles have no knowledge of the final structure they are meant to form. They simply follow a local rule: whenever two edges with matching colours meet and their connection is strong enough, the tiles stick together. At first, small clusters of tiles form randomly. But as time p