## Would you be willing to risk everything for the slim chance of creating an idea that could change the world?

## I did.

## And this is my story...

I have spent my entire life obsessively acquiring the skills and knowledge to become the ultimate fashion designer. From graduating at Central Saint Martins college, showing at London Fashion Week, to pioneering a Zero-Waste fashion label, my career was pretty much a dream run.

Life in London as a fashion designer was exciting. My work was starting to be recognised and it was time to seriously start thinking about expanding the label. Raise some capital, build a brand, make simpler more wearable clothing, do lots of marketing and press. It sounded like lots of fun. But something felt wrong, the more I grew the label into a business the less time I had to do research, and I had unfinished business.

There were problems I needed to solve, problems that only experts who publish in obscure academic journals know about, but affect us all. The greatest problems are not the obvious ones. It’s the problems which are invisible, the ones that are so deeply entrenched in the system that we cannot even imagine a system without them.

The greatest discoveries require a leap of imagination. No one sees them coming because they are unimaginable at the time. But once someone makes that leap we all see the world in a different way.

While developing zero-waste design I discovered that there were serious limitations in the accuracy of conventional patternmaking. Techniques that used linear measurements to create patterns around the body were limited in accuracy and constantly required the intervention of a skilled patternmaker. Linear measurements caused systemic fitting problems in ready-to-wear clothing sizing systems. 3D scanning algorithms which draft patterns were severely limited in their accuracy. Something was fundamentally wrong with fashion patternmaking.

To solve this problem, I went to a place where fashion designers fear to go…

The mathematics and sciences section of the library. I started to learn advanced mathematics and was able to use mathematical principles to make great advances in zero-waste design. At the time other designers could not understand what I was doing, so it just seemed like magic.

One day I realised that the geometry that fashion patternmaking was based on was the geometry of flat surfaces or Euclidean geometry. Since the 19th century mathematicians understood that curved or “Non-Euclidean” surfaces have completely different geometric properties and rules to flat surfaces. These rules are very different and often counter intuitive if you only know Euclidean geometry. I realised that fashion designers had been using flat Euclidean geometry on curved Non-Euclidean surfaces and these systems were incompatible.

No matter how accurate a patternmaker was, from a mathematical perspective they were going to be inaccurate. Fashion patternmakers were using a mathematical thought process which is was hundreds of years out of date. They only knew Euclidean geometry which is what they learned in school and did not understand Non-Euclidean geometry which is taught in universities. Non-Euclidean geometry could explain all of the systemic fitting problems and geometric inconsistencies in fashion patternmaking techniques!

It is easy to complain about a flaw in a system, but is it hard to come up with an alternative system. Someone would have to build a new “Non-Euclidean” patternmaking system to bypass our current imitations. In that instant I had a glimpse of a possible future and it was beautiful!

I had to make a tough decision: do I keep on designing zero-waste fashion collections or risk it all for the possibility of creating something new? I would have to put my label on hold and spend many years without distraction researching a PhD. Give up my growing reputation and embrace obscurity so that I would no longer fear: failure, making mistakes, embarrassment or tarnishing my existing achievements. To go off the grid from the fashion world in order to force myself to think like a scientist and challenge every assumption in fashion. I would have to give up the life of the fashion designer “Mark Liu” and become “Dr Mark Liu”. If I didn’t do it, no one else would. So I ended up being the only one who could do it. Strategically this was the best thing to do, sacrifice the present to gain in the future. Emotionally I knew it was going to be painful, but I did it anyway...

I spent years researching my PhD on Non-Euclidean patternmaking and pushed myself to the limits. I had to build a patternmaking system with advanced mathematics which was powerful, yet still simple enough for a fashion designer to understand. Discovering the ideas was fine, but the PhD process was so difficult and slow that it almost broke me. By the end I was so tired I could barely remember who I was or why I had started the research in the beginning. But luckily the risk was worth the reward at the end. I had built a new Non-Euclidean patternmaking system and this changed everything.

It is now possible to make garments with greater accuracy than ever before. New inventions such as the drapemeasure allow patternmakers to measure the curvature of a surface which bypassed the limitation of linear measurements. Parts of the fashion patternmaking process can be simplified by teaching the underlying geometry compared to rote learning many different traditional techniques. Writing a patternmaking system based on mathematical principles means it is compatible with modern technology making it possible to build accurate 3D fitting algorithms.

Non-Euclidean patternmaking can improve the efficiency of production, re-evaluate ready to wear sizing systems and help fit people with unconventional body shapes. It paves the way for a new generation of fashion garments and technologies. It can even be used to teach mathematics in school to students to do not engage with traditional mathematics education. I have always believed that a new generation of scientifically literate fashion designers who can talk to scientists and engineers will have a better chance to solve the systemic sustainability problems in the fashion industry and this starts the process. This is a version of the future that I could not have imagined 10 years ago. Now I just need to build it. This blog will reflect on my past and show the future applications of my research.