Dr. Rachel Traylor

Take the time to study some aspect of your field that you struggle with.


Dr. Rachel Traylor is the founder and lead researcher at The Math Citadel, an independent research firm in mathematics. She has worked as a research scientist for Dell EMC studying data protection, drive and system failure, and anomaly detection. She has 6 pending patents based on her work there. She also spent time at Lockheed Martin Aeronautics as a software engineer and DBA. Her academic career includes 5 years of teaching at the University of Texas at Arlington and Georgia Tech. She was responsible for designing two courses at UTA – Statistical Inference and Multivariate Analysis. She earned her PhD in Mathematics from the University of Texas at Arlington in 2016, with a dissertation focused in stochastic analysis and server reliability. She holds an MS Statistics and BS Applied Mathematics from Georgia Tech. Her research interests span all of mathematics, but are primarily focused on probability theory, queuing theory, and reliability. She is a competitive long-distance swimmer, surfs once in a while, and always looks forward to bacon for any meal of the day.

Where did the idea for The Math Citadel come from?

The Math Citadel was initially born to bring open-access mathematics research to business in an accessible way. Many times new research can take years to be applied somewhere because it gets shut away in journals only members of that field tend to read, and in formats and language that are unfriendly to those who aren’t full experts in very narrow disciplines. We began by publishing our own research on our site, but accompanying it with videos to give examples and overviews of the work. We have since expanded our mission to bring pure mathematics back to industry in a variety of ways. Many companies cannot afford an in-house research division, or to sponsor universities with large overhead costs. We reduce the cost of exploratory research by offering research partnerships to companies of all sizes at a fraction of the cost of traditional funding methods in exchange for full patent rights. We also offer tutorials and courses on the mathematics that comprises the foundation of many industries and technologies.

What does your typical day look like and how do you make it productive?

My typical day starts with exercise. I swim on a masters team and remain competitive. Exercise helps me focus and ensures that at the end of the day, I always feel productive. I catch up on emails over breakfast at home, and give myself half an hour to complete some set of house chores so those duties don’t pile up at the end of the week. I then check my calendar and fill in scheduled blocks for the necessary tasks. Those necessary tasks vary from day to day, but typically involve working on a new paper or article, outlining or designing a video, working on a proof for a new theorem, and studying new topics in mathematics to remain current.

How do you bring ideas to life?

The old-fashioned way – whiteboards and paper and a lot of frustration. New ideas come from anywhere and at any time, as most creative people will tell you. To bring them to life requires slow, methodical, uninterrupted time to think. When I’m stuck, I have to know when to take a walk to clear my head, or seek out my research partner to run the issue by him to see if a fresh set of eyeballs can shake my mind loose.

What’s one trend that excites you?

I like how many different platforms exist to produce and disseminate creative content and research. We do all our graphic design in-house thanks to an app called Canva. The intro animations to all our videos are created from time-lapse drawings we do by hand in Adobe Draw. The trend towards affordable technology to produce and share great content with relative ease and a small learning curve has allowed so many small businesses to grow their reach further and faster than even 20 years ago.

What is one habit of yours that makes you more productive as an entrepreneur?

I’m never idle. Even while I work on a paper, I’m outlining all the possible directions for future research. I never stop looking forward. Well, really not just forward, but everywhere. Finding new applications for my research involves looking laterally, so I have to always be mentally available to see something new.

What advice would you give your younger self?

Don’t scoff at the business classes. If your university offers seminars on the ins and outs of business administration, take the couple hours and attend them. Accept the free pizza as you learn what an LLC is, or how to list revenue streams, or how to communicate with people outside your field. Even if you don’t think you’d run your own business, knowing how businesspeople think and work will help you in your career anyway.

Tell us something that’s true that almost nobody agrees with you on?

I believe artificial intelligence and machine learning have become buzzwords, and that our thinking on these topics is on the wrong trajectory. Underneath both of these subjects is a healthy amount of provable mathematical rigor, but that rigor carefully defines limitations and assumptions that must be met when using these techniques. Most of the time, data doesn’t meet these assumptions, and practitioners brush it off, ignore it, or fudge some kind of Central Limit Theorem/convergence argument to push a solution through. That solution may work for a time, but it’s uninterpretable, unexplainable, and is highly dependent on the data you feed it. The trajectory of thinking to solve this problem is simply “more data”, “more computing power”, and “continuous incremental improvement”. I think we need to slow down and really examine the foundations of these topics and where they are weak. Right now we built a rickety wooden bridge and are managing to use it to get people across decently. But as we try to flood more people across, the limitations of the material and the shoddy construction will cause the bridge to collapse. It’s worth the time to study the problem and carefully construct a stone bridge that will last lifetimes. That’s mathematics – the slower construction that outlasts fads. We’ve lost that in turning AI/ML into buzzwords.

As an entrepreneur, what is the one thing you do over and over and recommend everyone else do?

Take the time to study some aspect of your field that you struggle with. For me, it was abstract algebra. I’m a probability theorist, and it’s easy to get caught up in only reading books and papers in measure theory and probability theory because that’s what’s comfortable. I forced myself to revisit abstract algebra after I saw a book in a bookstore on algebraic statistics. This is a quite new topic in mathematics that looks at probability theory through a totally different lens. The book was difficult for me to read, so I made myself study algebra again. Along the way, I learned about coding theory in a different way than my studies in information theory presented it. That led to me beginning a series into the mathematics of erasure coding for data protection, which filled in many mental gaps I had about the technology and allowed me to see a plethora of applications of my research to data protection. In short, force yourself to tackle those parts of your field you struggled with.

What is one strategy that has helped you grow your business? Please explain how.

Twitter engagements. Growing a network organically and honestly, by engaging with real people in the technology and storage industry has provided mutual benefit. I learn about their field, their problems, their priorities because I talk to them about it via Twitter. They, in turn, learn what a mathematician can do for industry, and why our more abstract approach to problems is desirable. The most important thing to me with networking is the mutual benefit. Speaking with engineers and computer scientists inspires my research, which in turn provides novel applications for them. My goal is to create a symbiotic relationship between mathematicians and engineers honestly, not through marketing.

What is one failure you had as an entrepreneur, and how did you overcome it?

I initially targeted the wrong type of funding model. I thought all companies in Silicon Valley got started the same way. The failed sets of conversations helped me retool my networking approach to be more organic rather than aiming for more traditional business funding methods.

What is one business idea that you’re willing to give away to our readers?

An app that allows me to text mathematics like typesetting LaTeX. There have to be more people like me who want to have a conversation about a theorem, homework, a proof, or mathematics in general over text. Or maybe I’m the only one…

What is the best $100 you recently spent? What and why?

An Audioflood underwater iPod shuffle. I have been swimming competitively for almost 20 years now, and that little device has been a life-changer. I can easily find I have been swimming constantly for over an hour and not have noticed. Bonus: I can also still have music when I run in the rain. Pity the iPod shuffle was discontinued. I don’t think these are made anymore.

What is one piece of software or a web service that helps you be productive? How do you use it?

The Grapher utility on a Mac is one of the most under-appreciated features Apple offers. I use it all the time to explore ideas and get a feeling for how different parameters in equations interact. It can graph in multiple coordinate systems, in 3D, do piecewise graphs, take derivatives, and many more surprising things. A simple utility that allows me to graph and play with some of the concepts I’m trying to study can yield entire theorems…or reveal ideas to be bad ones.

What is the one book that you recommend our community should read and why?

Quiet”, by Susan Cain. It’s a stunning book about the power of true introverts – how they think, how they work, how they contribute. It also discusses why we see so few of them as executives and founders, and why that should change. I learned quite a bit about myself – that it’s acceptable to need to withdraw and work alone for days, for example.

What is your favorite quote?

“Contradictions do not exist. Whenever you think that you are facing a contradiction, check your premises. You will find that one of them is wrong.” Ayn Rand, Atlas Shrugged. I believe this is as true in life as it is in mathematics.

Key Learnings:

  • Take the time to study some aspect of your field that you struggle with
  • Don’t scoff at the business classes
  • New ideas come from anywhere and at any time


MathCitadel onTwitter : @Mathpocalypse @MathCitadel

Research partnerships: www.themathcitadel.com/partnerships
LinkedIn: https://www.linkedin.com/in/racheltraylor-ph-d-b800a685/
The Math Citadel on LinkedIn: https://www.linkedin.com/company/18299603/