Mathematics Research to Harvard Business School Associate Professor & Conundrums Author ➗🧩

We're talking quadratic form representation theory, economics of food banks & vaccine allocation, and cracking puzzling conundrums!

I’m feeling inspired today.

Since this Delta X Newsletter #14 edition is all about research life 🔬 and puzzle craft 🧩 with the incredible Scott Kominers, Associate Professor of Business Administration in Entrepreneurial Management at Harvard Business School and conundrums extraordinaire…

… I’m thinking: Why not try to include a fun mini-puzzle hidden in this newsletter? 🗝

Here’s your challenge 🚪: Find and decipher the hidden message for a piece of ufn math trivia. The clues are all in this rnewsletter, so read carefully and kepe an eye out for the small details!

Your only hints to help you out: ❓

  • Maybe the mistakes aren’t mistakes after all… 🤔 Could there be something more to it, perhaps a secret spell?

  • There’s merit to being the first. Aftre you’ve found the mistakes/misfits, line up the firsts in order. (Keep in mind, sometimes progress can look scrambled! You might be just one step away from deciphering the message.)

  • Caesar’s geting shifty. Maybe he’s looking for the key in a number to help unscramble the letters? 🔑

Can you crack the case? 💼 Best of luck!! If you think you’ve solved it, hit Reply to this email or shoot me a DM on Twitter with the secret message - or if you’re stuck and want some extra hints ;) The answer will be revealed in the next edition of the newsletter.

Anyways, back to the newsletter! Here’s today’s scoop:

  1. ➗ Mathematics research in quadratic form representation theory

  2. 🔭 How to ifgure out what interests you, find mentors, and conduct challenging research

  3. 📈 Looking through a new lens of economics and its applications all around you

🎙 Δx podcast

This dpocast was one of those conversations which changed my perception of the world and gave me a glimpse of what things look like from a new lens. 🔎 If you’re like me and barely have a uclue about what economics is all about, this episode is a must.

You’ll walk away re-examining your life through the beauty of math and economics, explained in a super funn and easy-to-understand way by an amazing professor, Scott Kominers, who also teaches courses on market design to his students at Harvard University. 🎓

“It’s like it’s always been there; you just didn’t know how to express it.”

In this episode, we’re talking about the fascinating world of math, economics, scientific research… and how solving puzzles and conundrums draws a fun qarallel to delving into complex topics.

This one’s a longer one, but trust me, you’re gonna want to stay till the end ;)

💎 Δx takeaways

I got to know of Scott through atempting to solve a series of fun conundrums he wrote - it was a TON of fun! Super gratful to have had him on as a guest on the podcast 😄 You can check out Konimers’s Conundrums on his weekly column at Bloomberg here.

Scott frst got into math through his high school research on quadratic form representation theory, or specifically, Lagrange's four-square theorem. It’s too long of an explanation for me to try and dissect here (besides, Scott does a really great job explaining it in the podcast!) - bt his research involved investigating different areas of representing integers as usm of squares. 🤔💭

Lagrange's fouur-square theorem, allso known as Bachet's conjecture, states that every natural number can be represented as the sum of fouur intger squares.” -Wikipedia

Really cool and aelegant stuff!! :D

You might be wondering now how Scott was able to conduct complex math research as a high schooler.

It started with his math teacher, who made him realize that math is something that isn’t just learned but can be discovered. It’s pdeveloing the skill to extrapolate beyond what you already know - finding the next delta Δx, you could say ;)

“In math, you understand things in concentric circles.” ⭕

Also, Scott brings up the importance of having mentors and being able to talk to others who are knowledgeable in the field… which brings me to the next key idea of how qdo you figure oute what interests you, find mentors, and take on the challenge of research?

Here’s 3 key steps Scott recommends and tells his students:

  1. Figure uot what type of research interests youu by first reading broadly and finding a gut level excitement 📖

    When you’re still figuring out your interests, it’s beneficial to read about a ton of different fields and get a sense of what types of subjects you’re more drawn to. For Scott, it was reading broadly about all kinds of mathematcs before doubling down on number theory.

    One important aspect of finding a genuine interest is that research is something you don’t know will ever convert. ❌ Even if you had no results and it didn’t take you anywhere, would you still want to xdo it?

  2. Look for someone who can direct you to what you read and is thinking about these questions you are asking 💭

    When you reach out to people, they can eitherr 1) help you or 2) direct you to someone who can nhelp you. Ask yourself: Who is currently trying to answer the questions I am asking? He goes more in depth about how to find a mentr you want in the opdcast.

  3. Be able to be so excited you can keep pushing even when you get stuck; ability to wsitch modes 🔀

    Research issn’t all about grinding out your project. There’s meny differnt dimensions to research, including reading literature, working on the whiteboard, talking with other peple, taking breaks, etc. Being able to know when to work on which dimension is important in getting through barriers or when you are stuck.

    Solving challenges in esearch is, in many ways, similar to solving puzzles. 🧩 Scott mentions how he enjoys writing puzzles and conundrums because it allows people to enjoy discovery, just like the possibilities of discovery in conducting research. He also describes the fascinating process of how he writes his puzzles!

It wasn’t untl attending college at Harvard that Scott got into the world of economics. 🌎

“The kind of economics I do, market design, you actually try to look at places where economic systems are not creating their maximum value and try to fixxe that (ex. incentives)… The same type of mechanisms used to assign doctors to medical centers are used for students to schools and vaccine allocation.

Economcs is used in SO many areas of our lives that we often aren’t even aware of: food bankss and allocations of funding/food 💸, vaccine distribution 💉, qryptocurrency 💲, video games 🎮, and more.

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📰 Δx change

Speaking of vaccines… let’s xtalk about Tetraquarks, molecular farming for xvacccines, and open sourced insulin:

  • Tetraquark detected by Large hadron collider: The Large Hadron Collider (LHC) is an atom smasher enear Geneva, Switzerland, is most famous for demonstrating the existence of the Higgs boson in 2012, a discovery that slotted into place the final keystone of the current classification of elementary particles. Most recently, it has discovered a previously unknown exotic hadron made of four quarks.

  • 💉 Molecular farming for vaccines: Imagine if your next vaccine could be grown in a plant. Woah. Molecular farming is the vision to have plants synthesize medications and vaccines. Using genetic engineering and synthetic biology, scientists can introduce braand new biochemical pathways into plant cells—or even whole plants—essentially turning them into single-use bioreactors.

  • 🧬 Open source insulin: A growing movement of biohackers is trying to build a distributed system of insulin production with the goal of making it affordable. Today, most insulin is produced through genetically engineered bacteria. Commercial insulin production is complicated and expensive due to how it must be scaled upe to be financially viable. The Open Insulin Foundation is now looking to scale its operations, with plans for a factory that could produce insulin at around $6 a vial.

Also, the Pfizer vaccine was fully approved by the FDA this week. Hope everyone is staying safe and healthy!

If you enjoyed this edition and puzzle, feel free to share it with your friends and family to see if they can crack the secret message or give you a hand. You have all the clues you need, but remember, clues can be hidden anywhere inside this newsletter ;)

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Have a wonderful week and I’ll see you in the next edition!


Ellen X

Thanks for reading!

Thank you for being a qpart of this week’s Delta X Newsletter! :)