Designing a Math Notation System

One of the biggest things we’re working on is designing mathematical notation. We're getting a lot of feedback from users and evolving it literally every day. Let’s talk about why we’re not just using classic LaTeX fonts and design, why we’re not satisfied with the current notation system, and whether it’s even okay to change conventions that have existed for centuries.

Think of math as a language. And like any language, it has a writing system. The notation we use today, pioneered by Descartes, Leibniz and Euler, was designed for paper, not computers. And paper has its own constraints.

Now that we use computers, we deal with different constraints. That’s why programming languages use mathematical notation that looks very different from what we see in math papers.

But computers don’t just limit us—they also let us make notation more readable and intuitive.

We can use color to highlight math, just like how code editors use color schemes. This makes equations easier to read and follow. Variables can inherit their color throughout a document, so it’s much easier to track what’s happening in a complex expression.

For example, in the Poisson bracket:

variables are color-coded, you don’t need to decipher every symbol—your eyes immediately pick up the structure. The colors guide you.

Color coding is used a lot in teaching. When explaining something on a board, lecturers usually switch colors to highlight different parts. On paper, that’s a hassle—you’d need to constantly switch pens. But on a computer, there’s no reason not to use color to make math easier to read.

We’re just used to black-and-white equations because LaTeX has been the standard for so long. But that’s just a habit, not an actual reason to keep things that way.

LaTeX is just a layout system—it doesn’t contain any metadata, so it’s not semantic. But math isn’t just about layout; it has structure, rules, and meaning. If we know what each symbol represents in an equation, math can become more actionable. That’s why we can (and should) attach metadata to mathematical objects.

The simplest example? Giving math objects names. If you're not a cosmologist, you might not recognize what ­

Ω

Λ

­ is. But if you mouse over it, you’ll see its name in a tooltip. At the very least, you can google the name and understand what it means.

But eventually, we can add more data to each object and expression. Imagine being able to click over a function and instantly see its definition, properties, graph, or links to related theorems. Or getting a quick breakdown of what an operator does just by clicking on it. Instead of flipping through textbooks or searching online, all the context would be built right into the notation itself.

Math could be more than just symbols on a screen—it could be interactive, explorable, and self-explanatory.

Variables and constants don’t have to look the same. For instance, a variable ­

y

­ can be visually different from a constant like ­

k

­, and variable ­

x

­ can be distinct from constant ­

x

1

­, which represents evaluation at a specific point.

Consider the equation:

With shape-coded notation, you can instantly recognize that ­

E

­ and ­

m

­ are variables, while ­

c

­ is a constant. This improves clarity without changing the underlying mathematics—it just makes it easier to read and understand.

We can also use different shapes, line styles, or other visual cues to distinguish mathematical objects. These enhancements don’t alter the meaning of equations; they just make them more structured and intuitive. Complex expressions become easier to parse, reducing the cognitive load and making math more approachable.

Math symbols and letters need to look different from regular text. For example, the plus sign in math is usually bigger than the one in text (text: +, math: ­

+

­). Math fonts also need to be simpler and more modern, which is why we decided to go with a sans-serif style instead of the traditional serif fonts (serif fonts have decorative lines, while sans-serif fonts are cleaner).

Mathematicians use a ton of different symbols to distinguish between objects, operations, and concepts. That’s why there’s a need for many variations of the same symbol. For example, here are a few different versions of L: ­

L

­ ­

𝕃

­ ­

ℒ

­.

So, we decided to make our own font that gives scientists more ways to express things clearly. We're still working on it, and there's a lot to do, but the goal is to improve readability while keeping the style modern and intuitive.

So what we can do with font? We can create different styles of the same letters to help distinguish between different objects. For example, ­

ℇ

­ (Euler’s number) should look different from any other constant ­

e

­ in an equation.

This is something we haven’t implemented yet, but math can be interactive. Imagine clicking on a function to expand or substitute expressions, dragging and dropping elements within an equation, or adjusting parameters dynamically and seeing the results update in real time.

Equations don’t have to be static symbols on a screen—they can be something you interact with. Expand or collapse parts of an equation to focus on what matters. Break down long expressions step by step. Instead of manually rewriting things, make small changes and instantly see the outcome.

You’ll be able to change the color scheme, adjust symbol styles, or even define your own notation. But what if you wanted to create an entirely new notation system? Take Feynman’s famous trigonometry:

Some physicists and mathematicians develop their own shorthand to make equations more intuitive for their work. What if different users could apply their own notation styles without breaking compatibility with standard math? Computers let us adapt math notation to different ways of thinking without losing clarity or structure.

All of this—color, metadata, fonts, and symbols—is about making mathematical notation more readable, more intuitive, and more expressive. Math has been written the same way for centuries, but now that we’re working with computers instead of paper, we don’t have to be stuck with the same old constraints.

We’re not changing the math itself—just how we interact with it. Better visual distinctions, structured metadata, and customizable styles don’t replace the notation we already know; they enhance it. They make it easier to read, easier to write, and easier to understand.

If you have any ideas or needs: please shoot us a message!

Anton Gladkoborodov
CEO of Corca Research