Hey — here’s a quick write-up of a feature I just shipped and that I’m pretty excited about: the ability to choose different system prompts in Mathify.
I mentioned this briefly in the last video, but now it’s actually usable.
The idea
Up until now, Mathify has had a single default system prompt. That prompt contains a lot of guidelines for the AI model: how to structure animations, avoid overlaps, keep things readable, manage timing, camera framing, and so on. It’s general-purpose and works well for most cases.
But the more I used Mathify, the clearer it became that one prompt isn’t ideal for everything.
Sometimes you don’t want a “general math visualization.”
Sometimes you want something very specific.
So now, instead of just the default prompt, you can pick a style-specific system prompt depending on what you’re trying to visualize.
What kinds of system prompts?
Here are some examples of the kinds of system prompts you can choose from.
Pure mathematics (proof-centric)
Emphasis on structure, symmetry, and invariance. Step-by-step proof ideas, not just visuals.Counter-example / proof debugger
Visualize why a proof step works in one case but fails in another. This one explicitly tries to contrast opposing cases.Minimalist
One object on screen at a time. Slow reveals. Useful for short explanations or very focused visuals.Zero-text (visual only)
No labels, no narration in text. Just motion and transformation.Equation-heavy
Algebraic manipulation, derivations, step-by-step symbolic work. This actually performs noticeably better than the default prompt for this use case.3D-heavy / spatial
Strong camera rules, rotation constraints, and spatial reasoning. Much better defaults for 3D scenes.Pre-school / early intuition
Shapes, colors, slow motion. Extremely simple ideas, focused on intuition only.Lecture / slide style
More serious tone, suitable for university-level explanations.1-Minute-Physics-style
Visual-first, short, punchy explanations. White-background-friendly (I’ll improve that more soon).3Blue1Brown-style
Build intuition first, explain later. Motion is the explanation. No front-loaded equations.Economics / game theory
Domain-specific structure for things like Nash equilibria or pricing games.
Each system prompt encodes its own rules, priorities, and biases. That means you don’t have to restate all of that every time you write a request.
You just say what you want to visualize — the how and style is already baked into the system prompt.
What this looks like in practice
For example:
Visualizing the geometric meaning of a derivative with the default Mathify prompt gives you a very standard, clean result.
Using the counter-example prompt, the same idea becomes a contrast: a case where a proof step works, and another where it breaks. The whole animation is structured around that tension.
With minimalist, you might get a slow reveal of rotational symmetry in a single shape — perfect for a YouTube short.
With zero-text, you can show two shapes transforming differently under the same motion, with no labels at all.
With 3D-heavy, visualizing a plane rotating through 3D shapes produces noticeably better camera behavior than the default prompt.
With equation-heavy, deriving the quadratic formula is cleaner, more structured, and honestly better than what the default prompt produces.
With pre-school intuition, something as simple as “one shape becoming bigger than another” turns into a calm, slow, visually obvious transformation.
With lecture style, something like the law of large numbers becomes closer to an actual slide: diagram + equation + structure.
With 3Blue1Brown-style, the dot product example builds intuition visually first, then explains — motion is the explanation.
With economics, you can visualize how a Nash equilibrium emerges in a simple pricing game, using domain-specific structure.
The important thing is: the character of the output changes, and it changes in the way you’d expect.
What’s coming next
The next feature I’m working on is prompt remixing.
You’ll be able to:
Take an existing system prompt
Modify it
Create your own version
Share it with the community
The idea is that people will converge on prompts that work best for their actual use cases — lectures, shorts, proofs, kids, physics, economics, whatever.
You can already try the current version out now.
Let me know what you think, and I’m genuinely curious to see what kinds of prompts people come up with.
Thanks, and good luck.