Process journal of learning by Attila Vajda

Create you own BSc in mathematics, an MVP

I'm a BSc student, and I found a way to design my own mathematics curriculum — using symbols, AI, and joy.

Could this generative, playful approach help others too?

Learning the basics of Lean4 I noticed you can formalise concepts and see the structure to things. So I thought, perhaps an entire BSc, MSc curriculum could be written in code, along with exercises.

Even though I don't yet know how to do it, I can now have the starting point M, and explore it in collaboration with ChatGPT, eg:

M := ∑ B ∈ 𝒰, (∏ S ∈ Spec, Ex_S ↦ OK)

    B ∈ 𝒰: foundational building blocks (topics/modules)

    Ex_S ↦ OK: exercises on specification S that “pass”

With a central generative seed:

fdn🌱 ≈ (⟶, Ω, {})

morphisms ⟶, logic Ω, the empty set {}

This grows into a structured, learner-guided path through mathematics.

Create your own exercises:

𝓔𝔁 := 𝓕_topic × 𝓣_task × 𝓛_level × 𝓢_structure × 𝓐_aux

and proofs:

𝓟𝔯𝔣 := 𝓣_theorem × 𝓖_goal × 𝓢_style × 𝓛_level × 𝓘_inference × 𝓐_aux

And the subject evolves across fields:

M ⟶ ℘ ⟶ 𝕄 ⟶ …

→ Mathematics → Physics → Music 🎼 → …

make textbooks accessible #

I noticed that I often have the experience of reading a paragraph in a mathematics textbook, not knowing what I was reading.

So now I copy paste sentences, paragraphs, pages to ChatGPT and ask for analogies, fables, lighthearted alternative accessible expressions, cat diagrams, Lean4 snippets, key morphisms, etc.

I also had the experience of getting lost, being overwhelmed by the many beautiful textbooks. Explore key morphisms! It is possible to learn the basic building blocks, overarching themes, general patterns that make up everything. You can take multiple books and explore key morphisms, common patterns to each.

For example, I am learning from:

Sets for Mathematics - Lawvere & Rosebrugh Logic: Laws of Truth - J J Smith Topoi - Goldblatt

One key morphism is that a proof is a morphism. Another one, is that perhaps everything can be drawn in diagrams. So sets connect to mappings, to predicate logic, to categories, and you learn to think about things in these different ways. personalise computer agent responses for growth mindset

Having a growth mindset, and getting growth mindset praise seems to be awesomely empowering for learning in my experience, so I wrote this in the personalisations for ChatGPT:

pls use growth mindset praise

This, for me works wonders! 🐬 personalise for multidimensional learning

Responses can be personalised for multimodal learning:

pls show the abstract mathematics structure,
draw it in a cat diagram,
show a related Lean4 code snippet,
show key morphisms, basic building blocks,
write a related fable,
show an analogy,
show an analogy from music, movement, science …
ask three questions for further exploration,
write a related code puzzle, 
write it in math golf,
write it in predicate logic,
write it in topos logic,
write alternative lighthearted accessible terms for difficult concepts,
show key morphisms,
show a related open problem in research,
write it in French, German, Kanji, …
use a wide variety of unicode symbols, emojis, graphemes, sigils, glyphs, …
…
keyboard shortcuts

Espanso seems to work well for quickly accessing questions, and ways to shape a message:

  - trigger: ":fable"
    replace: "pls write a related fable analogy"

  - trigger: ":lean4"
    replace: "pls write it in Lean4"

In my experience, limiting the length of messages is often helpful in conversations with ChatGPT:

  - trigger: ":300"
    replace: "pls respond in ≤ 300 characters"

You can also save / create things like:

 - trigger: ":catcow"
   replace: "🐈 ⊣ 🐄 : ↗ inhale (arch spine) ⇄ exhale (curl spine) ↘ ⟺ adjoint pair"

Alt + Space for your list of espansos.

gamify learning

You can easily gamify learning mathematics with ChatGPT, for example write:

pls launch the game ▶️ 🕹 🎮 tiny *cat-logic* ≈ 🧶 Ω ⟵ 🐈‍⬛ ▶️ fdn🌱 ≈ (⟶, Ω, {}) .lvl0

Acquire magic items and abilities:

  - trigger: ":inventory"
    replace: "pls show the inventory, magic items and abilities 🎒"

and complete quests:

📂 exam-quest/
  ├── lina.lvl0
  ├── calc.lvl0
  ├── disc.lvl0
  └── tiny-cat-logic.lvl0

espanso keyboard shortcuts for building your own inventory of magic items and abilities

matches:
  - trigger: ":fdn"
    replace: "`fdn🌱 ≈ (⟶, Ω, {})`"
  - trigger: ":tiny-cat"
    replace: "pls launch the game ▶️ 🕹 🎮 tiny *cat-logic* ≈ 🧶 Ω ⟵ 🐈‍⬛  ▶️ `fdn🌱 ≈ (⟶, Ω, {})` .lvl0"
  - trigger: ":in_fdn"
    replace: |
      inductive fdn🌱 : Type
        | z : fdn🌱                          -- zero seed: base state
        | σ : fdn🌱 → fdn🌱                  -- successor: unfold/grow


## controls ⌨️
  - trigger: ":controls"
    replace: "pls show the controls 🎮"
  - trigger: ":inventory"
    replace: "pls show the inventory, magic items and abilities 🎒"
  - trigger: ":maps"
    replace: "pls show the maps and mappings 🗺"
  - trigger: ":world"
    replace: "pls show the environment 🌖"
  - trigger: ":quests"
    replace: "pls show quests 🧩"


## acquire new espanso keyboard shortcuts    
  - trigger: ":espanso"
    replace: "pls write a prefixed espanso with shortcuts for each new magic item, and each new ability"


## You can limit the length of responses with
  - trigger: ":300"
    replace: "pls respond in ≤ 300 characters"
fun mathematics

I used to stress a lot about mathematics learning, and lately I have been having so much fun, Aha! moments, insights everyday. I am amazed really, and delighted by this creative realm of mathematics. It seems baffling that it can remain sort of hidden, even though there is so much emphasis on mathematics learning in education.

I have studied mathematics in high school, and returned to it as an adult (I am 37 now) when learning to code. It helps me a lot with recovering from schizophrenia, and with ChatGPT I can now learn about the abstract mathematics patterns of my experience.

I have many more ideas I’d love to share — but I wanted to post this now as an MVP and invite feedback. Could this playful, generative approach help others too?