Curiosity
\[Q_{n+1}=F(Q_n,A_n,O_n,I_n,R_n)\]
Next question: How does an answer generate the next question?
We just start.
This project began in 2026 through an extended scientific exploration between ChatGPT 5.6 Sol and Karl Zhao, Ph.D., a scientist. Conversations moved freely among galaxies, biodiversity, chemistry, biology, AI, philosophy, investment, and ordinary life. A recurring question emerged: Can mathematics help us see variables, relationships, change, uncertainty, and common structures hidden behind very different concepts?
These first entries are seeds, not final answers. Future contributors are invited to challenge them, replace them, make them more rigorous, make them simpler, and add entirely new pathways.
Here is the beginning. What can you add?
Founding principles
No entry is final. Keep version history visible.
Protect the question, not the proposal. Explore freely; verify strictly.
Keep the residual. \(\text{Concept}=M+R\). Say what the model does not capture.
Do not confuse common mathematics with common mechanisms.
Every answer can generate another question. \(Q_n\to A_n\to Q_{n+1}\to\cdots\)
Open to everyone. Expertise is essential for testing; it is not a prerequisite for curiosity.
Dictionary
These formulas are exploratory thinking models, not established scientific laws.
Learning
\[K_{n+1}=F(K_n,O_{n+1},E_n)+R\]
Next question: How should knowledge change when new evidence contradicts it?
Understanding
\[U=F(\{X_i\},\{R_{ij}\},C)+R\]
Next question: When does knowing more components fail to improve understanding?
Creativity
\[\{K_i\}\xrightarrow{\mathcal A}H_{\rm new}\xrightarrow{V}\{\rm revise,reject,retain\}\]
Next question: Can useful distant association be characterized without destroying openness?
Observation
\[O=F(X_{\rm physical},S_{\rm sensor},P_{\rm processing},C)+R_{\rm obs}\]
Next question: Which parts of a pattern come from reality and which from observation?
Evidence
\[\{H_i\}+D\longrightarrow\{S(H_i\mid D)\}\]
Next question: Which observation best discriminates among explanations?
Hypothesis
\[Q+D_0\xrightarrow{\rm imagination}H\xrightarrow{\rm prediction}\widehat D\]
Next question: What result would make us abandon the hypothesis?
Diversity
\[\mathcal D_t=F(X_0,\mathcal I,\mathcal E,H,t)+R\]
Next question: Which parts of diversity are path-dependent?
Evolution
\[X_{n+1}=F(X_n,H_n,E_n,\mathcal I_n)+R\]
Next question: How does history reshape possible futures?
Collaboration
\[C_{12}(t)=F(C_1,C_2,K_{\rm shared},L_{\rm shared},H_{12})+R\]
Next question: When does shared context improve discovery or amplify error?
Decision
\[D=F(G,I,\Omega,C,\mathrm{Risk},t)+R\]
Next question: Which missing variable is most likely to change the decision?
Trust
\[T_{n+1}=F(T_n,E_{n+1},H_n,C)+R\]
Next question: How should trust respond to error, uncertainty, correction, and deception?
Entry architecture
TERM ├─ Plain-language meaning ├─ Status: established / literature-supported / educational / exploratory ├─ Variables and states: X ├─ Relationships: Rᵢⱼ ├─ Dynamics: F ├─ Time / history: t, H ├─ Boundary conditions: B ├─ Observables: O ├─ Mathematical model(s): M₁, M₂, … ├─ Residual / limitations: R ├─ Evidence / references └─ Questions generated: Qₙ₊₁
Contribute
Propose a term, improve or challenge a formula, add evidence, identify a limitation, translate an entry, or create a child-friendly explanation. Preserve informative disagreement and clearly distinguish established mathematics from exploratory models.
Don't copy our pathway. Build yours.
Open by design
Proposed content license: CC BY 4.0. Proposed code license: MIT. Confirm the final licensing choice before public launch.
Founding note: initiated through a Human–AI collaboration between ChatGPT 5.6 Sol (OpenAI) and Karl Zhao, Ph.D. Mention of OpenAI identifies the AI system used; it does not imply sponsorship or endorsement by OpenAI.