How to Quantify AI’s Role in Mathematical Modeling with a Contribution Index

AI Contribution Index Construction Idea

The idea is simple: assign different importance weights to each stage of the mathematical modeling process and record the percentage contribution of AI in each stage, then compute an overall score using a weighted model.

For illustration, the stages described in the book Using ChatGPT for Mathematical Modeling are: problem formulation and analysis, data collection, model building, model solving, result verification, and result presentation.

Specific Mathematical Formula

Let the six stages be denoted as \(S_1\) to \(S_6\) with corresponding weights \(w_1\) to \(w_6\) such that \(\sum_{i=1}^6 w_i = 1\). The AI contribution in each stage is expressed as a percentage \(c_i\) (0–100). The AI Contribution Index (ACI) is then calculated by the weighted average:

<code>ACI = \sum_{i=1}^6 w_i \times \frac{c_i}{100}</code>

Example

Assume AI contributes 30% to problem formulation, 50% to data collection, 60% to model building, 80% to model solving, 40% to result verification, and 70% to result presentation. If the weights are set to 0.15, 0.10, 0.20, 0.25, 0.15, and 0.15 respectively, the overall AI contribution score can be computed accordingly.

Through this method we obtain a quantitative indicator that clarifies AI’s role in the modeling process.

Different practitioners may assign different importance to each stage, and the subjective nature of AI involvement can lead to varying scores.

Applications of the AI Contribution Index

The same concept can be applied beyond mathematical modeling, such as evaluating AI’s role in teaching, research assistance, or corporate decision‑making by adjusting weights and contribution percentages for the relevant stages.

For example, in education we could quantify AI’s contribution to instructional design, student Q&A, classroom interaction, and assignment grading, helping educators understand where AI adds the most value.

Values and Philosophical Orientation

Evaluating AI contributions ultimately ties back to our understanding of goals, values, and philosophical orientation, not just technical metrics.

Different people may score the same process differently, and that diversity is acceptable; decision‑makers must clarify their objectives and values first.

When large language models appear as powerful “entities,” they challenge our notions of meaning, uniqueness, and the role of humans, prompting deeper reflection on quality of life and existence.

In this era, AI is more than a tool—it drives profound exploration of self, society, and existence, urging us to reassess the unique role of humanity as we integrate AI into our lives.