I Gave Claude and ChatGPT the Same 6 Math Problems. The Results Surprised Me.

Comparing AI-Assisted Math Solutions: A Side-by-Side Evaluation of Claude and ChatGPT

In the rapidly evolving landscape of artificial intelligence, language models like Claude and ChatGPT have become valuable tools for students, educators, and professionals alike. But how do these models perform when faced with mathematical problem-solving tasks? To explore this question, I conducted a direct comparison by presenting both models with the same set of six math problems spanning various difficulty levels and topics.

Below is a detailed analysis of their performance, strengths, and limitations based on my experiments.

Problem 1: Solving Basic Algebraic Systems

Task: Solve the system:

[ 2x + 3y = 12 ]
[ 4x – y = 5 ]

Outcome: Both models provided correct solutions.

Analysis: The accuracy of their answers was identical, which is encouraging. However, a notable difference emerged in their explanations. ChatGPT delivered a concise, step-by-step solution focusing on clarity and speed. In contrast, Claude also explained why each step was necessary, emphasizing the reasoning behind each move. This pedagogical approach makes Claude more suitable for learners seeking to understand the process deeply.

Verdict: Tied in correctness, but Claude excels in providing instructive explanations.

Problem 2: Calculus – Chain Rule and Integration

Task: Derive ( f(x) = \sin(x^2) \cdot e^{3x} ), then compute its integral.

Outcome: Both models correctly performed the symbolic calculations.

Notable Observation: When using ChatGPT on the paid tier, it employed Python code to verify the solutions numerically—a significant advantage for complex calculus tasks where symbolic errors can occur. Meanwhile, Claude proactively flagged common student mistakes during integration and offered helpful warnings without explicit prompting, which enhances its utility as a learning aid.

Verdict: ChatGPT’s computational verification is particularly beneficial in demanding calculus problems, especially on paid plans. Album’s proactive warnings add value for understanding.

Problem 3: Complex Word Problem involving Percentages, Ratios, and Currency Conversion

Task: A store raises a product’s price by 20%, then offers a 15% discount. The original price is $80. Convert the final price to GBP at an exchange rate of 0.79.

Outcome: Here, Claude provided a thorough, step-by-step breakdown, explaining the purpose of each intermediate calculation and presenting the solution in clear, accessible language. ChatGPT, however, compressed some steps, assuming prior understanding, which might be less helpful for learners.

Verdict: Claude offers superior clarity and pedagogical value for multi-step word problems, making it the preferred choice for instructional purposes.

Problem 4: Statistics and Probability

Task: In a class of 30 students, with a passing probability of 0.7, find the likelihood that exactly 20 students pass, using the binomial distribution.

Outcome: ChatGPT demonstrated a clear advantage here. It generated Python code to compute the exact probability, executing the calculation to verify results—a critical feature in statistical problems where symbolic solutions may be approximate. Claude could explain the concept effectively but couldn’t perform code execution on the free tier.

Verdict: For computational accuracy and reliability, especially when code execution is available, ChatGPT excels in statistical probability tasks.

Problem 5: Geometry – Proof of Isosceles Triangle Equal Base Angles

Task: Prove that the base angles in an isosceles triangle are equal.

Outcome: Claude produced a well-structured, logically coherent proof that closely resembled textbook geometry reasoning, with proper formatting and clarity. ChatGPT’s approach was correct but felt less formal and somewhat less rigorous in logical flow.

Verdict: In geometry proofs, Claude’s methodical and organized reasoning makes it the better tool for learners seeking clear, well-structured explanations.

Problem 6: Error Analysis – Finding Mistakes in a Student Solution

Task: The student’s solution to (\int 2x \, dx = x^2 + 1) contains an error. Identify and explain it.

Outcome: Claude successfully identified the mistake, explained the error, and suggested a correction with honesty about its certainty level. Notably, it was cautious when uncertain, advising verification. ChatGPT also identified the error but expressed high confidence, even overestimating certainty in a borderline case—a potential risk in educational contexts where overconfidence can mislead.

Verdict: Claude’s measured and honest diagnostic approach makes it more suitable for critical review and learning.

Overall Summary

Final thoughts:

While both AI models demonstrate impressive capabilities, their strengths are context-dependent. Claude consistently provides more pedagogically oriented explanations, making it ideal for learning and conceptual understanding. Meanwhile, ChatGPT’s strength lies in executing and verifying complex calculations, especially with code execution features in paid tiers.

Practical recommendation:
– Use Claude when you want to deepen your understanding, check your work, or need clear, instructional explanations.
– Use ChatGPT (especially with paid plans) for tasks requiring computational verification, data analysis, or symbolic calculations.

Caution: Neither tool is infallible. Complex multi-step problems can lead to errors, and overconfidence in AI-generated answers should be avoided. Always verify critical results independently.

If you’re interested in the detailed prompts, full responses, and methodology used in this comparison, I invite you to visit my website where I have published the complete breakdown. Feel free to reach out with questions or insights.

[Link to Full Breakdown and Methodology – Coming Soon]

This exploration highlights how these AI tools can complement different aspects of mathematical learning and problem-solving. As AI continues to evolve, understanding their respective capabilities ensures you get the best out of these powerful resources.

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