Ask AI To Check Its Math

Ask AI to Verify & Execute Math (AI Skill)

Overview

Large Language Models process numbers as textual tokens rather than numeric variables in an ALU (Arithmetic Logic Unit). When performing multi-step multiplication, compound interest calculations, or fractional conversions, models frequently suffer from "attention drift" and output confidently incorrect figures.

This skill teaches the Program-Aided & Chain-of-Thought Math Framework: prompting strategies that force the AI to break math into explicit, verifiable atomic steps or execute pure Python code for 100% computational determinism.

The 2 Paths to Zero-Error AI Math

┌──────────────────────────────────────────────────────────────┐
│                    Reliable Math Pathways                    │
│                                                              │
│  Path A: Program-Aided Language (PAL)                        │
│  Prompt ──► AI writes Python code ──► Code runs ──► Exact Ans│
│                                                              │
│  Path B: Explicit Scratchpad (Chain-of-Thought)              │
│  Prompt ──► Variable Table ──► Formula ──► Step-by-step math │
└──────────────────────────────────────────────────────────────┘

Master Math Prompt Templates

Pattern 1: The Program-Aided Math Directive (Recommended for Complex Math)

Forces the AI to write and execute code rather than guessing token probabilities:

Solve this calculation: [INSERT WORD PROBLEM / DATA]

Instructions:
1. Write a complete, executable Python script to compute the exact answer.
2. Define each variable clearly with its units.
3. Print the intermediate variables and the final formatted total.
4. Output the result from the code execution.

Pattern 2: The Explicit Step-by-Step Scratchpad (For Pure Text Interfaces)

When tool execution is unavailable, use this chain-of-thought constraint:

Calculate the following: [INSERT PROBLEM]

Rules for calculation:
1. State the given variables and their values in a bulleted list.
2. Write down the exact mathematical formula in standard notation.
3. Compute each intermediate step on a separate line. Do NOT combine operations.
4. Double-check your arithmetic in reverse (e.g., verify multiplication using division).
5. State the final answer clearly with units and appropriate rounding.

Real-World Examples

Example 1: Compound Annual Growth Rate (CAGR)

Fragile Prompt (Prone to Guessing)

"Our revenue was $1.2M in 2020 and grew to $3.4M in 2024. What is our CAGR?"

❌ Standard AI output often estimates ~30% without calculating $(3.4 / 1.2)^{1/4} - 1$.

Bulletproof PAL Prompt

User: "Calculate our CAGR from $1.2M (2020) to $3.4M (2024) using a Python calculation block."

# CAGR Formula: (End_Value / Start_Value) ** (1 / n_years) - 1
start_value = 1_200_000
end_value = 3_400_000
years = 2024 - 2020 # 4 years

growth_factor = end_value / start_value
cagr = (growth_factor ** (1 / years)) - 1
cagr_pct = cagr * 100

print(f"Growth Factor: {growth_factor:.4f}")
print(f"Exact CAGR: {cagr_pct:.2f}%")
# Output: Growth Factor: 2.8333, Exact CAGR: 29.73%

Example 2: Prorated Subscription Billing

Scratchpad Calculation Prompt

User Prompt: "A customer upgrades from a $40/month plan to a $100/month plan on day 12 of a 30-day billing cycle. Calculate the exact prorated invoice charge. Use an explicit step-by-step scratchpad."

AI Response:

1. Given Data:

• Old Plan Monthly Rate: $40.00
• New Plan Monthly Rate: $100.00
• Cycle Length: 30 days
• Days remaining in cycle: $30 - 12 = 18$ days

2. Daily Rates:

• Old Daily Rate: $\frac{$40}{30} = $1.3333\dots$ / day
• New Daily Rate: $\frac{$100}{30} = $3.3333\dots$ / day
• Daily Differential: $$3.3333 - $1.3333 = $2.0000$ / day

3. Prorated Charge Calculation:

• Charge = $18 \text{ days} \times $2.00/\text{day} = \mathbf{$36.00}$

4. Reverse Verification:

• Unused credit on old plan: $18 \times $1.3333 = $24.00$
• Cost of new plan for remaining period: $18 \times $3.3333 = $60.00$
• Net invoice addition: $$60.00 - $24.00 = \mathbf{$36.00}$. Confirmed.

Math Safety Heuristics