How to check an AI-generated math solution
Verify an AI math answer by preserving domain assumptions, auditing reversible steps, substituting into the original problem and checking completeness independently.
Do not judge an AI math solution by how fluent, detailed or confident it sounds. Copy the exact problem and record its domain, assumptions, definitions, units and requested result. Audit each line by asking whether the transformation is equivalent or only produces candidates. Substitute every candidate into the original statement, not merely the final derived equation; then check completeness through a genuinely separate method or independently entered calculator or CAS calculation. Report the first unsupported step and a corrected result. A calculator or CAS verifies only the expression, domain and assumptions it was given, while a formal proof checker verifies only the formal theorem and dependencies it actually checked.
Freeze the exact problem before checking the answer
Transcribe the complete question independently of the proposed solution. Preserve brackets, exponents, radicals, signs, equality or inequality symbols, diagram labels and every stated condition. For a photographed problem, compare the transcription with the image at high zoom because a missing minus sign or exponent changes the task before any reasoning begins. Record whether variables are real, complex, integer or otherwise restricted; note parameter ranges, units, definitions, required precision and whether the task asks for one value, every solution, an estimate or a proof. If the source leaves one of those facts ambiguous, state the interpretations separately or return an inconclusive verdict instead of silently selecting the convenient version.
- Copy the original expression and question without relying on the AI response.
- List the domain, parameter restrictions, units and defined notation.
- State whether an exact answer, approximation, construction or proof is required.
- Mark unreadable or missing information as unresolved before checking any steps.
Classify every transformation as equivalent or one-way
Move line by line and write the condition that makes each transition valid. Adding the same defined quantity to both sides is normally reversible. Dividing by an expression can discard the case where that expression is zero. Multiplying by an expression, squaring both sides or clearing a denominator may create candidates that satisfy the transformed equation but not the original one when the reasoning is read backward. Roots, logarithms, inverse trigonometric functions, absolute values and complex powers bring domain, sign, periodicity or branch conditions. Replacing an exact value with a rounded decimal also changes what can be proved. Locate the first unjustified transition even when later arithmetic is flawless; correcting only the final number hides the actual failure.
Test every candidate against the original statement
Substitute each proposed value into the untouched original equation, inequality, recurrence, constraint or geometric condition. Prefer exact fractions, radicals and symbolic identities before decimal approximations. Check all simultaneous equations, denominator restrictions, endpoints, sign conditions, units and requested ordering. For inequalities, test boundary inclusion and the intervals between critical points rather than one convenient value. A zero residual can support an approximate root only at the declared precision; it does not prove exact equality, and a nonzero residual may reflect either a false candidate or ordinary floating-point error. Candidate checking establishes validity one candidate at a time, but it does not establish that the list is complete.
Recompute independently and inspect the tool's assumptions
Use a route that does not merely repeat the proposed steps: substitute before simplifying, factor instead of applying a memorized formula, derive a bound, inspect a graph, test a counterexample or use a formal argument suited to the problem. If a calculator or CAS is helpful, enter the original problem independently so a copied transcription error does not contaminate both checks. Record exact versus floating-point mode, angle units, variable domain, solver assumptions, branch choice, starting values, precision and returned conditions. Graphs can hide roots outside the window or merge nearby behavior, numerical solvers can depend on starting points, and a CAS may return a conditional, partial or inconclusive result. Agreement between two tools that received the same mistaken model is not independent confirmation.
Check completeness, repair the result and state the evidence limit
Give one of four verdicts: correct under stated conditions, incorrect, incomplete or inconclusive. Name the first unsupported line, explain whether it added a false candidate, lost a valid case or changed the problem, and show the smallest repair. Then justify completeness: prove that the valid candidates exhaust the domain, or explicitly say that only candidate validity was checked. A fluent sequence of steps is not a proof. A calculator display or CAS result is not mathematical authority. A formal proof assistant provides stronger evidence because its kernel checks a formal proof term, but even that establishes the encoded theorem only relative to its definitions, imported results and axioms; it does not prove that the encoding matches the intended classroom or real-world problem. High-stakes engineering, financial, scientific or safety calculations require review by a qualified person using the governing methods and tolerances.
Check the primary references
Check the source against the result
Original fictional MCXAI exercise — Problem: Solve √(x + 6) = x over the real numbers. Proposed AI solution: “Square both sides to get x + 6 = x². Rearrange: x² − x − 6 = 0. Factor: (x − 3)(x + 2) = 0. Therefore x = 3 or x = −2, so the solution set is {−2, 3}.”
Verdict — incorrect as stated. The principal square root is nonnegative, so the original equation requires x ≥ 0. Squaring produces candidates, but it is not an unconditional equivalence when that sign condition is omitted. Exact original-problem checks give x = 3: √9 = 3, so it is valid; and x = −2: √4 = 2, not −2, so it is extraneous. The corrected real solution set is {3}. A separately entered graph or numerical residual check also supports one intersection at (3, 3): the residual √(x + 6) − x is 0 at 3 and 4 at −2. That numerical check confirms the two tested values but is not the completeness proof; completeness follows because, on the required domain x ≥ 0, squaring is reversible and the resulting factorization has no other roots.
The proposed factorization and arithmetic are correct, but the omitted sign condition makes its final set wrong. The fluent sequence of steps is not proof, and exact substitution into the original equation—not agreement with the derived quadratic—rejects −2. A calculator or CAS could reproduce the corrected result only for the expression, domain and settings entered; its display is not independent authority. Likewise, a formal proof check would establish the formal statement it received, not that the transcription matched the intended exercise. The problem, proposed response and audit were written for MCXAI and do not reproduce an external worked example.
Review how MCXAI separates claims from evidence
MCXAI does not currently publish a live math solver whose output can be treated as authoritative. Read the editorial policy for the evidence, review and limitation standards applied to worked examples.
Read the editorial policy