Math Inspector
Paste a piece of math and find out what kind it is. Math Inspector reads equations, formulas, unit expressions, datasets, rule sets and problem sizes, checks units and logic, says whether the problem can be solved exactly, numerically or not at all, works out the quick answers and points you to the tool for the rest.
How to Use
- Paste or type into the box: an equation, a formula, a unit expression such as
120V * 15A, a list of numbers, rules such as “A requires B”, an algorithm size such asO(n^2), n = 1000000, or a counting problem. - Read the report: the detected type and branch, a confidence bar, the solvability verdict (exact, numerical, contradiction, too large for brute force and so on) and any Bunker Warnings.
- Follow Show the work and Why / What next, which explain the obstacle: no formula in radicals, mixed units, exponential growth or a logic conflict.
- Use the one-click handoff to open the recommended tool with your input filled in, or Copy report / Export JSON to keep the result.
- Paste several lines to get one verdict per line (the worksheet scan example has 6), or try the example chips.
Math Inspector recognizes and computes a huge range of math, but it’s a heuristic and can occasionally misread an unusual input — double-check anything important and open the linked tool to confirm.
Paste an equation, formula, dataset, unit expression, logic rule or algorithm size. Math Inspector identifies what kind of math it is, checks for mistakes, detects hidden complexity, warns when brute force gets impossible, and routes the problem to the right Utilities Bunker tool.
Worked Example
A quadratic. The box opens with x² + 4x + 4 = 0. The inspector reads a = 1, b = 4, c = 4, finds the discriminant Δ = 4² − 4·1·4 = 0, and so reports one repeated root, x = −4 ÷ 2 = −2, with the factorisation (x + 2)² = 0. The verdict is exact, and the handoff opens the Quadratic Formula Calculator with a, b and c filled in.
Solving for x by search. x!/(x − 3)! = 120 means x(x − 1)(x − 2) = 120, three consecutive whole numbers multiplying to 120: 6 × 5 × 4, so x = 6. “x is smallest n with exactly 28 divisors” is answered the same way, by testing numbers in order: 960 = 2⁶ × 3 × 5 has (6 + 1)(1 + 1)(1 + 1) = 28 divisors, and no smaller number does.
The common mistake: adding different units. Typing power = voltage + current or 120V + 15A is flagged as a contradiction: volts and amps have different dimensions, so a sum such as 120 + 15 = 135 means nothing. Power is the product, P = V × I, and 120V * 15A gives 1,800 W (1.8 kW).
Show Work
Formulas
The Math Map: 362 Branches
Math Inspector classifies what you paste into one of these 362 branches of mathematics. ⚡ Compute branches calculate a numeric answer right here when you give them the numbers; → Route branches recognize the topic and send you to the right dedicated tool or lab.
Knowing What Can Be Solved
Some of the inspector’s verdicts rest on old results. Paolo Ruffini gave an incomplete proof in 1799 that the general quintic has no solution in radicals, and Niels Henrik Abel completed it in 1824; Évariste Galois then explained which equations can be solved that way, in work published in 1846, fourteen years after his death. Methods for quadratics go back to Babylonian tablets, and together with the rational root test they are still the quickest exact checks.
Joseph Fourier set out the rule that every term of a physical equation must have the same dimensions in 1822. Breaking it still costs: NASA lost the Mars Climate Orbiter in 1999 because one team’s software reported thruster impulse in pound-force seconds while the navigation software expected newton-seconds. The O notation used for algorithm costs was introduced by Paul Bachmann in 1894 and spread by Edmund Landau.
About This Tool
Math Inspector is a front door rather than a solver. It runs your input past more than 200 pattern analysers, keeps the most confident match, and reports the type, the branch, the solvability, a unit check and any warnings, with the working for the parts it can compute and a link to the tool built for the rest. It is a heuristic and can misread an unusual input, so check anything important in the linked tool.
Everything runs in your browser; nothing you paste is uploaded.
Related tools: Symbolic Algebra Engine, Quadratic Formula Calculator, and Derivative Calculator.
Frequently Asked Questions
How is this different from a calculator?
A calculator needs to be told what to do. Math Inspector first works out what kind of problem it has been given, whether it is valid and whether it can be solved exactly, and only then answers or hands it on. Give it x⁵ − x + 1 = 0 and it reports a degree-5 polynomial with no rational roots (the only candidates, 1 and −1, both give 1) and no formula in radicals, and sends you to a numerical solver, which finds the one real root near −1.1673.
What kinds of input does it understand?
Polynomial equations and systems, physical and electrical formulas, unit expressions, datasets, counting problems, Big-O sizes, modular and elliptic-curve arithmetic, matrices, logic rules and plain arithmetic, plus many everyday calculations. The math map below lists 362 branches: 298 compute an answer on the spot and 64 recognise the topic and send you to the right tool. Anything it cannot place is reported as unrecognised, with examples of what does work.
How does the unit check work?
Each unit carries a dimension in length, mass, time and current: a volt is kg·m²·s⁻³·A⁻¹ and a watt is kg·m²·s⁻³. Multiplying or dividing always works and gives a new dimension, so 120 V × 15 A is 1,800 W (1.8 kW). Adding or subtracting needs the same dimension on both sides, so power = voltage + current is flagged as a contradiction and the valid forms P = V × I, V = I × R, P = I² × R and P = V² ÷ R are listed instead.
Why does it say a quintic has no exact formula?
Because of the Abel–Ruffini theorem: there is no general formula in radicals for polynomial equations of degree 5 or higher. Quadratics always have one (x² + 4x + 4 = 0 gives Δ = 16 − 16 = 0 and the single root x = −2), and cubics and quartics have messier ones. For degree 5 and up the inspector looks for rational roots to factor out, and otherwise recommends numerical root-finding.
How does it spot a problem that is too big?
It estimates the size before anyone tries to enumerate it. 8 choices across 40 options is 8⁴⁰ = 2¹²⁰, exactly 1,329,227,995,784,915,872,903,807,060,280,344,576, or about 1.33 × 10³⁶; at a billion checks a second that would take about 4.2 × 10¹⁹ years. O(n²) at n = 1,000,000 is 10¹² operations, rated “extreme”: about 17 minutes at a billion simple operations a second, where an O(n log n) method would need about 2 × 10⁷.
How do I use the Math Inspector?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Check a formula
power = voltage + current is flagged: volts and amps cannot be added.
Size a search
8 choices across 40 options is 8⁴⁰, about 1.33 × 10³⁶ combinations.
Algorithm cost
O(n²) at n = 1,000,000 is 10¹² operations, too many to brute-force casually.
Solve-for-x puzzles
x!/(x − 3)! = 120 gives x = 6; the smallest number with 28 divisors is 960.
Sanity-check data
In 12, 15, 18, 999, 21 the 999 pulls the mean to 213 while the median is 18.
Scan a worksheet
Paste 6 problems, one per line, and get a verdict for each.
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