No: the result does not mean that a particular Mario level is impossible for a person to beat. It means that for certain formal versions of several Mario games, no algorithm can always determine whether every possible level is solvable. The theorem depends on assumptions such as unlimited enemy counts and expanded or absent timers, so it should not be read as a result about every ordinary retail level.
What “mathematically unsolvable” means
In computability theory, a decision problem is undecidable when no algorithm can always give the correct yes-or-no answer for every valid input. Here, the input is a level in one of the formalized games, and the question is whether there is a sequence of player inputs that beats it.
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The result does not say that every level is unwinnable, or that a specific commercial level has no winning route. A level that is beatable has a finite successful input sequence. A search can try sequences and eventually find one when it exists; if no solution exists, that search may run forever. That is different from a difficult but decidable problem, where an algorithm will eventually answer correctly, even if it takes impractically long.
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The authors prove the result for several 2D game families: New Super Mario Bros., New Super Mario Bros. Wii, New Super Mario Bros. U, New Super Mario Bros. 2, Super Mario Maker in its four styles, and Super Mario Maker 2 in its five styles, including 3D World style. The authors’ paper says: “We prove RE-completeness (and thus undecidability) of several 2D games in the Super Mario Bros. platform video game series.” The paper first appeared as a preprint in 2024; its journal version was published in Theoretical Computer Science in 2026.
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Super Mario Wonder is not included in the theorem. The authors identify it as an open question, noting that its mechanics need further study before an undecidability claim can be made.
How can enemies turn a level into a computer program?
The proof encodes a counter machine, a simple theoretical computer whose program changes counters and branches based on their values. In the construction, the number of enemies at a location represents a counter value. Game mechanics—including events, switches and carefully restricted paths—make it possible to carry out operations and tests that mimic the machine’s instructions.
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The level is built so that the simulated machine reaches its accepting state if and only if the player can complete the level. Since the machine’s behavior can encode an undecidable problem, deciding whether every such constructed level is beatable would decide that problem too. That is why no general algorithm can solve the entire level-solvability problem.
Why “constant-size level” needs a qualification
The construction can use levels and screens of constant size; the paper also gives a universal counter-machine construction within a single-screen New Super Mario Bros. Wii level. But constant map size does not mean the entire mathematical input has bounded resources. The formal settings allow arbitrarily many enemies at a location and on screen, as well as an exponentially large timer or no timer.
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Those assumptions matter. The theorem is not evidence that the usual enemy caps and timers in ordinary commercial play automatically satisfy the proof’s conditions. It establishes undecidability for the specified generalized game families, not for every settings-limited version of each release.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What the result says about playing Mario
- It does not establish that any named retail level is impossible to beat.
- It does not mean that finding a route through a normal level is necessarily undecidable; the theorem concerns a general decision problem across all levels allowed by the formal model.
- It does show that adding seemingly simple mechanics and resources can make a platform game expressive enough to simulate computation.
The formal result is RE-completeness: solvable instances have finite witnesses that can be found by enumeration, while no procedure can always halt with the correct answer for both solvable and unsolvable instances. The result is a statement about the limits of universal algorithms, not a judgment of player skill or game difficulty.
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