The world's unsolved problems
993 open questions across 14 fields, gathered from Wikipedia. Pick one and start thinking.
Showing all 993 problems · surprise me
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Barendregt–Geuvers–Klop conjecture
Is every weakly normalizing pure type system also strongly normalizing?
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Is multiplicative-exponential linear logic decidable?
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Is the Aanderaa–Karp–Rosenberg conjecture true?
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Černý conjecture
If a deterministic finite automaton with n states has a synchronizing word, must it have one of length at most (n - 1)^2?
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Generalized star-height problem
Can all regular languages be expressed using generalized regular expressions with a limited nesting depth of Kleene stars?
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Separating words problem
How many states are needed in a deterministic finite automaton that behaves differently on two given strings of length n?
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What is the Turing completeness status of all unique elementary cellular automata?
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Determine whether the length of the minimal uncompletable word of M is polynomial in l(M), or even in sl(M). It is known that M is a…
Determine whether the length of the minimal uncompletable word of M is polynomial in l(M), or even in sl(M). It is known that M is a variable-length code if for all u_1,...,u_n,v_1,...,v_m \in M, u_1...u_n = v_1...v_m implies n = m and u_i = v_i for all 0...
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Determine all positive integers n such that the concatenation of n and n^2 in base b uses at most k distinct characters, for fixed b and k.
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Cambridge capital controversy
The Cambridge capital controversy is a dispute in economics that started in the 1950s. The debate concerned the nature and role of capital goods and a critique of the neoclassical vision of aggregate production and distribution. The question of whether the...
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Transformation problem
The transformation problem is the problem specific to Marxist economics, and not to economics in general, of finding a general rule by which to transform the values of commodities based on socially necessary labour time into the competitive prices of the...
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Revealed preference
Does revealed preference theory truly reveal consumer preference when the consumer is able to afford all of the available options? For example, if a consumer is confronted with three goods and they can afford to purchase all three (A, B, and C) and they...
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Tâtonnement
The act of tâtonnement (trial-and-error) plays a key role in the formulation of general equilibrium theory. The claim is that if an initial contract does not lead to an equilibrium, it is ended and new contracts are formulated. If the initial contract is...
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Unified models of human biases
Neoclassical economics has concentrated on the development of models that reflect an idealized economic agent, sometimes referred to as Homo economicus, as a way of studying economics. In the period spanning the 1970s to the 1990s, research began to emerge...
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Equity premium puzzle
The equity premium puzzle is thought to be one of the most important outstanding questions in neoclassical economics. It is founded on the basis that over the last one hundred years or so the average real return to stocks in the US has been substantially...
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Dividend puzzle
The dividend puzzle is the empirically observed phenomenon that companies that pay dividends tend to be rewarded by investors with higher valuations. At present, there is no explanation widely accepted by economists. The Modigliani–Miller theorem suggests...
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Improved Black–Scholes and binomial options pricing models
The Black–Scholes model and the more general binomial options pricing models are a collection of equations that seek to model and price equity and call options. While the models are widely used, they have many significant limitations. Chief among them are...
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Home bias in trade puzzle
The home bias in trade puzzle is an empirical observation that even when factors such as economic size of trading partners and the distance between them are considered, trade between regions within a given country is substantially greater than trade...
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Equity home bias puzzle
This puzzle concerns the observation that individuals and institutions in many countries only hold modest amounts of foreign equity, despite the ability for vast diversification of their portfolios in the global economy. While some explanations do exist,...
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Backus–Kehoe–Kydland puzzle
The Backus–Kehoe–Kydland consumption correlation puzzle is the empirical observation that consumption is much less correlated across countries than output. Standard economic theory suggests that country-specific output risks should be collective and...
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Feldstein–Horioka puzzle
The Feldstein-Horioka puzzle originates from an article in the 1980s that found that among OECD countries, averages of long-term national savings rates are highly correlated with similar averages of domestic investment rates. Standard economic theory...
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PPP Puzzle
The PPP puzzle, considered one of the two real exchange rate puzzles, concerns the observation that real exchange rates are both more volatile and more persistent than most models would suggest. The only clear way to understand this volatility would be to...
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The exchange rate disconnect puzzle
The exchange rate disconnect puzzle, also one of the so-called real exchange rate puzzles, concerns the weak short-term feedback link between exchange rates and the rest of the economy. In most economies, the exchange rate is the most important relative...
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Formalist–substantivist debate
The opposition between substantivist and formalist economic models was first proposed by Karl Polanyi in his work The Great Transformation (1944). Formalists such as Raymond Firth and Harold K. Schneider asserted that the neoclassical model of economics...
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Lower bound
\Omega(n^2)
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Upper bound
O\left(n^{n^{n^{n^{n^{n}}}}}\right).
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For n=3, there is an algorithm with 54 queries.
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For n\geq 4, no finite algorithm is currently known.
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For n=3, there is an algorithm that attains 1/3, which is optimal.
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For n=4 (the smallest open case), there is an algorithm that attains 1/7.
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Data last refreshed 2026-10-20 03:01 UTC.