# Questions tagged [open-problems]

If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"

**112**

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### Why polynomials with coefficients $0,1$ like to have only factors with $0,1$ coefficients?

**79**

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### Volumes of Sets of Constant Width in High Dimensions

**74**

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### Converse to Euclid's fifth postulate

**65**

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### 2, 3, and 4 (a possible fixed point result ?)

**45**

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### Set-theoretic reformulation of the invariant subspace problem

**32**

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### Converse of the Archimedean property of the sphere

**31**

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### A Combinatorial Abstraction for The “Polynomial Hirsch Conjecture”

**26**

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### Finite-dimensional subalgebras of $C^\star$-algebras

**25**

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### Milnor's cartography problem

**24**

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### Decidability of equality of elementary expressions

**24**

**1**answer

### When is a compact topological 4-manifold a CW complex?

**23**

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### Is it still an open problem whether $\mathbb{R}^\omega$ is normal in the box topology?

**22**

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### Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

**22**

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### Smooth proper schemes over Z with points everywhere locally

**20**

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### The oriented homeomorphism problem for Haken 3-manifolds

**20**

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### Avoidable words

**17**

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### Actions on ℍⁿ generated by torsion elements

**16**

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### Does $S^4$ have a “symplecto-homeomorphic” structure?

**16**

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### Comparing the Kazhdan-Lusztig and Steinberg pre-orders

**15**

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### Decidable open problems

**15**

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### An open problem in convex geometry

**15**

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### Special values of Artin L-functions

**15**

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### MNOP conjecture

**15**

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### Finite Rank Commutators

**15**

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### Optimal Monotone Families for the Discrete Isoperimetric Inequality

**13**

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### Second duals of Grothendieck spaces

**13**

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### 3-piece dissection of square to equilateral triangle?

**13**

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### Razborov's response to Almost Natural Proofs

**12**

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### How can an approach to $P$ vs $NP$ based on descriptive complexity avoid being a natural proof in the sense of Raborov-Rudich?

**12**

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### Pencils with many completely decomposable fibers

**11**

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### Hilbert 16th problem and dynamical Lefschetz trace formula

**11**

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### Stability of analytic Zariski structures

**10**

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### Dissecting trapezoids into triangles of equal area

**9**

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### Is it an open problem whether fast-growing hierarchies can be defined without fundamental sequences?

**9**

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### Bang's open question strengthening Tarski's planks problem

**9**

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### Randomly placing nonoverlapping unit cuboids

**9**

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### Convergence in $L^2$ of iterated expectations

**9**

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### Once differentiable, piecewise degree three polynomials on triangulated planar domains

**8**

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### Plank invariant measures on convex bodies

**8**

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### Is $Q_n(x)=\sigma_{n+1}(x)/\sigma_n(x)$ logarithmically convex on $\mathbf{R}$?

**7**

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### When do two knots have isomorphic fundamental bikeis?

**7**

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### An open problem in Sobolev spaces

**7**

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### A question related to Conways 99 graph problem

**7**

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### Status of two Banach space theory open problems posted by Pełczyński

**7**

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### On a question of Coste & Roy from 1979

**7**

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### Limit cycles as closed geodesics(2)

**7**

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### Does every model of $I\Delta_0$ has an end extension to a model of $I\Delta_0+\Omega_1$?

**7**

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### Graphs with graphic imbalance sequences

**7**

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### How many values a polynomial map misses?

**7**

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