Looking for problems in cs that need to be solved! Actually, **Undecidable problems** in computer science are questions or challenges that have yet to be resolved or addressed.

**These problems** can be theoretical, practical or both. They often involve fundamental questions about the nature of computation and the limits of what can be computed.

Unsolved problems can be found in a wide range of areas within computer science including,

- algorithms,
- complexity theory,
- data structures,
- programming languages,
- and more.

Many of these problems have been studied for decades. These are still continuing to attract the attention of researchers from around the world.

Some unsolved problems may eventually be resolved through the development of new technologies.

But others may remain open indefinitely and need more attention.

## The P vs NP Problem

This unresolved issue in computer science raises the question: Can a computer solve problems quickly (in polynomial time), or does it require an exponential amount of time?

### Explanation

The crux of the matter is determining if every problem that can be efficiently verified (in polynomial time) by a computer can also be efficiently solved.

This problem holds significant weight in the world of algorithms and could potentially reveal if some problems are inherently challenging to solve.

## Hodge Conjecture

**Statement: **Given a topological space, can it be represented as the geometric curvature of some smooth manifold?

Hodge Conjecture Problem |

### Explanation

In simple terms, this problem asks whether every topological space can be described as the curved shape of a smooth object.

It delves into the relationship between topological spaces and smooth manifolds. If it could be solved, provide insight into the geometry of our world.

## Riemann Hypothesis

**Question**: Are the nontrivial zeros of the Riemann zeta function solely on the critical line of 1/2?

### Explanation

The Riemann Hypothesis deals with the distribution of prime numbers in number theory. It suggests that the nontrivial zeros of the Riemann zeta function are limited to the critical line of 1/2. Despite numerous tests, this hypothesis remains unproven.

## Birch and Swinnerton-Dyer Conjecture

**Query**: Can the L-function determine the rank of an elliptic curve?

### Explanation

The Birch and Swinnerton-Dyer Conjecture is a challenge in arithmetic geometry that relates to elliptic curves. It questions if the behavior of an elliptic curve’s L-function can predict its rank. This conjecture offers insight into the structure of elliptic curves.

## Collatz Conjecture

**Problem**: Does the function f(n) = n/2 (if n is even) or 3n + 1 (if n is odd) when applied to any positive integer eventually lead to the cycle of 4, 2, 1?

Collatz Conjecture Problem |

### Explanation

The Collatz Conjecture is a mathematical mystery involving the iteration of the function f(n). Despite attempts to solve it, this conjecture remains unanswered. It states that when the function is applied to any positive integer, it will eventually reach the cycle of 4, 2, 1.

## Continuum Hypothesis

**Question**: Is the minimum size of an infinite set located strictly between the size of integers and the size of real numbers?

### Explanation

The Continuum Hypothesis is a set theory puzzle concerning the size of infinite sets. The hypothesis asks if the minimum size of an infinite set lies strictly between the size of integers and the size of real numbers. This problem was first introduced by mathematician Georg Cantor and still awaits resolution.

## Poincaré Conjecture

**Statement**: Does every closed, simply connected 3D manifold equate to the 3-sphere in terms of topology?

### Explanation

The Poincaré Conjecture is a topology puzzle that deals with 3D manifolds.

It queries whether every closed and simply connected 3D manifold has the same topological properties as the 3-sphere.

Grigori Perelman famously solved this problem, but his solution isn’t universally accepted.

## Yang-Mills Existence and Mass Gap

**Statement**: Do gauge theories always admit stable particles with finite mass, referred to as a mass gap?

### Explanation

The Yang-Mills Existence and Mass Gap issue is a theoretical physics puzzle that involves gauge theories.

It inquires if every gauge theory allows for stable particles with finite mass, known as a mass gap.

This problem holds significant meaning for our understanding of matter’s fundamental nature.

## Navier-Stokes Existence and Smoothness

**Statement**: Does the Navier-Stokes equation always have a smooth solution?

Navier-Stokes Existence and Smoothness |

### Explanation

The Navier-Stokes Existence and Smoothness is a challenge in fluid dynamics concerning the fundamental partial differential equation, the Navier-Stokes equation.

It poses the question of whether the equation has a smooth solution in all cases.

The answer to this problem would give insight into the nature of fluid behavior.

## Birkhoff’s Conjecture

**Statement**: Does every locally compact group possess a Haar measure?

### Explanation

Birkhoff’s Conjecture is a question in the field of abstract algebra that focuses on locally compact groups.

It asks whether every such group has a Haar measure, a measure that remains unchanged under translation.

This conjecture deals with the principle of invariance and could enhance our understanding of symmetry.

## List of 21 Unsolved Problems in Computer Science

Here are 20 more names of unsolved problems in computer science:

- The Non-Determinism Problem
- The Decidability Problem
- The Lambda Calculus Unsolvability Problem
- The Riemann Hypothesis for Function Fields
- The Birch and Swinnerton-Dyer Conjecture
- The ABC Conjecture
- The Collatz Conjecture
- The Hodge Conjecture
- The Kadison-Singer Problem
- The Birch Conjecture
- The Beal Conjecture
- The Connes Embedding Conjecture
- The Erdős Discrepancy Problem
- The Jones Polynomial Conjecture
- The Poincaré Conjecture
- The P/NP Problem
- The Unique Games Conjecture
- The Birch and Swinnerton-Dyer Conjecture for Abelian Varieties
- The Boolean Pythagorean Triples Problem
- The Monotone Circuit Conjecture.
- The Finite Model Theory Problem

## FAQs: Unsolved Problems in Computer Science

Let’s discuss some **unsolved computer science problems**!

FAQs |

### What are some Unsolved Problems in Computer Science?

A few unanswered issues in **computer science include** the P vs NP problem, the Hodge Conjecture, and the Riemann Hypothesis.

### Why are these problems crucial?

These challenges in computer science hold great significance as they stand as the biggest hurdles and enigmas in the field. Addressing these problems can steer research and innovation, and their resolution can enhance our understanding of computation and the world.

## The Final Word

The above-mentioned problems are just a few examples of numerous unresolved issues in computer science. Although some of these puzzles might appear abstract or theoretical, they all have the capability to revolutionize our comprehension of computation and the world.

Hence, these problems continue to draw the attention of researchers from various domains, and it is likely that many exciting breakthroughs and discoveries await us in the future.