### Browsed byCategory: Famous Math Problems

Who formulated the halting problem?

## Who formulated the halting problem?

### Input interpretation:

halting problem – formulator

Alan Turing

### Basic information:

full name – Alan Mathison Turing

date of birth – Sunday, June 23, 1912 (104 years ago)

place of birth – London, Greater London, United Kingdom

date of death – Monday, June 7, 1954 (age: 41 years) (62 years ago)

place of death – Wilmslow, Cheshire, United Kingdom

Continuum hypothesis

## Continuum hypothesis

### Input interpretation:

continuum hypothesis (mathematical problem)

### Statement:

There is no infinite set with a cardinal number between that of the “small” infinite set of integers and the “large” infinite set of real numbers.

### Solution:

undecidable

Smale’s fifteenth problem

## Smale’s fifteenth problem

### Input interpretation:

smooth solution to the Navier-Stokes equations problem (mathematical problem)

### Statement:

Do the Navier-Stokes equations on a 3-dimensional domain Omega in R^3 have a unique smooth solution for all time?

### Alternate name:

Smale’s fifteenth problem

Transcendence of pi

## Transcendence of pi

### Input interpretation:

transcendence of pi (mathematical problem)

### Statement:

Is pi transcendental?

Angle trisection

## Angle trisection

### Input interpretation:

angle trisection problem (mathematical problem)

### Statement:

Divide an arbitrary angle into three equal angles using only a straightedge and compass.

Knapsack problem

## Knapsack problem

### Input interpretation:

knapsack problem (mathematical problem)

### Statement:

Given a finite set U, for each u element U a size s(u) element Z^+ and a value v(u) element Z^+, and positive integers B and K, is there a subset U'(subset equal)U such that sum_(u element U’)s(u)<=B and such that sum_(u element U’)v(u)>=K.

### Statement:

The set of all sets is its own power set. Therefore, the cardinality of the set of all sets must be bigger than itself.

Konigsberg theorem

## Konigsberg theorem

### Input interpretation:

Königsberg bridge problem (mathematical problem)

### Statement:

Can the (historical) seven bridges of the city of Königsberg (now Kaliningrad) over the river Pregel all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began?