David Hilbert was one of the most influential mathematicians of the 19th and early 20th centuries.

On August 8, 1900, Hilbert attended a conference at the Sorbonne, Paris, and presented a list of unsolved mathematics problems at the time. Hilbert presented ten of the problems on that day. To show his support to Cantor, Hilbert chose a question about Cantor’s continuity hypothesis to be his first. Then, he would add thirteen more questions.

The complete list of 23 problems was published later in the *American Mathematical Society* Bulletin by Mary Frances Winston Newson.

### Hilbert’s Problem #1

Continuum Hypothesis: The continuum hypothesis (that is, there is no set whose cardinality is strictly between that of the integers and that of the real numbers) To mathematicians, all…

### Hilbert’s Problem #2

The Compatibility of the Standard Axioms of Arithmetic: Prove that the axioms of arithmetic are consistent. Hilbert’s second problem was…

### Hilbert’s Problem #3

Equidecomposability: Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces that…

### Hilbert’s Problem #4

The Straight Line as The Shortest Distance Between Points: Construct all metrics where lines are geodesics. Hilbert’s fourth problem is about what happens…

### Hilbert’s Problem #5

Understanding Lie Groups: Are continuous groups automatically differential groups Hilbert’s fifth problem concerns Lie groups, which are algebraic objects that describe continuous transformations….

### Hilbert’s Problem #6

The Axiomatization of Physics: Mathematical treatment of the axioms of physics (a) axiomatic treatment of probability with limit theorems for foundation of statistical physics…

### Hilbert’s Problem #7

Irrationality and Transcendence of Certain Numbers: Is ab transcendental, for algebraic a ≠ 0,1 and irrational algebraic b A number is called algebraic if it can be the…

### Hilbert’s Problem #8

Problems of Prime Numbers: The Riemann hypothesis(“the real part of any non-trivial zero of the Riemann zeta function is ½”)and other prime number problems, among…

### Hilbert’s Problem #9

Reciprocity Laws and Algebraic Number Fields: Find the most general law of the reciprocity theorem in any algebraic number field. Hilbert’s ninth problem is…

### Hilbert’s Problem #10

Solvability of a Diophantine Equation: Find an algorithm to determine whether a given polynomial Diophantine equation with integer coefficients has an integer…