Hilbert problems

1. What are the Hilbert problems?
2. What is Hilbert's 10 problems?
3. How many Hilbert problems have been solved?
4. What is Hilbert 20 problem?
5. Why L2 is a Hilbert space?
6. Is our universe a Hilbert space?
7. What is Hilbert 18 problem?
8. What is Hilbert's 11th problem?
9. Who solved Hilbert's 10th problem?
10. Why is L1 not a Hilbert space?
11. Who solved Goldbach conjecture?
12. Which of Hilbert's problems are solved?
13. What is Hilbert 18 problem?
14. What is Hilbert's 11th problem?
15. What is Hilbert's ninth problem?
16. Which of the 7 Millennium Problems are solved?
17. Who Solved Collatz conjecture?
18. Is Hilbert's 12th problem solved?

What are the Hilbert problems?

Hilbert's first problem, also known as the continuum hypothesis, is the statement that there is no infinity in between the infinity of the counting numbers and the infinity of the real numbers. In 1940, Kurt Gödel showed that the continuum hypothesis cannot be proved using the standard axioms of mathematics.

What is Hilbert's 10 problems?

Hilbert's tenth problem is to give a computing algorithm which will tell of a given polynomial Diophantine equation with integer coefficients whether or not it has a solutioninintegers. Matiyasevic proved that there is no such algorithm.

How many Hilbert problems have been solved?

Of the 23 Hilbert problems, problems 3, 7, 10, 11, 13, 14, 17, 19, 20, and 21 have a solution that is accepted by consensus.

What is Hilbert 20 problem?

Hilbert's twentieth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether all boundary value problems can be solved (that is, do variational problems with certain boundary conditions have solutions).

Why L2 is a Hilbert space?

There is (up to linear isomorphism) only one Hilbert space of each finite dimension, and as we shall see, there is only one infinite-dimensional separable Hilbert space — we can think of it as L2(S1), or in a sense as the infinite-dimensional complex vector space C∞.

Is our universe a Hilbert space?

The universe is described by an element of Hilbert space. All of our usual classical notions should be derived from that, not the other way around. Even space itself.

What is Hilbert 18 problem?

Hilbert's 18th problem is a collection of several questions in Euclidean geometry. First, for each n, does Euclidean space of dimension n have only a finite number of fundamentally distinct translation-invariant symmetries? In 1910, Ludwig Bieberbach answered this part of the question in the affirmative.

What is Hilbert's 11th problem?

As stated by Kaplansky, "The 11th Problem is simply this: classify quadratic forms over algebraic number fields." This is exactly what Minkowski did for quadratic form with fractional coefficients. A quadratic form (not quadratic equation) is any polynomial in which each term has variables appearing exactly twice.

Who solved Hilbert's 10th problem?

Hilbert's 10th problem, to find a method (what we now call an algorithm) for deciding whether a Diophantine equation has an integral solution, was solved by Yuri Matiyasevich in 1970. Proving the undecidability of Hilbert's 10th problem is clearly one of the great mathematical results of the century.

Why is L1 not a Hilbert space?

Therefore if L1 were to be a Hilbert space it must also be separable and reflexive. However, L1's topological dual is L∞ which is not separable (which can be verified using the indicator functions I[0,1/4] and I[0,1/3]) where-from the reflexivity of L1 implies it is not separable either, a contradiction.

Who solved Goldbach conjecture?

The first breakthrough in the effort to prove Goldbach's conjecture occurred in 1930, when the Soviet mathematician Lev Genrikhovich Shnirelman proved that every natural number can be expressed as the sum of not more than 20 prime numbers.

Which of Hilbert's problems are solved?

Of the cleanly formulated Hilbert problems, problems 3, 7, 10, 14, 17, 18, 19, and 20 have resolutions that are accepted by consensus of the mathematical community.

What is Hilbert 18 problem?

Hilbert's 18th problem is a collection of several questions in Euclidean geometry. First, for each n, does Euclidean space of dimension n have only a finite number of fundamentally distinct translation-invariant symmetries? In 1910, Ludwig Bieberbach answered this part of the question in the affirmative.

What is Hilbert's 11th problem?

As stated by Kaplansky, "The 11th Problem is simply this: classify quadratic forms over algebraic number fields." This is exactly what Minkowski did for quadratic form with fractional coefficients. A quadratic form (not quadratic equation) is any polynomial in which each term has variables appearing exactly twice.

What is Hilbert's ninth problem?

Hilbert's ninth problem, from the list of 23 Hilbert's problems (1900), asked to find the most general reciprocity law for the norm residues of k-th order in a general algebraic number field, where k is a power of a prime.

Which of the 7 Millennium Problems are solved?

Poincare Conjecture. The only Millennium Problem that has been solved to date is the Poincare conjecture, a problem posed in 1904 about the topology of objects called manifolds.

Who Solved Collatz conjecture?

Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades. Take a number, any number.

Is Hilbert's 12th problem solved?

A solution in the more special case of totally real quadratic fields, also resting on p-adic methods, was given by Darmon, Pozzi and Vonk. The general case of Hilbert's 12th Problem is still open as of 2022.