Unsolved Millennium Problems

What’s the Deal with 𝜋+e?
➖➖➖➖➖➖➖➖➖
Given everything we know about two of math's most famous constants, 𝜋 and e, it's a bit surprising how lost we are when they're added together.

This mystery is all about algebraic real numbers. The definition: A real number is algebraic if it's the root of some polynomial with integer coefficients. For example, x²-6 is a polynomial with integer coefficients, since 1 and -6 are integers. The roots of x²-6=0 are x=√6 and x=-√6, so that means √6 and -√6 are algebraic numbers.

All rational numbers, and roots of rational numbers, are algebraic. So it might feel like "most" real numbers are algebraic. Turns out, it's actually the opposite. The antonym to algebraic is transcendental, and it turns out almost all real numbers are transcendental—for certain mathematical meanings of "almost all." So who's algebraic, and who's transcendental?

The real number 𝜋 goes back to ancient math, while the number e has been around since the 17th century. You've probably heard of both, and you'd think we know the answer to every basic question to be asked about them, right?

Well, we do know that both 𝜋 and e are transcendental. But somehow it's unknown whether 𝜋+e is algebraic or transcendental. Similarly, we don't know about 𝜋e, 𝜋/e, and other simple combinations of them. So there are incredibly basic questions about numbers we've known for millennia that still remain mysterious.

Goldbach’s Conjecture
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
One of the greatest unsolved mysteries in math is also very easy to write. Goldbach's Conjecture is, "Every even number (greater than two) is the sum of two primes." You check this in your head for small numbers: 18 is 13+5, and 42 is 23+19. Computers have checked the Conjecture for numbers up to some magnitude. But we need proof for all natural numbers.

Goldbach's Conjecture precipitated from letters in 1742 between German mathematician Christian Goldbach and legendary Swiss mathematician Leonhard Euler, considered one of the greatest in math history. As Euler put it, "I regard [it] as a completely certain theorem, although I cannot prove it."

Euler may have sensed what makes this problem counterintuitively hard to solve. When you look at larger numbers, they have more ways of being written as sums of primes, not less. Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach's Conjecture is an understatement for very large numbers.

Still, a proof of the conjecture for all numbers eludes mathematicians to this day. It stands as one of the oldest open questions in all of math.

Nigerian professor have solved 156 year old maths problem?
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
One of the most important problems in mathematics - the Riemann Hypothesis - said to have finally solved by a Nigerian professor in 2015. but still it was not confirmed by clay mathematics institute. it said unsolved problem.

Dr Opeyemi Enoch claims he made a key breakthrough in 2010 which later enabled him to solve the puzzle, which is one of the seven Millennium Problems in Mathematics.

The Riemann Hypothesis was proposed by mathematician Bernard Riemann in 1859 and concerns the distribution of prime numbers.
It has become arguably the most famous problem in mathematics, since Fermat's Last Theorem was solved in the 1990s.

At its most simple, the distribution of prime numbers among all others doesn't follow a regular pattern.

However, Riemann noticed that the frequency of prime numbers is very closely related to the behavior of an elaborate function called the Riemann Zeta function.

The hypothesis asserts that all solutions of the equation ζ(s) = 0 lies on a certain vertical straight line, according to the Clay Mathematics Institute.

While this has been checked for the first 10,000,000,000 solutions, it is only now that a 'proof' explaining their distribution beyond this has been found.

However, The Clay Mathematical institute has neither confirmed nor denied that Dr Enoch has officially solved the problem, simply saying it does not comment on solutions to the Millennium Problems.

This has led to critics claiming the story is a hoax and MailOnline has contacted the professor for more information.

Dr Enoch, who teaches at the Federal University of Oye Ekiti (FUOYE) in Nigeria, said he was motivated to solve the 156-year-old problem because of his students.

He told the BBC that they wanted him to make money from the internet.

'The motivation was because my students trusted that the solution could come from me - not because the financial reward and that was why I started trying to solve the problem in the first place,' he said.

THE MILLENNIUM PRIZE PROBLEMS
The Millennium Prize Problems were launched on 24 May, 2000.

They include seven problems considered by the Clay Mathematics Institute to be 'important classic questions that have resisted solution over the years'.

These include: P versus NP, The Hodge conjecture, The Poincaré conjecture, The Riemann hypothesis, Yang–Mills existence and mass gap, Navier–Stokes existence and smoothness and The Birch and Swinnerton-Dyer conjecture.

The full details of each are available from the institute's website.

The first person to solve each of the problems will receive $1 million (£658,000).

The professor presented his proof on 11 November during the International Conference on Mathematics and Computer Science in Vienna, Nigerian news site Vanguard reported.

Join our new Telegram channel: https://t.me/unsolvedmillenniumproblems

Can you solve this?
Find the number that can substitute the blue, green, and red color.