Here are ten of the most difficult math problems that remain largely unsolved.

Math isn’t for the faint of minds, obviously. Think of it, what was the difficult math problem you feared at school. From algebra to calculus to geometry to quadratics to let us stop freaking you out in this article, huh? Well…, buckle up and get ready for more arithmophobia (the fear of math). Some math problems seem not to have a solution, at all. Or not yet. These are brain-busters that seem impossible to crunch, but maybe not for long. Here are ten of the most difficult math problems yet unsolved.



#1. Birch And Swinnerton-Dyer Conjecture

This conjecture describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory, meaning anyone can have a go at it. An elliptic curve is a special kind of function which takes the form of something like y²=x³+ax+b. Weird, huh?



#2. Collatz Conjecture

The infamous Collatz conjecture says that if you start with any positive integer, you’ll always end up in this loop. However, the conjecture isn’t infamous for only that reason. Although every number ever tried ends up in that loop, we’re still not certain if that’s accurate. Thence cometh the problem.



#3. Euler’s Number (𝜋+e)

Euler’s number, name after mathematician Leonhard Eulere is the base of the natural logarithms. This is the ratio of the circumference of any circle to the diameter of that circle. And no matter the size, it’s ratio will always equal pi (𝜋). Spoiler, it wasn’t invented by Euler, it was rather invented by John Napier.



#4. Gamma’s Rationality

Is γ a number? Sounds not, but it is. However, the number γ has not been proven to be an algebraic or transcendental number, yet. And as a matter of fact, it is not known whether it is even irrational. In 1997, the Greek physician Georgios Papanikolaou proved with a continued fraction analysis that if γ is rational, its denominator must be greater than 10^244663.



#5. Goldbach’s Conjecture

This is the oldest unsolved math problem in number theory and in all of mathematics. It simply states that every even whole number greater than 2 is the sum of two prime numbers. Is every even number greater than 2 the sum of 2 primes? Goldbach says, yes. For instance, 4=2+2, 6=3+3, 8=3+5, and so on.



#6. Kissing Number Problem

This problem isn’t romantic if you think it is. It seeks to ask the maximal number k(n) of equal size non-overlapping spheres in n-dimensional space that can touch another sphere of the same size. It became the subject of a famous discussion between Isaac Newton and David Gregory in 1694.



#7. Riemann Hypothesis

Mathematically, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 12. Many mathematicians consider this to be the most important yet unsolved problem left in pure mathematics.



#8. The Large Cardinal Project

This project is about the large cardinal axiom which states that there exists a cardinal (perhaps many of them) with some specified large cardinal property. Most set theorists believe that the large cardinal axioms that are currently being considered are consistent with Zermelo-Fraenkel set theory (ZFC).



#9. Twin Prime Conjecture

Also known as Polignac’s conjecture, in number theory, is an assertion that there are infinitely many twin primes, or pairs of primes that differ by 2. For instance, 3 and 5, 5 and 7, 11 and 13, and 17 and 19 are twin primes. By contrast, the sum of the reciprocal of the primes diverges to infinity.



#10. Unknotting Problem

The unknotting problem, in mathematics, is just as its name says. It is the problem of algorithmically unknotting a knot. In one word, untie. For example, a representation of knots in a knot diagram. There are several types of unknotting algorithms.

Let us know which problem you think we left out.


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Written by: Nana Kwadwo, Thu, Dec 16, 2021.

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