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.

**Related media: The Simplest Math Problem No One Can Solve – Collatz Conjecture**

**#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 Euler, *e* 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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