Cardinal Cryptography

These Math Problems Remain Unsolved For Over 100 Years!

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Mateusz Raczyński
28 May 2020, by Mateusz Raczyński
It's easy to think that everything has been already solved and invented...but that's not the case!

We’re living in the most technologically advanced times known to humankind. However, this statement could be true to all major periods as we have the tools to solve many, many problems. In some cases, it’s no longer about the tools, but about the will and resources to resolve poverty or hunger.

But even though we have advanced so much as a civilization and it’s easy to feel everything’s been already invented, it’s obvious we haven’t invented everything yet. There’s still plenty of room for improvement. For example, some mathematical problems haven’t been solved yet.

In 1900, a mathematician named David Hilbert, who represented the pinnacle of mathematical thought on the brink of the XIX and XX centuries, formulated a list of 23 problems that up until then haven’t been solved. Little did he know that his thesis will drive the mathematical advancements of the XX century.

The list contains really complicated stuff that won’t be easy to understand for someone whose contact with mathematics is limited to splitting bills. Those with engineering background should understand at least some terms, like calculus of variations or linear differential equations. Let’s keep it friendly though, and refrain from diving too deep into this mumbo jumbo.

All you need to know is that those Hilbert’s problems were troubling mathematicians so much for the last 100 years that as they have been solved one by one, they moved the whole of mathematics forward. Up to the state in which we are now, with cryptography being the underpinning of blockchain technologies.

But some problems are unsolved to this day. Some have been marked as non-mathematical or too generic to solve but others are fully legit – it’s just that they have been too hard to answer for more than 120 years.

The Unsolved Math Problems:

  • 8th: The Riemann hypothesis (“the real part of any non-trivial zero of the Riemann zeta function is ½”) and other prime number problems, among them Goldbach’s conjecture and the twin prime conjecture
  • 12th: Extend the Kronecker–Weber theorem on Abelian extensions of the rational numbers to any base number field.
  • 13th: Solve 7th degree equation using algebraic (variant: continuous) functions of two parameters.
  • 16th: Describe relative positions of ovals originating from a real algebraic curve and as limit cycles of a polynomial vector field on the plane.

We might not solve the Hilbert’s problems, but we’ll definitely solve yours! Contact us!