One of the most important and complex problems that confuse the entire **world mathematical community** is called the **Riemann Hypothesis** . A **problem** that is not easy to tackle, especially for those who have trouble with mathematics. But **what is it and why will a million dollars be paid to whoever solves it?**

The Riemann Hypothesis: The Million Dollar Math Conundrum

We are talking about **one of the seven problems of the Millennium Prize Problems** , a series of mathematical problems, still unsolved, for which **the Clay Institute of Mathematics has offered a prize money** . The person who manages to solve it will not only have free access to the “great hall of immortal thinkers” but will win the incredible sum of a million dollars.

Thus, anyone who wants to solve this mathematical puzzle and win the million dollars must start with the **Prime Number Theorem** . Carl Friedrich **Gauss** had introduced an approximation to **define and identify these numbers, based on a Cartesian graph** with a logarithmic trend. A student of his, Bernhard **Riemann** , introduced, in 1859, a conjecture that explained the **“fluctuations”** of the model mentioned by Gauss himself.

**Riemann’s work has had a great impact** on many aspects that we take for granted today, from computer cryptography for **encrypted security codes** **, to differential geometry calculus,** to the basis for the development of **general relativity.**

The zeta function, the fundamental cornerstone for analyzing the distribution of prime numbers, was originally considered and solved by Euler for the set of real numbers (R). **Riemann’s** version, associating it with complex numbers (C), attempted to determine **a more precise distribution of “zeros” that identified the position of the prime numbers.**

Having shown that **the first ten trillion zeros follow the expected course,** the conjecture has been assimilated as true. However, until there is proof to confirm and it is definitively proven that all zero follows this distribution **, the theory remains unsolved.**

**Yet the Riemann hypothesis is so fundamental in many well-known areas of mathematics** , to the point that it led mathematician Peter Sarnak to assert that: *‘If it is not true, then the world is a very different place. The whole structure of integers and primes would be very different from what we might imagine. In a way, it would be more interesting if it were false, but it would be a disaster because we have built so much around the assumption of its truth* .

Now, after 160 years and a series of “false positives,” joined over time by mathematicians who have claimed to have found the solution, **this problem remains unsolved and may never be** . At this point, one might wonder what sense it makes, for the field of mathematics and for future generations, to continue to analyze it.

**The answer can be identified in the intrinsic process of science itself** which, on its way to the search for concrete and often “impossible” answers, discovers a series of collateral knowledge that it would never have imagined finding, **effectively changing the very conception of the world.** .