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. .
