In recent centuries, science has answered many questions about nature and the laws that govern it. We have been able to investigate the galaxies and the atoms that make up matter . We have built machines that can calculate and solve problems that no human being can solve. But even though we have solved old math problems and created theories that gave math new puzzles to solve, there is still a good range of scientific problems that remain unsolved today.
Riemann hypothesis
It is a mathematical conjecture that was first formulated by Bernhard Riemann in 1859. It is one of the great open mathematical problems in history. So much so, that the Clay Institute of Mathematics offers a million dollars to whoever develops an effective proof of this conjecture (there are six other mathematical problems in the air with such great reward for their solution).
The Riemann hypothesis has profound implications in various branches of mathematics, but we can summarize it in that the behavior continues along the proposed line, infinitely. Riemann developed the hypothesis and the function while studying the prime numbers and their distribution. Despite the current power of supercomputers, we still cannot find a solution to the Riemann hypothesis.
Goldbach’s conjecture
It is one of the oldest open problems in the field of mathematics. The Goldbach conjecture says that: “Every even number (greater than two) is the sum of two primes.” With small numbers it can be verified, but the problem is that we need proofs for all natural numbers. The Swiss mathematician and physicist Leonhard Euler himself (known by the number e or Euler’s identity, among other things) once commented that, “I consider it to be a completely true theorem, although I cannot prove it .” Apparently the Goldbach conjecture is a euphemism for very large numbers.
Collatz conjecture
Another great unsolved conjecture despite the advances of the prolific mathematician Terence Tao just a few years ago. It was stated by the mathematician Lothar Collatz in 1937. The conjecture deals with the function f (n), which takes even numbers and cuts them in half, while odd numbers are tripled and then added to 1. If we take any number natural, and we apply f, and then f over and over, eventually we’ll get to 1, for every number we’ve checked . The conjecture is that this is true for all natural numbers (positive integers from 1 to infinity). Collatz’s conjecture is based on the branch of Dynamic Systems, or the study of situations that change over time in semi-predictable ways. Why is it so difficult to answer such a basic question? It seems that it will still take decades to solve it.
Other unsolvable scientific problems would be: the Polignac conjecture, enunciated by Alphonse de Polignac in 1849 or the Birch and Swinnerton-Dyer conjecture exposed in 1965 by the English mathematicians Bryan Birch and Peter Swinerton-Dyer.
