Yesterday, At the Heidelberg Laureate Forum, retired mathematician Michael Atiyah delivered the proof of the Riemann hypothesis, which is a big challenge that has haunted around the minds of his peers for almost 160 years. If this hypothesis is proven to be correct as Michale Atiyah claimed, mathematicians would handle a compass to navigate the sea of all such prime numbers, leading to that $1 million prizes, from Clay Mathematics Institute, belongs to him. Atiyah does not prove this hypothesis in a direct way, instead, he claims to reach a logical contradiction for indicating the Riemann hypothesis must be correct.
However, Michale Atiyah does not convince other mathematicians apparently, since many of them are holding cautious skepticism.
As for me. I admire Michael Atiyah for his spirit of adventure. Anyone like him, one of UK’s most eminent mathematical figures with two awards referred to as the Noble prizes of mathematic(the Fields medal and the Abel Prize), could probably do nothing but enjoy the retirement, avoiding the damage to reputation due to making mistake. Michael Atiyah hopes that his proof will inspire the younger generation to extend his work to challenge the Riemann hypothesis in all the scientific areas, such as physics. That is what impresses me the most.
The history of human beings relies on the development of theories, the scientific definition, and reasoning. We are keen to seize a general method to explain the universe. When we reveal something mysterious, we define it, trying to include it in a new theory. Math is one of the products of this process. For example, people created integers to cover the cases in which the subtraction of natural numbers leads to be negative. Furthermore, when the negative integer can not be used for square-root, people created as well as defined the complex number and even the Euler’s Formula to deal with this ‘weird ’ situation. The Riemann hypothesis is no exception. We can consider it as the general rule of prime numbers.
However, mathematically, a particular function has its own domain of definition, suggesting we can not extend the function or rule to whatever we want. For instance, the Riemann function is based on the restricted domain of definition, or else we can get some ridiculous cases like 1+2+3+4+…=-1/12. Just as Riemann function is developed from Euler’s function with the support of certain ‘analytic extension’, to some extent, we should apply the same principle and method, figuring out whether derivatives are existing in all the reasoning process, to our conclusion. If the domain of definitions among cases is not the same, the results of them are probably totally different, because the differentiation, the process of finding a derivative, is impossible in both cases that were compared with each other while derivatives are existing at every point in its domain. In other words, if someone wants to share his or her own experiences, you should think twice before making decisions – h0w similar is your case to others’ or is it processing continuously throughout all the storytellers express?