Riemann Hypothesis Quotes

If I were to awaken after having slept for a thousand years, my first question would be: has the Riemann Hypothesis been proven?

Riemann Hypothesis,

The Riemann zeta function was a simple enough looking infinite series expressed in terms of a complex variable. Here, “complex” means not difficult or complicated, but refers to a variable of two distinct components, “real” and “imaginary,” which together could be thought to range over a two-dimensional plane. In 1860, Georg Friedrich Bernhard Riemann made six conjectures concerning the zeta function. By Ramanujan’s time, five had been proven. One, enshrined today as the Riemann hypothesis, had not

Boston and Chicago are two great seats of mathematical research located in major American cities. Until they won in 2004, if you asked a baseball fan in Boston what they most hoped to see in their lifetime, they would have answered a World Series win for the Boston Red Sox. Chicago Cubs fans are still waiting. Ask a mathematician in either of those cities or anywhere else in the world what they would most hope to see in their lifetime, and they would most likely answer: "A proof o the Riemann hypothesis!" Perhaps mathematicians, like Red Sox fans, will have their prayers answered in our lifetimes, or at least before the Cubs win the World Series.

The Riemann hypothesis states that the roots of the zeta function (complex numbers z, at which the zeta function equals zero) lie on the line parallel to the imaginary axis and half a unit to the right of it. This is perhaps the most outstanding unproved conjecture in mathematics with numerous implications. The analyst Levinson undertook a determined calculation on his deathbed that increased the credibility of the Riemann-hypothesis. This is another example of creative work that falls within Gruber and Wallace's (2000) model.

Finding a method to categorize transcendental numbers was one of David Hilbert's great unsolved maths problems (along with the Riemann Hypothesis), and it remains justbas unsolved today.

The Riemann Hypothesis states that all the non-trivial zeroes of the zeta function are on this line. If we can prove the Riemann Hypothesis is true, then we'll also have proved the method for counting the prime numbers. In some weird twisted act of mathematical logic, at a fundamental level the alignment of these zeroes stems from the same logic as the density of the primes. It doesn't seem to make sense. But if we can understand this mysterious alignment, we understand where the numbers are hiding their primes.

There has been some progress on proving the Riemann Hypothesis, but it remains unsolved. In 1914, Hardy managed to prove that there are infinitely many zeroes on that line, but he couldn't prove that there aren't any extra zeroes off the line. We currently know that 40 percent of the non trivial zeroes are definitely on that line, but we need to know it's true for 100 per cent. So much as a single zero somewhere else, and the Riemann hypothesis would be disproved, causing our apparent understanding to come crashing down. But it hasn't. Everything has uncannily indicated that we are on the right track, but we can't yet prove it for sure.

On our unnamed alien hero’s home world, Vonnadoria, mathematics has transformed his people, giving them the ability to create a utopian society where knowledge is limitless and immortality attainable. But when Cambridge professor Andrew Martin cracks the Riemann hypothesis, opening a door to the same technology that the alien’s planet possesses, the narrator is sent to Earth to erase all evidence of the solution and kill anyone who had seen the proof. He struggles to pass undetected long enough to gain access to Martin’s research. But as he takes up the role of Professor Martin in order to blend in with the humans, he begins to see a kind of hope and redemption in the humans’ imperfections, and he questions his marching orders. Mathematics or not, he becomes increasingly convinced that Martin’s family deserves to live, forcing him to confront the possibility of forgoing everything he has ever known and become a human. TOPICS AND QUESTIONS FOR DISCUSSION 1. In the preface, our narrator explains his purpose and asks his people back home to set aside prejudice in the name of understanding. How is this plea to his fictional reader also directed at us, the actual readers? What prejudices must we set aside to understand our alien hero? 2. Our hero’s entrance into human life is . . . rocky, at best. How did his initial impressions of human life—noses, clothes, rain, and Cosmopolitan—shape the rest of his journey? Which of his first disconcerting realizations did you find the most surprising? 3. Starting with the possibility that the purpose of humanity is to “pursue the enlightenment of orgasm,” our hero is constantly seeking the solution to the meaning of human life. What does he

The rules of evidence can deliver very persuasive results, sometimes contrary to the strictly argued certainties of mathematics. […] Hypothesis: No human can possibly be more than nine feet tall. Confirming instance: A human being who is 8'11¾" tall. The discovery of that person confirms the hypothesis … but at the same time casts a long shadow of doubt across it!

The Riemann hypothesis, first tossed off by Bernhard Riemann in 1859 in a paper about the distribution of prime numbers,