The publication of the ENCODE data is a big deal, make no doubt about it. But it has been overhyped and misreported in the popular press. Interestingly, this is not the fault of science journalists, but rather a consequence of the lead scientists in charge of publicity for this project. UC Berkeley biologist Michael Eisen has a coupleblog posts addressing this issue, as does University of Guelph biologist T. Ryan Gregory.
Two of the main criticisms directed at the publicity surrounding ENCODE are:
(1) The fact that noncoding DNA is functional does not count as "news." Far from it. Biologists have known for many, many years that functional elements make up a significant portion of the genome.
(2) The 80% figure, which is being widely reported as the proportion of the genome that is functional, is inaccurate and misleading. A more truthful statement is that 80% of the genome is biochemically active, but this is decidedly not the same thing (a point addressed by Eisen in the second post linked above). The headline on the Slashdot article is completely wrong.
The data produced by ENCODE is extremely important and will lay the groundwork for many future studies. But it should be lauded for that, and not for the hyperbole currently surrounding it.
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The publication of the ENCODE data is a big deal, make no doubt about it. But it has been overhyped and misreported in the popular press. Interestingly, this is not the fault of science journalists, but rather a consequence of the lead scientists in charge of publicity for this project.
UC Berkeley biologist Michael Eisen has a couple [michaeleisen.org] blog posts [michaeleisen.org] addressing this issue, as does University of Guelph biologist T. Ryan Gregory [evolverzone.com]. Two of the main criticisms directed at the publicity surrounding ENCODE are:
(1) The fact that noncoding DNA is functional does not count as "news." Far from it. Biologists have known for many, many years that functional elements make up a significant portion of the genome.
(2) The 80% figure, which is being widely reported as the proportion of the genome that is functional, is inaccurate and misleading. A more truthful statement is that 80% of the genome is biochemically active, but this is decidedly not the same thing (a point addressed by Eisen in the second post linked above). The headline on the Slashdot article is completely wrong.
The data produced by ENCODE is extremely important and will lay the groundwork for many future studies. But it should be lauded for that, and not for the hyperbole [telegraph.co.uk] currently surrounding it.
From quickly glanced through the paper, it doesn't seem to me that the authors have actually proved any theorems - at least not in the mathematical sense of the word "proof." They *have* provided ample numerical evidence that indicates Benford's Law applies to primes, but their explanation for why this is so is because the primes have a 1/log(x) density - nothing deeper than that.
It's a cool paper to be sure, but there doesn't seem to be much significance for mathematics.
There are generalizations of the Riemann hypothesis which are known as Dedekind zeta functions; the Riemann zeta function is one of these, corresponding to the field of rational numbers. It is also believed that the Dedekind zeta functions have all their zeros lying on the line Re(s) = 1/2. Viewed in this way, the Riemann hypothesis can be considered as a special case of a larger conjecture.
The first sentence that you quote indicates that Li is claiming to have "only" proven the Riemann hypothesis for the regular Riemann zeta function, but that he believes his techniques could be generalized to prove the related conjectures for other Dedekind zeta functions.
The Riemann Hypothesis and RSA encryption both have to do with prime numbers, but the relationship between the two pretty much ends there.
To break RSA you need to know how to factor large numbers quickly. RH, on the other hand, pretains to the distribution of prime numbers. It's pretty unlikely
that a proof would make computers any faster at factorizing.
So this begs the question that a lot of people have been asking on this thread: why should you care? There tongue-in-cheek answer is that a solution is worth $1,000,000.
While that response may suffice for non-mathematicians, mathematicians would have another, more important reason to celebrate. RH and its generalization, the Grand Riemann Hypothesis, have an absolutely enormous number of profound impliations in number theory, and it is difficult to overstate how critical a proof of either would be. (The implications are too technical to write about here, but you can read about them in most good survey books on analytic number theory; for example, see section 5.8 of Iwaniec & Kowalski). A successful proof probably won't affect your life in any meaningful way (unless you work with analytic number theory for a living), but it would be monumental in the world of math - indeed, this is precisely why there's a reward for solving it.
If that's not enough for you, just remember that many mathematicians are motivated not by fame or money but by the beauty and elegance of mathematics, and any proof of RH would establish a truly beautiful and amazing result.
Of course, there's also the question: is Li's proof correct? I certainily don't know, and I doubt anyone will for quite some time, but there's an interesting story. Li's Ph.D. adviser was Louis de Branges who,
as noted on this very website, claimed to prove RH in 2004. His proof has not been accepted by the mathematical community and is widely considered to be incorrect, in large part because the method he wclaims to use was shown, in a 2000 paper co-authored by none other than Xian-Jin Li, to have holes in it.
Slashdot Mirror
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The publication of the ENCODE data is a big deal, make no doubt about it. But it has been overhyped and misreported in the popular press. Interestingly, this is not the fault of science journalists, but rather a consequence of the lead scientists in charge of publicity for this project. UC Berkeley biologist Michael Eisen has a couple blog posts addressing this issue, as does University of Guelph biologist T. Ryan Gregory.
Two of the main criticisms directed at the publicity surrounding ENCODE are:
(1) The fact that noncoding DNA is functional does not count as "news." Far from it. Biologists have known for many, many years that functional elements make up a significant portion of the genome.
(2) The 80% figure, which is being widely reported as the proportion of the genome that is functional, is inaccurate and misleading. A more truthful statement is that 80% of the genome is biochemically active, but this is decidedly not the same thing (a point addressed by Eisen in the second post linked above). The headline on the Slashdot article is completely wrong.
The data produced by ENCODE is extremely important and will lay the groundwork for many future studies. But it should be lauded for that, and not for the hyperbole currently surrounding it.
Whoops... forgot to log in before posting. The publication of the ENCODE data is a big deal, make no doubt about it. But it has been overhyped and misreported in the popular press. Interestingly, this is not the fault of science journalists, but rather a consequence of the lead scientists in charge of publicity for this project. UC Berkeley biologist Michael Eisen has a couple [michaeleisen.org] blog posts [michaeleisen.org] addressing this issue, as does University of Guelph biologist T. Ryan Gregory [evolverzone.com]. Two of the main criticisms directed at the publicity surrounding ENCODE are: (1) The fact that noncoding DNA is functional does not count as "news." Far from it. Biologists have known for many, many years that functional elements make up a significant portion of the genome. (2) The 80% figure, which is being widely reported as the proportion of the genome that is functional, is inaccurate and misleading. A more truthful statement is that 80% of the genome is biochemically active, but this is decidedly not the same thing (a point addressed by Eisen in the second post linked above). The headline on the Slashdot article is completely wrong. The data produced by ENCODE is extremely important and will lay the groundwork for many future studies. But it should be lauded for that, and not for the hyperbole [telegraph.co.uk] currently surrounding it.
From quickly glanced through the paper, it doesn't seem to me that the authors have actually proved any theorems - at least not in the mathematical sense of the word "proof." They *have* provided ample numerical evidence that indicates Benford's Law applies to primes, but their explanation for why this is so is because the primes have a 1/log(x) density - nothing deeper than that. It's a cool paper to be sure, but there doesn't seem to be much significance for mathematics.
Extremely highly-regarded mathematician Terence Tao has said, in response to a comment left on his blog, that the proof is probably incorrect.
There are generalizations of the Riemann hypothesis which are known as Dedekind zeta functions; the Riemann zeta function is one of these, corresponding to the field of rational numbers. It is also believed that the Dedekind zeta functions have all their zeros lying on the line Re(s) = 1/2. Viewed in this way, the Riemann hypothesis can be considered as a special case of a larger conjecture.
The first sentence that you quote indicates that Li is claiming to have "only" proven the Riemann hypothesis for the regular Riemann zeta function, but that he believes his techniques could be generalized to prove the related conjectures for other Dedekind zeta functions.
The Riemann Hypothesis and RSA encryption both have to do with prime numbers, but the relationship between the two pretty much ends there. To break RSA you need to know how to factor large numbers quickly. RH, on the other hand, pretains to the distribution of prime numbers. It's pretty unlikely that a proof would make computers any faster at factorizing.
So this begs the question that a lot of people have been asking on this thread: why should you care? There tongue-in-cheek answer is that a solution is worth $1,000,000. While that response may suffice for non-mathematicians, mathematicians would have another, more important reason to celebrate. RH and its generalization, the Grand Riemann Hypothesis, have an absolutely enormous number of profound impliations in number theory, and it is difficult to overstate how critical a proof of either would be. (The implications are too technical to write about here, but you can read about them in most good survey books on analytic number theory; for example, see section 5.8 of Iwaniec & Kowalski). A successful proof probably won't affect your life in any meaningful way (unless you work with analytic number theory for a living), but it would be monumental in the world of math - indeed, this is precisely why there's a reward for solving it. If that's not enough for you, just remember that many mathematicians are motivated not by fame or money but by the beauty and elegance of mathematics, and any proof of RH would establish a truly beautiful and amazing result.
Of course, there's also the question: is Li's proof correct? I certainily don't know, and I doubt anyone will for quite some time, but there's an interesting story. Li's Ph.D. adviser was Louis de Branges who, as noted on this very website, claimed to prove RH in 2004. His proof has not been accepted by the mathematical community and is widely considered to be incorrect, in large part because the method he wclaims to use was shown, in a 2000 paper co-authored by none other than Xian-Jin Li, to have holes in it.
Scott McNealy is actually no longer the CEO of sun; that title now belongs to Jonathan Schwartz. McNealy should be referred to as a former CEO.