[QUOTE=Orgasmic Troll;205911]You're more likely to prove an unsolved problem before you will make a decent conjecture.[/QUOTE]
That, of course, depends upon what this "unsolved problem" is...

[QUOTE=R.D. Silverman;205916]I am well aware that many people misuse many words. But the word
"ignorant" means "without knowledge". The fact that it is misused is a reflection of both ignorance [b]and[/b] stupidity.

I would expect people in [b]this[/b] forum not to make such a mistake.

Calling someone an ignoramus is a perjorative, because it means
"generally ignorant". But saying that someone is mathematically ignorant
is not and should not be a perjorative. It is a simple statement of fact.

I am more careful in my use of language. Especially in an academic
discussion.[/QUOTE]

Prescriptivism is just silly.

[QUOTE=flouran;205923]That, of course, depends upon what this "unsolved problem" is...[/QUOTE]

No, I said solving [b]an[/b] unsolved problem. There are plenty of them out there.

[QUOTE=R.D. Silverman;205914]Ah. presumably you thought that the only way to do a prime test on n was
by trial division up to sqrt(n), and therefore testing all numbers up
to N would require at least O(N sqrt(N) time)?[/QUOTE]

At that point I had just discovered that you only needed to test up to the square root. My earlier prime-finder (written at age 9-10) used the yet-more-naive N^2 algorithm, and optimizations like "test only odds" or "exit the loop once you find a factor" were the best improvements I had.

[QUOTE=R.D. Silverman;205912]Why do you say "When Bob uses the word ignorant"??? Why single me out? Do [b]you[/b] use the word differently?? Do others?[/QUOTE][QUOTE=xilman;205915]Yes, others do use the word differently.[/QUOTE][QUOTE=R.D. Silverman;205916]I would expect people in [b]this[/b] forum not to make such a mistake.[/QUOTE][QUOTE=Dougal;205920]Uncwilly was pointing out that when you use the word "ignorant",you use its proper meaning,whereas others tend to misuse it.[/QUOTE]You all are more or less correct. The reason I singled you out is that you [B]had[/B] used it, and Tomer seemed to be upset. Since he is a non-native English speaker, I would assume that much of his knowledge of comes from 'common usage' (entertainment media, news media, and street usage). Most of these commonly misuse ignorant (to mean unintelligent). I, too, would expect that most on this forum are more exacting in their usage. I tend to reserve the use of the word myself to audiances that are astute enough to not mistake the intent. I have told my supervisor (who has multiple degrees, in different, one at a doctorate level) that he was ignorant of something, because I knew that he knew what the word acutally means. I would, however, be careful of my use of the word with a teenager, as they will frequently misunderstand.

[QUOTE=Uncwilly;205931]You all are more or less correct. The reason I singled you out is that you [B]had[/B] used it, and Tomer seemed to be upset. Since he is a non-native English speaker, I would assume that much of his knowledge of comes from 'common usage' (entertainment media, news media, and street usage). Most of these commonly misuse ignorant (to mean unintelligent). I, too, would expect that most on this forum are more exacting in their usage. I tend to reserve the use of the word myself to audiances that are astute enough to not mistake the intent. I have told my supervisor (who has multiple degrees, in different, one at a doctorate level) that he was ignorant of something, because I knew that he knew what the word acutally means. I would, however, be careful of my use of the word with a teenager, as they will frequently misunderstand.[/QUOTE]

Allow me to be even more pedantic.

Mathematics is a language where it is possible to say precisely what one
means. Exact usage of language in mathematics is more important than in
other domains.

[QUOTE=R.D. Silverman;205934]
Mathematics is a language where it is possible to say precisely what one
means. Exact usage of language in mathematics is more important than in
other domains.[/QUOTE]

Hogwash! You mustn't be ignorant of other domains when you make such a claim.

Though precise articulation is a vital component in mathematical discourse, the exact usage of language in mathematics is certainly [B]NOT[/B] more important than in other domains. It is common practice in English literary prose to be concise and to-the-point with one's assertions (though many post-modernist writers tend to disagree :wink:). Furthermore, the way in which rhetoric is phrased is crucial to its interpretation by the reader and forms the basis of many literary debates.

[QUOTE=R.D. Silverman;205916]I am well aware that many people misuse many words. But the word
"ignorant" means "without knowledge". The fact that it is misused is a reflection of both ignorance [b]and[/b] stupidity.

I would expect people in [b]this[/b] forum not to make such a mistake.

Calling someone an ignoramus is a perjorative, because it means
"generally ignorant". But saying that someone is mathematically ignorant
is not and should not be a perjorative. It is a simple statement of fact.

I am more careful in my use of language. Especially in an academic
discussion.[/QUOTE]You appear to accept that, because of common (mis-)usage, you are liable, perhaps likely, to be misunderstood. Yet you (correctly in my view) set a high premium on the use of precise language which is not easily misunderstood.

An element of willful perversity, perhaps?

Paul

[QUOTE=xilman;205946]You appear to accept that, because of common (mis-)usage, you are liable, perhaps likely, to be misunderstood. Yet you (correctly in my view) set a high premium on the use of precise language which is not easily misunderstood.

An element of willful perversity, perhaps?

Paul[/QUOTE]

Perhaps it is simply that I accept that my wishes in this matter are not
shared by most people. I accept the reality, even if I don't agree with it.

While I clearly am not always perfect in my use of language, I do make
a conscious attempt to say what I mean, and to apply the correct
meaning to words, even if others misinterpret them in practice.

Don't we have a separate thread for 'pet language peeves' in the lounge??

One phrase that really annoys me is "very unique" or "extremely unique".

A large number of people use the word 'unique' either as a subsitute for
'rare', or as a substitue for 'unusual'. Of course it means neither.

Silverman,
As you told me, I stopped conjecturing.
I'm reading the book "Solved And Unsolved Problems In Number Theory" by D. Shanks as you told me.
When you say teachers, you mean lecturers in the university or school teachers?
My teachers at school aren't going to deal with me questions as: "should I try to find new conjectures?", "which book to read".
They will suggest me to learn by a school book.

[quote=wblipp;205886]

1. Estimate the number of primes between N[sup]2[/sup] and N[sup]2[/sup]+2n using the prime number theorem.
2. Use Step 1 to estimate the probability of zero primes in the range using the Poisson Approximation.
3. Use Step 2 to estimate the number of counter of examples for all N > N[sub]tested[/sub], and approximate this sum with an integral.

I think you'll find it a learning experience to give these a try. Let us know how you come along. If you get stuck, post back with information about what you have tried and where you are stuck. See #29 in the ElevenSmooth Math FAQ if you need help with the [URL="http://elevensmooth.com/MathFAQ.html#Poisson"]Poisson Approximation[/URL]

William[/quote]
First of all, I know about the prime numbers theorem, but I can't really use it because I won't use it legal or even logical becuase of my ingnorance. I'll read about the Poisson approximation and if I won't understand something I will tell you.
Thanks Tomer.