Mathematicians Make a Major Discovery About Prime Numbers

[TBoneJack]

http://www.wired.com/2014/12/mathematicians-make-major-discovery-prime-numbers/

 

[heckler73]

Paul Erdos...
Rather appropriate, actually.

 

[TBoneJack]

Paul Erdos...
Rather appropriate, actually.

Yes. He was amazing, wasn't he?

As a young math major in the mid 1980s, I was very interested in prime number theory. And at that same time, a 10-year-old prodigy was being schooled by a patient Paul Erdos. And that prodigy is the one responsible for the recent breakthrough.

 

[heckler73]

Yes. He was amazing, wasn't he?

As a young math major in the mid 1980s, I was very interested in prime number theory. And at that same time, a 10-year-old prodigy was being schooled by a patient Paul Erdos. And that prodigy is the one responsible for the recent breakthrough.

Amazing? That's an understatement.
Amped-up is more what I was thinking
So I guess you know how many people one needs to invite to a dinner party to guarantee at least 3 people know each other or do not know each other.

 

[TBoneJack]

Amazing? That's an understatement.
Amped-up is more what I was thinking
So I guess you know how many people one needs to invite to a dinner party to guarantee at least 3 people know each other or do not know each other.

Not off the top of my head. But I know how many people it takes for there to be an expectation of a birthday (month and day) match.

 

[heckler73]

Not off the top of my head. But I know how many people it takes for there to be an expectation of a birthday (month and day) match.

Oh!
You would probably like this book:

Seriously...if you like Tao and Erdos, that book will "amaze" you It was the strangest "textbook" I have ever read, and one I need to revisit. Part textbook on Ramsey Theory and combinatorics, part history, part treasure hunt (lots of unsolved problems with prizes in there).

This is a good journal on the field:
http://www.integers-ejcnt.org/

 

[TBoneJack]

Oh!
You would probably like this book:

Seriously...if you like Tao and Erdos, that book will "amaze" you It was the strangest "textbook" I have ever read, and one I need to revisit. Part textbook on Ramsey Theory and combinatorics, part history, part treasure hunt (lots of unsolved problems with prizes in there).

This is a good journal on the field:
http://www.integers-ejcnt.org/

Too cool man. I've got an after-Christmas present coming, and I think you just sold me on what I should choose. I gotta give that a good read, SOON.

 

[TBoneJack]

I'm a wannabe-mathematician-turned-software-engineer...but it keeps me warm and safe and dry...much like the great Dan Fogelberg said in song...

 

[Moebius]

Not off the top of my head. But I know how many people it takes for there to be an expectation of a birthday (month and day) match.

How many? ..
30?

 

[TBoneJack]

How many? ..
30?

http://en.wikipedia.org/wiki/Birthday_problem

When the group has 23 people, the probably of a birthdate match (month and day) is 50%. At 30 people it's about 70%. At 70 people it's almost 100%.

n p(n)
5 2.7%
10 11.7%
20 41.1%
23 50.7%
30 70.6%
40 89.1%
50 97.0%
60 99.4%
70 99.9%
100 99.99997%
200 99.9999999999999999999999999998%
300 (100 − (6×10−80))%
350 (100 − (3×10−129))%
365 (100 − (1.45×10−155))%
366 100%

 

[Moebius]

When the group has 23 people, the probably of a birthdate match (month and day) is 50%. At 30 people it's about 70%. At 70 people it's almost 100%.

n p(n)
5 2.7%
10 11.7%
20 41.1%
23 50.7%
30 70.6%
40 89.1%
50 97.0%
60 99.4%
70 99.9%
100 99.99997%
200 99.9999999999999999999999999998%
300 (100 − (6×10−80))%
350 (100 − (3×10−129))%
365 (100 − (1.45×10−155))%
366 100%

Not a bad guess from me though! @30 .... so on a public bus with 30 people on board it is more likely than not (70.6%) that your birthday is shared with another passenger.

http://en.wikipedia.org/wiki/Birthday_problem

When the group has 23 people, the probably of a birthdate match (month and day) is 50%. At 30 people it's about 70%. At 70 people it's almost 100%.

n p(n)
5 2.7%
10 11.7%
20 41.1%
23 50.7%
30 70.6%
40 89.1%
50 97.0%
60 99.4%
70 99.9%
100 99.99997%
200 99.9999999999999999999999999998%
300 (100 − (6×10−80))%
350 (100 − (3×10−129))%
365 (100 − (1.45×10−155))%
366 100%

 

[Moebius]

The problem with that question is what does 'expectation' mean and how do we objectively measure that.? What is expected by one person may not be expected by someone else. ... so the question as you have phrased it does not 'strictly' have a relation to that table of mathematical probability.

 

[TBoneJack]

The problem with that question is what does 'expectation' mean and how do we objectively measure that.? What is expected by one person may not be expected by someone else. ... so the question as you have phrased it does not 'strictly' have a relation to that table of mathematical probability.

The terms "probability", "expectation", and "liklihood" are often used somewhat interchangeably in math talk.

As in "50% probability", "you can expect 50 of 100", or "50% liklihood".

"If you buy a lottery ticket every hour of every day forever, you could expect to win once every 300 years".

Things like that. But strictly speaking, you're probably (no pun intended) right that "probability" is the best choice of words to use.

 

[Moebius]

In the

The terms "probability", "expectation", and "liklihood" are often used somewhat interchangeably in math talk.

As in "50% probability", "you can expect 50 of 100", or "50% liklihood".
"If you buy a lottery ticket every hour of every day forever, you could expect to win once every 300 years".

Things like that. But strictly speaking, you're probably (no pun intended) right that "probability" is the best choice of words to use.

But youre mistaking the term 'probability' in math with the subjective notion of human 'expectation'. They're two completely different things and have been shown so in numerous scientific experiments.


EDIT:
sorry I missed your last sentence. ..I think you understood my point.

 

[TBoneJack]

In the


But youre mistaking the term 'probability' in math with the subjective notion of human 'expectation'. They're two completely different things and have been shown so in numerous scientific experiments.


EDIT:
sorry I missed your last sentence. ..I think you understood my point.

Although not as straightforward as the term "probability", the term "expectation" is an objective mathematical term that is used in probability theory and statistics.

http://mathworld.wolfram.com/ExpectationValue.html

Probability is a term that is equally applicable to one event, or multiple events. For instance, the probability that you will draw a blue ball out of a basket that contains 4 red balls and one blue ball is 20%. But what can you expect? I'm not sure.

But if you repeat that same draw 100,000,000 times (resetting the basket after each draw), you can expect to draw a blue ball 0.20 * 100,000,000 = 20,000,000 times.

Not exactly, I know. But the probability density function is at its peak at 20,000,000 times. And expectation is defined in terms of the probability density function.

 

[Moebius]

Although not as straightforward as the term "probability", the term "expectation" is an objective mathematical term that is used in probability theory and statistics.

http://mathworld.wolfram.com/ExpectationValue.html

Probability is a term that is equally applicable to one event, or multiple events. For instance, the probability that you will draw a blue ball out of a basket that contains 4 red balls and one blue ball is 20%. But what can you expect? I'm not sure.

But if you repeat that same draw 100,000,000 times (resetting the basket after each draw), you can expect to draw a blue ball 0.20 * 100,000,000 = 20,000,000 times.

Not exactly, I know. But the probability density function is at its peak at 20,000,000 times. And expectation is defined in terms of the probability density function.

Although not as straightforward as the term "probability", the term "expectation" is an objective mathematical term that is used in probability theory and statistics.

http://mathworld.wolfram.com/ExpectationValue.html

Probability is a term that is equally applicable to one event, or multiple events. For instance, the probability that you will draw a blue ball out of a basket that contains 4 red balls and one blue ball is 20%. But what can you expect? I'm not sure.

But if you repeat that same draw 100,000,000 times (resetting the basket after each draw), you can expect to draw a blue ball 0.20 * 100,000,000 = 20,000,000 times.

Not exactly, I know. But the probability density function is at its peak at 20,000,000 times. And expectation is defined in terms of the probability density function.

Nothing to do with your original mathematical conundrum. terrible. I'm out.
http://en.wikipedia.org/wiki/Straw_man
http://en.wikipedia.org/wiki/Straw_man

 

[TBoneJack]

Nothing to do with your original mathematical conundrum. terrible. I'm out.

Man, I was trying to be as nice to you and informative as possible. And this is what I get for my trouble.

I wish you well.

 

[Doer]

What does a drowning number theorist say? “Log log log log … ”

Interesting article. IAF (ignore all fools)