Mathematics

[Gear300]

Physics and Mathematics are legends that humankind has adopted. But uhh...we've only gone so far, so...I would like to know for Math, what are the unsolved problems, or situations presented without an effective solution thus far.

[robert Ihnot]

Physics and Mathematics are legends that humankind has adopted.

I find that a confusing statement, care to elaborate?

[Gear300]

I was just trying to find an introduction. I'm supposing you might prefer "...that humankind has created." instead?

[HallsofIvy]

I am perfectly willing to accept that mankind has "invented" mathematics, in the same sense that he "invented" the hammer, but mankind has no more invented physics that it has invented biology or meteorology.

Also, in order not to come to the conclusion that you are being condescending, I have to assume that you do not know the meaning of the word "legend".

And may I ask why this is specifically in the "Number Theory" area rather than "General Mathematics"?

[CRGreathouse]

I would like to know for Math, what are the unsolved problems, or situations presented without an effective solution thus far.

Well, since you posted in the number theory section:
Riemann hypothesis
abc conjecture
twin prime conjecture, or more generally
de Polignac's conjecture on prime gaps, or more generally
Hardy-Littlewood prime constellation conjecture
infinitude of various sets (Mersenne primes, Cullen primes, Woodall primes, Wiefrich/non-Weifrich primes)
Goldbach conjectures (weak and strong)
Collatz/hailstone conjecture
and one of my favorites, the odd perfect conjecture

[Gear300]

heh...well...I see, so these are all current subjects. Thanks. This may be kind of a stupid question, but...what exactly is number theory? Oh and HallsofIvy...I wasn't trying to be condescending...just that I couldn't come up with the right words to define the two (Physics and Mathematics); I just find it amazing that the universe can actually be modeled through the usage of these two. And the reason why this is in the number theory area is probably just because 'number theory' sounded cool so I decided to post in here.

[al-mahed]

some popular and nice books for the lay person know something about math and specially number theory:

http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1202855311&sr=8-2

http://www.amazon.com/Music-Primes-Searching-Greatest-Mathematics/dp/B000BLNP46/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1202855462&sr=1-1

there is a book talking about some of the most difficult unsolved problems in math:

http://www.amazon.com/Millennium-Problems-Greatest-Unsolved-Mathematical/dp/0465017290/ref=sip_rech_dp_7

[Howers]

Well, since you posted in the number theory section:
Riemann hypothesis
abc conjecture
twin prime conjecture, or more generally
de Polignac's conjecture on prime gaps, or more generally
Hardy-Littlewood prime constellation conjecture
infinitude of various sets (Mersenne primes, Cullen primes, Woodall primes, Wiefrich/non-Weifrich primes)
Goldbach conjectures (weak and strong)
Collatz/hailstone conjecture
and one of my favorites, the odd perfect conjecture

I personally think twin primes will fall apart somewhere :P

[ice109]

I am perfectly willing to accept that mankind has "invented" mathematics, in the same sense that he "invented" the hammer, but mankind has no more invented physics that it has invented biology or meteorology.

Also, in order not to come to the conclusion that you are being condescending, I have to assume that you do not know the meaning of the word "legend".

And may I ask why this is specifically in the "Number Theory" area rather than "General Mathematics"?

ofcourse physics was invented. a model is never the thing it models.

[CRGreathouse]

I personally think twin primes will fall apart somewhere :P

You think there are a finite number of twin primes?

[HallsofIvy]

ofcourse physics was invented. a model is never the thing it models.

I bow my head.

[arildno]

I just find it amazing that the universe can actually be modeled through the usage of these two.
Is declaring your personal incredulity the same as a valid argument for your claim?

[ramsey2879]

ofcourse physics was invented. a model is never the thing it models.

Amen to that

[Gib Z]

Physics, by definition of what it means to do physics, is to model the universe. Hence it is not so amazing if it models it. In the process of doing physics we must use some mathematical tools.

[HallsofIvy]

To echo Gib_Z, you are essentially saying that you find it remarkable that a tool designed to do a specific job actually does that job!

Of course, physics models what we know of the universe- it does not model the universe perfectly.