Physics and Mathematics - what are the unsolved problems?

In summary: There are still unknowns. However, we can make educated guesses about what is out there based on what we know.In summary, although the universe is vast and mysterious, humankind has made significant progress in understanding it through the use of physics and mathematics. There are still many unsolved problems and mysteries in these fields, but that is only due to the fact that there is still much to be learned.
  • #1
Gear300
1,213
9
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.
 
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  • #2
Physics and Mathematics are legends that humankind has adopted.

I find that a confusing statement, care to elaborate?
 
  • #3
I was just trying to find an introduction. I'm supposing you might prefer "...that humankind has created." instead?
 
  • #4
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"?
 
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  • #5
Gear300 said:
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
 
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  • #6
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.
 
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  • #8
CRGreathouse said:
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
 
  • #9
HallsofIvy said:
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.
 
  • #10
Howers said:
I personally think twin primes will fall apart somewhere :P

You think there are a finite number of twin primes?
 
  • #11
ice109 said:
ofcourse physics was invented. a model is never the thing it models.

I bow my head.
 
  • #12
Gear300 said:
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?
 
  • #13
ice109 said:
ofcourse physics was invented. a model is never the thing it models.

Amen to that
 
  • #14
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.
 
  • #15
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.
 

Related to Physics and Mathematics - what are the unsolved problems?

1. What is the current understanding of the connection between physics and mathematics?

The current understanding is that physics and mathematics are deeply intertwined, with mathematics providing the language and tools for describing and predicting physical phenomena. However, there are still many unsolved problems in both fields that require further research and collaboration.

2. What are some examples of unsolved problems in physics and mathematics?

Some examples include the unification of general relativity and quantum mechanics, the nature of dark matter and dark energy, the existence of parallel universes, and the Riemann hypothesis.

3. How do unsolved problems in physics and mathematics impact our daily lives?

Unsolved problems in physics and mathematics may not have an immediate impact on our daily lives, but they are crucial for advancing our understanding of the fundamental laws of the universe and developing new technologies. For example, the development of quantum computers is heavily reliant on solving problems in quantum mechanics and mathematics.

4. What role do scientists and mathematicians play in solving these problems?

Scientists and mathematicians work together to solve these problems by conducting research, developing new theories and models, and testing them through experiments and simulations. Collaboration and interdisciplinary approaches are key to making progress in these complex and challenging problems.

5. Are there any efforts being made to solve these problems?

Yes, there are numerous efforts being made by scientists, mathematicians, and research institutions around the world to solve these problems. Many conferences, workshops, and research projects are dedicated to tackling these challenges, and new technologies and advancements in computing are also aiding in the progress towards solving these problems.

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