Challenge: Submit Extremely Difficult Math Problems

[HeisenBerg46]

I am looking for extremely challenging math equations/problems to solve. I would appreciate any problems in any field of mathematics (almost nothing is too difficult). Note that I am looking for straightforward problems with an answer (not proving someone else's conjectures). Who knows, others may even appreciate the challenge.

 

[jhae2.718]

Prove that the nontrivial zeros of the Riemann zeta function have a real part of 1/2.

Oh, you wanted problems with an answer...

Maybe try finding the shortest path for a circular object to roll down? ( I.e. the brachistochrone problem.)

 

[HeisenBerg46]

Prove that the nontrivial zeros of the Riemann zeta function have a real part of 1/2.

Oh, you wanted problems with an answer...

Maybe try finding the shortest path for a circular object to roll down? ( I.e. the brachistochrone problem.)

Yes... I was looking for original problems with an answer, not just proofs. But to answer your initial problem, they correspond to the real part of the roots of the xi function, which are more easily calculated. These problems are very interesting though...

 

[micromass]

Find a curve with a given circumference such that the surface area that it covers is maximal. For example, a rectangle with dimensions 3 and 1 has surface area 3. But this is not maximal, because a square with length 2 has the same circumference (i.e. 8), but has surface area 4. Now, what is the curve that has a maximal surface area?

Another, easier, problem is the following. Say that you stand on a point in the earth. And you walk with a velocity v. You always walk in the direction of the moon. But of course, the moon change position, so you would always walk in a different direction.
Find a differential equation which describes the previous process. Now, let's say that you actually did the previous process, then what would happen asymptotically? I.e. if you kept on walking, would you converge to a certain point?

 

[glennroast]

I am looking for extremely challenging math equations/problems to solve. I would appreciate any problems in any field of mathematics (almost nothing is too difficult). Note that I am looking for straightforward problems with an answer (not proving someone else's conjectures). Who knows, others may even appreciate the challenge.

Hi, I am looking for a solution to what I believe is a complex problem (at least for myself but maybe not for you!). I am a computer technican, and I have to get an unlock code for some software on a weekly basis. This can take 5 minutes or over per phone call, and I work with a large team who also have to suffer the same deal, and wanted to save myself and my team a lot of time by generating the codes we need ourselves. The 4 digit codes generated are based on the system date. I know this because I can change the system date in the laptop, and the code for that day works on the software we need to use it for. It's a "code of the day" type problem which I have not found a solution for anywhere else. I have several days worth of codes and their corresponding dates which I can list here:

Code for 09/09/11 is 0953
Code for 10/09/11 is 7487
Code for 11/09/11 is 6993
Code for 12/09/11 is 4955
Code for 13/09/11 is 8361
Code for 14/09/11 is 6999

What I wanted to know is, what is the algorithm used to generate the 4 digit codes based on the systems date? There could be other implications such as the week number in the year being used for the working formula, date shifting, division, subtraction, multiplication or addition with a constant set of numbers being used to generate the code. If you could help me, I would greatly appreciate it and pay homage to your superior intellect! So far, nobody I know and nobody on the internet has managed to write code to solve this, and I would really like to write a program to generate the code if I knew the algorithm/formula used.

Many thanks for your time,

GlennRoast.com

 

[disregardthat]

http://mks.mff.cuni.cz/kalva/

I'm sure you'll get stuck at some point here ;)

 

[LCKurtz]

Maybe try finding the shortest path for a circular object to roll down? ( I.e. the brachistochrone problem.)

I think you mean least time. A frictionless bead slides down a curve from point A to point B under the acceleration of gravity. Find the curve resulting in the least time to traverse.

 

[mathwonk]

let π be the finite degree projection from the space parametrizing lines on all cubic surfaces in P^3 to the space of all such cubic surfaces. prove that if (L,S) is a point of the domain corresponding to a cubic surface S and a line L on S, that the differential of π has as image exactly the vector space of those cubic surfaces which meet S at least along the set where L meets the singular set of S. (For definitions, see Mumford, Algebraic geometry I, Complex projective varieties), last chapter.)

or if you want this phrased so that it is a problem and not a "proof", compute that image without me telling you the answer.

 

[HallsofIvy]

Find two sets, P and Q, satifying these properties:
1) P and Q are both completely contained in the square in R² determined by -1\le x\le 1 and -1\le y\le 1.

2) P contains the diagonally opposite points (-1, -1) and (1, 1) and Q contains the diagonally opposite points (1, -1) and (-1, 1).

3) P and Q are both connected sets (in the usual topology for R²).

4) P and Q are disjoint.

 

[pwsnafu]

Solve the log-sine integrals. That is define
S_k = (-1)^k \int_0^1 \log^k (\sin \pi x) dx
and show
S_k = \frac{(-1)^k}{\sqrt\pi 2^k} \frac{d^k}{d\alpha^k} \frac{\Gamma(\alpha+1/2)}{\Gamma(\alpha+1)}
with \alpha=0.

Find the recurrence for the S_k, and hence show
S_4 = \frac{19 \pi^4}{240}+\frac{1}{2} \pi^2 \log^2 2 + \log^4 2 + 6 \log 2 \, \zeta(3)

Show the following:
\int_0^1 \log \log (1/x) \frac{dx}{1+x^2} = \frac{\pi}{2}\log (\sqrt{2\pi} \Gamma(3/4) / \Gamma(1/4))

 

[BloodyFrozen]

I think you scared him away.

 

[thembonez]

Challenging Math

Hello,
I have been trying to solve this problem and then I came across this thread on google and I thought I'd submit it to you.

Basically, the formula is y=x/log(x).

I want to solve this for x.

So basically, y equals a number divided by is natural logarithm.
But what if I have y, can I solve what number divided by its natural log equals that.

Is that possible?

Thank You
Barry

 

[micromass]

Hello,
I have been trying to solve this problem and then I came across this thread on google and I thought I'd submit it to you.

Basically, the formula is y=x/log(x).

I want to solve this for x.

So basically, y equals a number divided by is natural logarithm.
But what if I have y, can I solve what number divided by its natural log equals that.

Is that possible?

Thank You
Barry

You can probably solve it with the Lambert W function. Otherwise, no. http://en.wikipedia.org/wiki/Lambert_W_function

 

[MathematicalPhysicist]

Prove/disprove God's existence and/or uniquness.

Godspeed!

 

[HallsofIvy]

Hi, I am looking for a solution to what I believe is a complex problem (at least for myself but maybe not for you!). I am a computer technican, and I have to get an unlock code for some software on a weekly basis. This can take 5 minutes or over per phone call, and I work with a large team who also have to suffer the same deal, and wanted to save myself and my team a lot of time by generating the codes we need ourselves. The 4 digit codes generated are based on the system date. I know this because I can change the system date in the laptop, and the code for that day works on the software we need to use it for. It's a "code of the day" type problem which I have not found a solution for anywhere else. I have several days worth of codes and their corresponding dates which I can list here:

Code for 09/09/11 is 0953
Code for 10/09/11 is 7487
Code for 11/09/11 is 6993
Code for 12/09/11 is 4955
Code for 13/09/11 is 8361
Code for 14/09/11 is 6999

What I wanted to know is, what is the algorithm used to generate the 4 digit codes based on the systems date? There could be other implications such as the week number in the year being used for the working formula, date shifting, division, subtraction, multiplication or addition with a constant set of numbers being used to generate the code. If you could help me, I would greatly appreciate it and pay homage to your superior intellect! So far, nobody I know and nobody on the internet has managed to write code to solve this, and I would really like to write a program to generate the code if I knew the algorithm/formula used.

Many thanks for your time,

GlennRoast.com

Since you have given 6 values, it would be pretty easy to find a 5th degree polynomial that will give those 6 values. But there is no reason to believe that would give the next value. There is NO way to determine, from just a finite number of values, what is the algorithm.

 

[WaaWaa Waa]

How 0.(9) should be converted to fraction?

 

[micromass]

How 0.(9) should be converted to fraction?

That would be the fraction $\frac{1}{1}$. That was not a difficult problem

 

[WaaWaa Waa]

That would be the fraction $\frac{1}{1}$. That was not a difficult problem

Right, and IMHO, the best argument for demonstrating that 0.(9) and 1 are exactly equal

 

[WaaWaa Waa]

That would be the fraction $\frac{1}{1}$. That was not a difficult problem

Could you show me the process please and how $\frac{1}{1}$ is to be onverted back to 0.(9), if its not too much trouble

 

[Enigman]

A monk climbs to the top of a certain mountain with unequal speeds and random stops of random durations, he reaches the top at the sunset of the 13th day from the start. After meditating there for a week, he starts climbing down the mountain at the sunrise with unequal speeds and random stops. The speed while climbing down is obviously greater than speed climbing up. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.
Mr.E

 

[BrettJimison]

prove aⁿ+bⁿ ≠ cⁿ unless n ≤ 2.

Are you good at elliptic curves and modular functions?

 

[pwsnafu]

A monk climbs to the top of a certain mountain with unequal speeds and random stops of random durations, he reaches the top at the sunset of the 13th day from the start. After meditating there for a week, he starts climbing down the mountain at the sunrise with unequal speeds and random stops. The speed while climbing down is obviously greater than speed climbing up. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.
Mr.E

That one is trivial. Instead of one monk traveling on two days, you visualize two monks traveling on a single day. The two monks must meet at some point along the trail.

 

[WaaWaa Waa]

@OP, I would be very grateful if you explain Godel's Incompleteness Theorem in simple English and in a very easy to understand manner.

 

[Robert1986]

That one is trivial. Instead of one monk traveling on two days, you visualize two monks traveling on a single day. The two monks must meet at some point along the trail.

You seem to be confusing "trivial" with "the solution is short to write down."


I don't think that this problem is all that trivial, and your solution is certainly not. I haven't really given it much thought, but I think most people would use the intermediate value theorem or something. Your solution, on the other hand, is more elegant and not at all trivial.

 

[rumsant]

I don't know how to figure this out. I hope I explained it in a way that's understandable.

 

[mfb]

Sidewards forces (as in the last image) make the problem underdetermined, the answer will depend on unknown details of the blocks like elasticity and so on.

 

[rumsant]

Sidewards forces (as in the last image) make the problem underdetermined, the answer will depend on unknown details of the blocks like elasticity and so on.

Granted, this is all out of my realm of expertise, but would it be possible to solve if you made some assumptions in order to simplify the problem as much as possible? i.e.: no elasticity, etc. (basically assuming a very simplified, isolated environment for this problem).

 

[mfb]

No elasticity is exactly what makes it underdetermined.
You can modify x to make some forces equal, but as long as the green shape is bounded by A and B on both sides as in the sketch sidewards forces cannot be calculated in a meaningful way.

 

[IndigoLaser]

Consider this recursive function: (2¹⁶ = 65536)

I've concluded that x_i will be equal to 0 again for any positive odd integers a and b where i ≤ 2¹⁶
If a and b can let this recursive function generate 2¹⁶ non-repeating x values (x_2¹⁶ is equal to 0 again), (a,b) is considered a solution.
How do I find solutions to this function?
I've created a https://04d0baa7da66c2f6a93b52f50a7fe97d93f53104.googledrive.com/host/0B6SNz1_WgxrsUGhWa3lzWWp2ZHc to find solutions (there are a lot of solutions, but I don't know how to get to them). Along with it is some additional information of the code.