most hardest maths problems remain unsolved#maths #viral #top10 #hardestdifficulty #shorts #fyp

[dustymiller]

...I wonder what my mom is making for dinner?

[A_real.genius_munkh]

The expression given in the image defines the Euler-Mascheroni constant, denoted by \(\gamma\):

\[
\gamma = \lim_{n \to \infty} \left( \sum_{k=1}^n \frac{1}{k} - \ln n \right)
\]

The Euler-Mascheroni constant arises in number theory and analysis and is defined as the limiting difference between the harmonic series and the natural logarithm.

To determine whether \(\gamma\) is rational, we need to explore the properties of this constant.

### Steps to Understand \(\gamma\):

1. **Harmonic Series**: The harmonic series \(\sum_{k=1}^n \frac{1}{k}\) grows without bound as \(n \to \infty\), but it does so very slowly.

2. **Natural Logarithm**: The natural logarithm \(\ln n\) also grows without bound, but it does so more smoothly compared to the harmonic series.

3. **Limiting Difference**: The constant \(\gamma\) is defined as the difference between the harmonic series and the natural logarithm as \(n\) approaches infinity. This difference converges to a finite value.

### Rationality of \(\gamma\):

The exact nature of \(\gamma\) (whether it is rational or irrational) is still an open question in mathematics. No proof currently exists to definitively show whether \(\gamma\) is rational or irrational. Most mathematicians believe \(\gamma\) to be irrational due to its properties and the nature of other constants defined similarly, but this has not been proven.

### Conclusion:

The expression provided defines the Euler-Mascheroni constant \(\gamma\). As of now, it remains unknown whether \(\gamma\) is rational or irrational. This is one of the many open problems in mathematics. This is the answer to the first one...

[insert_very_cool_name]

On the 1st No, \( \gamma \) is not rational.

The constant \( \gamma \) is known as Euler's constant or the Euler-Mascheroni constant. It is defined as the difference between the harmonic series and the natural logarithm of \( n \) as \( n \) approaches infinity. In other words, \( \gamma \) is the limit of the sequence \( \left(\sum_{k=1}^{n} \frac{1}{k}-\ln n\right) \) as \( n \) tends to infinity.

The rational numbers are numbers that can be expressed as the ratio of two integers. However, \( \gamma \) is an irrational number, which means it cannot be expressed as the ratio of two integers. It has been proven that \( \gamma \) is transcendental, meaning it is not a root of any non-zero polynomial equation with integer coefficients. Therefore, \( \gamma \) is not a rational number. Also the "\(/gamma \)" and other stuff doesn't work in youtube lmao

[dustymiller]

If an intelligent A.I. looked at the problem but could not come up with a solution, would it really "bother" the A.I.? Alternately, does finding a solution to a problem not directly affecting life and living, really matter?
Is there a boundary where the realm of Practicality ends and you cross over into the realm of Theory? Should you really expend the energy to do so?

[KOl-xjjt]

function loop test 1=1, n=1 all solved

[Chintu]

I heard that Riemann Hypothesis was solved by an Hyderabad professor 2 years back

[SunshineMember]

well wanna know how to solve "The Collatz Conjecture" well *Here how it works*

1. Start with any positive integer 𝑛.

2. If 𝑛 is even, divide it by 2.

3. If 𝑛 is odd, multiply it by 3 and then add 1.

4. Repeat this process with the resulting number.

Hope this helps! *I am honest that i solve this by myself and the help of my smartest friend!*

[tagabukidviners]

Yeah I think my brain it's just flew up

[HavocX]

Me thinking I am smart able to do algebra😮

[The_Prime_MEMEister]

Answer to number nine is approximately 5.859

[Michael-smpi]

The 9 is easy is 3, 14 plus e
3, 14plus 5 total is1, 39

[jojobladerz]

1st. If u do a rational math and non rational to get the answer it’s not rational,

2nd. The deal is that the rotations in the plane are exponentiations in complex number.

3rd. What is the largest cardinal project? Easy! It’s a project full of hard and complex math! And also, the largest and complex numbers expanding!

4th. What’s the unknotting equation? Easy! It’s the equations that look like a circle and get more complex! With the numbers for example, 7⁶ but its the down version

5th. Whats the kissing number? simple! Its equations about geometric problems that ask the amount of spheres that can be arranged tangent to a given sphere!

6th. The birch and switterton info? Simple! In the mathematics, this describes tue only set of rational solutions ti the equations shown for this for defining an elliptical curve

7th. The riemann hypothesis. This is a conjecture of mathematics, that the riemann zeta function itself has only zeros, even negative integers

8th. The twin prime conjecture. The same as cojecture as the birch and swinnerton. Ig

9th. The goldbach's conjecture. A triangle of numbers, that is one of the most well-known unsolved problemsin all of the number theory, still remains unsolved.

10th. The collatz conjecture. Consider the following operaion on a arbitrary positive integer 1. If the number is even, divide it by 2, if the number is odd, triple it and add one. From what we read of the wiki

[Exnokagam]

😂😂😂the collaz conjesture
Easy if we could pick any number lets take 3 devide by 2 equal 1.5 in ther we brokes the problem they you end withe 1 4 problem nah
We finish 1.5 devide by 2 give you 0.75 devide by 2equal 0.375 do the same thing until we get 0 so (n)equal 0 0done

[guyfromDK]

9th one
e is the exponential value = 1.73....
π is + 3.14...


4.87.... is the answer