I was playing around with number strings and noticed a really strange pattern. If you break consecutive numbers into groups that grow by one each time, a math magic trick happens where Pi (π) suddenly appears.

Here is how the grid starts:

* Group 1: 1

* Group 2: 2, 3

* Group 3: 4, 5, 6

* Group 4: 7, 8, 9, 10

* ...and so on.

Let's take Group 4 (7, 8, 9, 10) as an example. The size of this group is 4 numbers.

Now, pick each number in the group and find the absolute differences between it and all the other numbers in the same group, then add those differences up:

* For 7: The differences to 8, 9, and 10 are 1, 2, and 3. (1 + 2 + 3 = 6)

* For 8: The differences to 7, 9, and 10 are 1, 1, and 2. (1 + 1 + 2 = 4)

* For 9: The differences to 7, 8, and 10 are 2, 1, and 1. (2 + 1 + 1 = 4)

* For 10: The differences to 7, 8, and 9 are 3, 2, and 1. (3 + 2 + 1 = 6)

Next, take the reciprocal (1 divided by the sum) for each number, and add them all together:

* (1/6) + (1/4) + (1/4) + (1/6) = 0.8333

Finally, multiply that total by the size of the group (which is 4):

* 0.8333 × 4 = 3.3333

Here is the crazy part: As you go deeper down the grid and the groups get bigger, this final number locks directly onto Pi (3.14159...)!

* With a group size of 10, the answer is 3.1709

* With a group size of 100, the answer is 3.1418

* With a group size of 1,000, the answer is 3.14159

High school Students btw ;(

So for a while now,I have been seeing not many people being active on this sub as before. You can only find them under a new open problem proof, is this the observation with you guys too or am I missing something?

Also,it would be great if you can share your thoughts on other experiences of yours also related to this sub lately along these lines :)

Are there any good mathematics discord servers that are more focused on math discussion/research than homework help? I just joined the first math server I could find and was a bit dismayed to discover it is filled with hapless students. Is there anything better?

As the title states, also how complex can it get?

I genuinely want to learn mathematics, physics, programming, computer science, and AI. I want to build a career in computer science, pursue AI research, and hopefully do a PhD someday. But lately, I've been feeling increasingly demotivated.

The problem is that I rely on AI to learn almost everything. Whenever I have a question, I ask GPT. Whenever I don't understand a concept, I ask AI to explain it. And the more I learn this way, the more I wonder: What's the point of learning anything when AI will always know more than I ever could?

Even the most basic AI models seem to possess more knowledge than I could acquire in a lifetime. And with new models becoming increasingly capable, I keep wondering whether the knowledge I'm working so hard to gain will even matter in the future.

With GPT-6, Claude Opus 5.5, Gemini 4, and other models competing to become more capable, it feels like the gap between human intelligence and AI capabilities will only continue to grow.

I want to understand the mathematics behind AI, learn physics, become a better programmer, and contribute to actual research. But sometimes I question why I'm putting in the effort when AI can explain concepts faster, write code better, and potentially solve problems that I might spend years learning to solve myself.

And even when I genuinely want to learn, I'm confused about what I should prioritize learning and whether any of it will remain valuable by the time I become proficient.

I'm not necessarily saying that learning is useless. I genuinely love the idea of understanding how things work. But I'm struggling to reconcile that curiosity with the feeling that AI might eventually outperform me at almost everything I want to become good at.

For those of you studying computer science, mathematics, physics, or AI, how do you deal with this feeling? How do you stay motivated to learn when AI is advancing so rapidly? Do you think deep technical knowledge will still matter for people pursuing AI research and PhDs, or should we be approaching learning differently now?

Yeah so I have this question as a non math student in commerce but I have friends who have taken applied math and I can understand the reason but the thing is that they were upset because my school didn't give the option of taking core math with commerce and I was confused asf like why do you want to do trigonometry etc what's the point? Can people here tell me the reason 🤔.

This rather surprising 4x4 magic square features 13 cells that revolve around three constants: 11, 13, and 15. By extension, 24 (11 + 13) and 28 (15 + 13) also appear.

I do not think I have discovered everything in this magic square, which is why I am asking for your help.

So, the proof in question is simplified (look, I know just enough to get into trouble) as .9 repeating is equal to 1. And the reason for that is because there's no number in-between 1 and .9 repeating, as well as 3/3 is equal to both .9 repeating and 1.

So now that we have that explained, now to follow another train of logic, which is the concept of infinity, or more specifically the concept of infinity+1, as we all should know about the infinite hotel concept, I shall paraphrase. The infinite hotel goes as such "you have an infinite hotel with infinite rooms, they are all booked, someone comes in and asks for a room, you get the idea to move everyone one room over, thus giving you a free room to house the new guest, which comes out to mathematically, infinity+1."

With those two concepts given, my proposed proof is this, you could have a number in-between 1 and .9 repeating if you do this equation, ".9 repeating+.0 repeating9" (I apologize for the formating, mobile isn't the best)". Why does this not work? I do realize that my idea is very elementary at best, but I am very curious in the explanation (due to my elementary understanding of infinity and the such).

Edit: I had a full misunderstanding on .999... (I learned a better way to display it) and how Hilbert's Hotel works, thank you guys for explaining it better than how've I been explained prior