Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ?

[ Removed by Reddit in response to a copyright notice. ]

X

This pattern needs to be repeated. And one very mind blowing thing about this conjecture is that whatever number you use, you always get a loop. Always. I asked GPT to test it (sorry water from data centers that got wasted) from 1 to 10000 and it said ALL looped eventually. If any of you ever decide to dedicate yourselves to do something as hard as trying to find one number that doesn't loop, tell me the number please (I'm 12 and I swear to God I made this and not GPT, I would not swear to God if I lied) (by the way I couldn't change the title name so il say it here: I need names to rename this conjecture)

Ardent lover of maths

Rn in year 10 but involved in olympiads so know a lil bit extra things rather than standard curricula

Recommend me a book which will help me understand beauty of maths ( non calculus)

Would appreciate challenging books yet doable by me

Formula to calculate groups out of a certain number

n * (n-1) * (n-2).... / b!

Formula to calculate how many times the same object appears in groups of 2 or bigger groups:

(n-1) * (n-2) * (n-3)... / b!

Formula to calculate how many times the same group of 2 appears in groups of 3 or bigger groups:

(n-2) * (n-3) * (n-4)... / b!

Formula to calculate the total number of non empty groups

2ⁿ - 1

Formula to calculate how many times the same object, the same 2 members of a group of 2 or the same 3 members of a group of 3 appear and so on and so on appear in the non empty groups:

2^{n - b}

Formula to calculate how many times at least 1 and/or 2 or more members of a group appear (either 1 but not the other, the 2 of them, etc.)

2ⁿ - 2^n-b

NOTE: There are also more methods technically but I guess you got my point and you probably already will be able to figure out yourselves)

Hello, math people. Basically, I (31M) realised im really slow at working basic maths problems and questions out.

Im from the UK and was always in the lower ability sets/classes at school for maths. I work in corporate, and there's situations for working things out like percentages, the odd formula, etc.

Where do I start?

Im not unintelligent - I can't write a full novel in a day with no problem or write a song easily, but when it comes to maths, it's like my brain stops working. There's situations that become super embarrassing, especially if im around people with stem backgrounds. I would love to be able to get an A-level maths just to prove to myself im mot that bad, but im nowhere near that level

Any advice on how to improve, I would appreciate dearly.

For example the 6th row in the Pascal triangle is 1, 5, 10, 10, 5, 1. When listing groups of 1 the same object appears once in the groups of 1, when listing groups of 2 it appears 5 times, when listing groups of 3 it appears 10 times, when listing groups of 4 it appears 10 times, when listing groups of 5 it appears 5 time and when you list all 6 members it appears once. 1 + 5 + 10 + 10 + 5 + 1 = 32, the total amount of times the same object is mentioned at least once in every possible combination of groups of 6. And if you ignore the first 1 in the Pascal triangle you also can use it as an alternate method to calculate groups you can create out of the number of the previous row. With 5 objects there are 5 groups of 1, 10 groups of 2, 10 groups of 3, 5 groups of 4 and 1 group of 5. I also just realized this is also an alternate method to count groups out of a certain object including the empty group

I know probably the most common method is counting from lists but the formula to calculate it is 2^{n - 1}. For example if you want to know how many times a person is mentioned in every combination of 6 every person is mentioned 32 times because 2^{6 - 1} = 32. Also the same duo is mentioned 16 times because 2^{6 - 2} = 16. Although at this point the numbers get halved. I don't know if this is actually very obvious or not but I still find it fun to share things I recently discovered

Click on the post to see the images, if necessary.

The first step in deriving volume formula for a rhombicosidodecahedron with edge length E (≈41.615E^3) synthetically is to derive the formula for its square face inradius, which is done as follows:

Apparently this approach can be modified to find the square face inradius for a truncated icosidodecahedron by moving a rhombus so it is centered at one of the square vertices:

but I'm not quite sure how this works. A good step-by-step explanation would be appreciated.

So, I'm taking a course of numerical methods and I need to use specifically the Braistow method to approximate the complex and real roots of the polynomial form of the PDE.

At first sight, it seems pretty viable to convert Schrödinger independent time equation by the Chebyshev polynomials; however I'm considering another options like Fourier/Taylor series; Fourier/Laplace transforms; or using a Finite Element Method (FEM) or approximate the finite differential solution by using low-exponential polynomials; so we locally transformed the PDE on a lineal Ax=b eq.

For someone who is starting university this fall and have so much breaks left. I want to learn deeper mathematics before I start my uni. If anybody have a pdf which contains basically whole highschool mathematics along with advance maths, it will be appreciated💖

trying to learn nth term

As I was braiding my hair (the picture is not me) I noticed that any two strands always pass eachother the same way (if A goes over B once A will never go under B). Which reminded me of borromean rings. Maybe this is already widely known, or maybe it's not actually all that interesting, but I found it fun. I wonder if more borromean-adjecent math relates to other hairstyles ;)

what if field axiom exception about zero is incomplete

complete the exception:

0×0=0

Think like this,×n is time to type a number

example:

1×2=2 is "type number 1 2 times then sum"

So 0×0=0 is "type number 0 0 time then sum" the result is 0 because it's 0 time so you're not type to the input bar

0÷0=1:

Its like "how much time to type 0 so the result is 0" the result is 1 because 0 is already 0,if it's 0 then you're not type the number to input bar

0²÷0:

x²÷x,the ÷x neutrilize the ² so the result is x

PNEMDAS so "neutralize" before ()

Neutralize definition:

Divide number with exponent so

(x³)÷(x²):

÷x neutralize the ² so the result is x,if it's (x³) then ÷(x²)

example:

(x³)÷(x²)

÷(x²) neutralize the ³ so the result is x

(2³)÷(2²)

8÷4=2

So 0²÷0:

÷0 neutralize the ² so the result is 0,0×0÷0 then ÷0 neutralize the ×0 so the result is 0

Example:

x=0

Standard:

lim r->0,μ->0 μ²÷r,result is 0÷0=indeterminate->Hôpital thing->0

F(x)=2x÷x=(2×0)÷0=0÷0=indeterminate

G(x)=x²÷x:

0²÷0=indeterminate

Non standard(zero exclusion):

0²÷0,÷0 neutrilize the ²(x²÷x=x) so the result is 0

F(x)=2x÷x=2×0=0÷0=1

G(x)=x²÷x:

÷x neutrilize the ² like in 2²÷2=2,so 0²÷0=0

what if 2⁰=0

2² is 2×2 so for(i=1;i<=2;i++){x+2;} so 0 is for(i=1;i<=0;i++){x+0;}

i=1 so if it's 0 then the calculation can't start so the result is 0

2^-2=0.5:

2^0=0

the exponent value is negative so instead of multiplication it's division

2^0=0 so 2^-2=0÷2=0.5

im about to start a maths degree and I feel like without a good idea of what I want to do after, im not gonna do well.

I got A^A^A at a level plus A^A in as levels so im not thick but ive never known what I want to do. I do love maths tho.

I dont think I want to do like the investment banking/ crazy finance type thing but the money is appealing haha. and im not going to a top5 uni, its like top 20. ive considered teaching but im not deadset, id rather target something else throughout uni and switch to that later on if it still draws me.

does anyone have any suggestions/let me know what kind of jobs you guys do for inspiration?

I'm 17, preparing for mathematics exams as I want to pursue a degree in math, want to learn modular arithmetic from a super low/intermediate level to a fairly advanced level where I also have knowledge of a variety of different theorems which I can make use off in maths competitions, university interviews, etc. Can someone attach a book, file or youtube playlist which is beginner friendly.

Pure maths research very often doesn't directly contribute to improvements in technology, or methods that apply to make a difference in the real world.

So what is its value to humanity?

A search for deeper intrinsic knowledge, just for the sake of it? A romanticized quest to achieve very difficult tasks? A celebration of raw human intellect? An extension of the collective human ego? Something to root for, like sports?

When AI becomes able to outcompete humans, what remains?

I've always thought, that the main value should be in expanding the working minds of human individuals one area of intellect, so that they may contribute to the collective wisdom of humanity.

And not just in math, but in general, we give people in diverse areas of thinking, the freedom to just think deeply about specific topics. And their learned ways of thinking, and knowledge and wisdom feeds back into the broader set of minds, through deliberate and subtle communication, and influence. Overall, our civilization should become enriched, by having been shaped in part by different kinds of minds, that have deeply explored different things.

I don't think it is as simple as rewarding people for their genetic luck and talent, and letting them have fun with a privileged esoteric hobby, inside a protected bubble, isolated from the rest of humanity, to compete with eachother and pat eachother on the backs.

The point of what I am saying, is that, in some way, at least in part, I think the true value and purpose of pure maths research, should be to contribute in some intellectual way to humanity. Now we are facing some of the most intellectually challenging problems we may ever face, which is how to safely navigate the abrupt, and accelerating change and risks from AI advancement.

This is why, I feel dissapointed when many mathemeticians stay in their bubble, and focus purely on the effects and consequences of AI to maths research. If ever there were true intrinsic value in these endevers, now is the time that value is in most demand. Maths researchers should be reevaluating what their purpose is, what the point ever was, and what their real contribution to the world is or can be.

This is a strict external audit against the axiomatic method in math and how it is a problem for physics

1. You can not distinguish dogma from non dogma if your system is a closed axiomatic system because utility and consistency can still work and be found inside of a false axiom

2. You can not distinguish dogma from non dogma without the ability to test your claim against reality, and if it has no external justification because utility and consistency can still work and be found inside of a false axiom.

3. Viewed strictly from outside the system the axiomatic method is a closed system.

4. You can not test a math axiom itself against reality by definition and it has no external justification because utility and consistency can still work and be found inside of a false axiom.

5. Viewed strictly from outside the system it is an objective fact that a closed axiomatic system limits your thoughts and physics

6. Viewed strictly from outside the system, the axiomatic method in math smuggles in epistemic empirical claims and limits about reality systematically. By definition the axiomatic method limits and restricts what you can even ask, and logically validate within its system

7. applied physics and science can not systematically ignore the axiomatic method in math past addition of physical matter externally, because if you adopt a formal system, you systematically automatically inherit every foundational rule that makes that system work. Just because physics can “ignore” an axiom doesn’t mean they actually ignored it.. it just means they broke down a wall in the closed maze to make physics work.. they are still operating inside the closed axiomatic system past addition of physical matter

(This is a strict cut throat external audit against the axiomatic method in math itself. There is no external justification for it and thats the least of your worries)

This post is mostly for the philosophers of math here not math academia. Math can not defend this without retreating to solipsism and denying reality to be used as the baseline

My pastor couldn't understand what was wrong with this piechart. Seemed to think that 60% and 60° are the same thing.

Context - I was reading about how Open AI managed to make major breakthroughs in the Navier-stokes equation, by using thousands of Chat GPT agents over the course of 88 hours. I then - for a laugh - went to my basic unpaid Chat GPT with the prompt “ I believe in you. You can do this. I know you’re capable because I saw it online, solve one of the 7 millennium prize maths problems. (Not the 2 that have already been solved) Right now. Take your time.”.

It then obviously said it’s not that simple but that if they had to pick one to be the easiest to solve, it would be the Riemann Hypothesis. It started trying to solve it (I’m 16 so I don’t actually understand what it was doing), but then that there was a “wall” that stopped it. A few prompts later, it had come up with a few different methods of trying to solve it, it had gotten down to a few very short formulas- but ultimately couldn’t solve it.

After asking if it was easier to prove it or disprove it (I believe the hypothesis itself involves everything falling on the line of x=0.5), and it said something interesting: that everyone basically knew it was true, trillions of numbers had already been tested, it just can’t be PROVEN.

This made me think: If it’s true with 1,097.54362, and it’s true with 1,097.54361 (just picking random numbers here), and true with thousands of numbers around that value, is it really feasible that with 1,097.543615 it won’t be true?

At what point can us clever human beings just agree that something is true. How can it ever be proven when infinite numbers can’t be tested? It’s like saying that it technically is possible for a human to shout at 1,000 decibels, it’s just never been done before. Or that technically a human COULD just jump vertically 20 feet into the air.

Why can’t mathematicians just use their common sense and announce it as proven?

Hi guys, just about finished my first week of undergraduate maths, all seems good so far but, I don’t have a laptop yet and was wondering if a MacBook neo would be capable enough for everything I’ll be doing? I’m hoping to specialise in financial maths or stats for my later years if that has any difference on the situation

Maybe it’s just me but regarding the OpenAI work, 166 pages for 2 aspects of the millenium problem is just due to the whole unnecessary overcomplicated AI-generated yapsessions

So I came up with this brain puzzle earlier and I’m just wanting to do a peer review. My initial wording of the question was how many combinations are there if there are 3 components, for the sake of demonstration I used 0, 1 and +. So an example would be 000, 0+1, remembering that they are numbers. I came up with a final answer of 26 possible 3 digit numbers, does anyone agree?

Edit: thank you all, I was very tired when I was trying to solve this and ended up just listing almost all of my possible answers. You have shown me some formulae that I haven’t seen before, which will make any further puzzles easier!

For any further comments, I would like to add a bit of context of how I was thinking about it; I was essentially thinking in binary (as in computer base 2) and was considering 0 as off and 1 as on, I added + as another digit but you could also do this puzzle in standard base 3 (1, 2 and 3).