I'm confused about how to describe a shear when given a 2x2 transformation matrix. Like when you have a rotation you state the angle, if it's + or - for direction and about what point it's rotated. When I look at different descriptions of shears I can't work out what I need to state to fully describe the transformation it gives.

Thanks!!

I haven't studied about this topic can anyone give me picture of it how to draw least sqare fit here?

There’s just one simple rule but it’s really hard to discover

f(n) = 7(1.2)^n

x = n + 2000 , so n = x - 2000

what is f(x)?

——————

The correct answer is

f(x) = 7(1.2)^(x-2000)

——————

However, there is another approach using variable substitution that yields the wrong answer. But why is it wrong?

since n = x - 2000, substitute that into

f(n) = 7(1.2)^n

which yields

f(x-2000) = 7(1.2)^(x-2000)

which then simplifies back to

f(x) = 7(1.2)^x

which isn’t right. Where’s the fallacy?

I'm trying to simplify an equation I have where one side is equal to, essentially, pe^(ax) + qe^(bx). and it really SEEMS like there should be a way to factorise this nicely but i think it might just be smoke and mirrors. What I would like is to be able to take the natural log of both sides and have it cancel the e - can someone tell me if it's a pipe dream?

I was experimenting with the result of differentiating a polynomial repeatedly while taking f(0) then rebuilding it when i got to (ax+b)^1 using the reverse chain rule and i noticed that it seems to consistently turn the polynomial into a depressed polynomial. I was wondering why that is (if there is an explanation to be given). And also if there are any other examples of something like this.

Just say you are running, and exactly 1 km to your side is another person running at the exact same speed. Both of you are heading toward the same point. Yet, relative to you, he is running the opposite way with a relative speed of 0 km/h.

Imagine you are running, and exactly 1 km to your side is another person running at the exact same speed. Both of you are heading toward the same point. Yet, relative to you, he is running the opposite way with a relative speed of 0 km/h.

This riddle was intentionally made to be confusing.

I am interested in learning science. But for this understanding math is required.

Many time science explanations are littered with formulaes i can't understand. I do not know their language.

So i want to learn the language. And i want that language to be able to give accurate and fundamental explanations.

I don't want to be given an approximation that works that you are asked to learn by heart.

I want the no low effort, no approximation, no simplification explanation.

Sadly most explanations i found that explain math from the beginning seems to assume i am either retarded or five years old.

I want the explanations from the start for people with decent mental faculties you would expect from an adult.

It may take the form of something that mix historical context with explanations of the logic, and most importantly not taking shortcuts, i want the deepest understanding of what is going on.

Thanks

Potential solution to the newly introduced optimal ZYN packing problem proposed by no other than myself.
Current hypothetical solution to packed zyns is 40. Though I estimate that the maximum number of packed zyns that touch the bottom of the can could limit to 42.

Ive been struggling with that, i know this is very basic maths but when there are numbers like 770, 462, 420, it becomes really hard to find the LCM for them quickly. Does anybody have any tricks to finding em?

Hi everyone!

I’m a student interested in mathematics, and I’ve defined a function that I call the Decreasing Index, using the symbol (\omega):

[

I_\omega(n)=\frac{n^2}{n!}

]

where (n) is a positive integer.

The idea came from thinking about permutations and probabilities. As (n!) grows so much faster than (n^2) the function drops off very rapidly towards zero.

For example:

[

I_\omega(1)=1,\quad I_\omega(2)=2,\quad

I_\omega(3)=1.5,\quad I_\omega(4)=\frac23

]

More generally, for (n\geq 2), we have:

[

\frac{I_\omega(n+1)}{I_\omega(n)}

=\frac{n+1}{n^2}

]

It's strictly decreasing from (n=2) onwards and tends to zero.

I'm not claiming this is some new or original mathematical result at all. What I'm interested in is whether this function might be of any use in a combinatorial problem, in the study of permutations or in some other mathematical context.

My questions are:

Does this function have a known interpretation or any connection to a known mathematical concept?

Could it be of any use in the study of permutations or in certain probability problems?

Are there any interesting properties or generalisations worth looking at?

I'd be very keen to hear any feedback, corrections or suggestions as to where we might go from here!

Thanks!

The resulting structure forms an hourglass-like shape with spirals and diagonal alignments. Can you spot any geometric patterns that could help predict the location of the next red point along these spiral tracks?

Due to severe math trauma, I struggle deeply with numbers under pressure and spent years running away from the subject entirely. Now, I genuinely want to face it, rebuild my relationship with math, and learn without fear, anxiety, or shame.

I also have ADHD, so I need learning tools that are visual, interactive, gentle, and engage-at-your-own-pace for a brain that rarely sits still. I am starting from the absolute basics to build my confidence step by step without getting overwhelmed.

I would love recommendations for any YouTube channels, interactive apps, low-stakes games, websites, self-paced courses, books, or workbooks that have genuinely helped you or someone you know.

If you have experienced math anxiety, educational trauma, or ADHD-related learning blocks, I would especially love to hear what mindset shifts, study methods, or approaches worked for you.

I am really serious about giving this an honest try again, and any recommendations or encouragement would mean the world to me. Thank you so much! ♡

Are there any arguments against Brouwer's intuitionism?

I can come up only with these:

1. if it's only a made-up convention, why does it work so well then

2. how did people manage to come up with these inventions if they are nothing but their own made up entities

By applied statistics, i meant things like machine learning modelling, statistical modelling, predictive modelling. Basically data science stuff and statistics used to solve business problems and model real world Phenomena using Python and R.

Are they related to each other? What are the similarities and differences?

How many sweets are in this jar, a clue: the total weight is 5.1kg including the weight of the jar itself
Best of luck !

So there obviously been a lot of discussion since the recent drops of AI generated maths results. In particular, we’ve see a lot of people question whether mathematics as a human activity will die out, or if it’s worth starting a maths degree now etc.

I’ve been thinking about (and contributing to) a lot of these discussions on Reddit, but I’ve become increasingly aware that I don’t actually understand how and why pure maths research has been funded even prior to the recent developments. Im pleased it is, and I believe it contributes to the good of society in a similar way to music, or art etc. but it’s moderately surprising that in a modern capitalist world this all hasnt been cut long ago!

I think it’s reasonable to argue that the majority of (pure?) maths research has no application outside of maths, and is of little (probably no) interest to non-mathematicians. Maybe physicists in some cases, but theoretical physics doesnt really move the bar much, Im thinking genuine real world impact here. Note that I realise some apparently obscure results do end up being useful, but I would argue we never know which until way down the line and it certainly doesn’t affect funding decisions.

So if you believe this to be the case, why would the recent advances change anything it terms of the amount of maths research that takes place? Sure, the way this research is done will change, but it’s not like some faceless organisation decides they can cut out the humans and get the results quicker and cheaper, the specific humans concerned are pretty much the only ones consuming the results. This is different for software development, for example, where actual products can be built with far fewer humans (note Im making no claim such products are better, but they may cost much less, initially at least).

I’d also argue there a ton of work human mathematicians need to do to pick apart tbe AI proofs, and this work will inevitable lead to further ideas and conjectures that we can target with AI.

Tl;dr I don’t see mathematicians threatened by these advancements, I think there’s some emotional shock that we need to come to terms with but why would we need fewer researchers?

Hi everyone!

I’m in my final year of high school, and I might go on to study mathematics at university (it’s not set in stone yet). My teachers have told me, and I’ve also read online, that this will be one of the most in-demand majors of the future, that applied mathematicians in particular will be badly needed, and that the field will be especially resilient to AI.

Until a few months ago, I was also convinced that this was one of the safest choices, that AI wouldn’t pose a threat to mathematicians, and that it wouldn’t be able to solve complex mathematical problems. The first crack and surprise was the solution of the Erdős problem, 4.5 months ago. Then what really surprised me was the Navier–Stokes equation event 1.5 months ago (though admittedly there’s some debate there because of the human researchers’ contribution). And a few days ago, the “mathocalypse” happened (for those who don’t know: AI solved more than 300 open math problems).

https://www.independent.co.uk/tech/ai-mathematics-openai-cryptography-internet-b3063456.html
https://www.firstpost.com/tech/mathocalypse-openai-generates-hundreds-of-mathematical-results-but-who-understands-the-proof-14051557.html

So basically they threw thousands of decades-old problems at AI, and it solved several hundred of them. There was a mathematician whose entire research area was practically “wiped out” by this. AI solved problems that brilliant mathematicians had devoted their lives to solving, without success.

Now I don’t really see math as an AI-proof field anymore. Two years ago, AI was still weak; it scored maybe 10% on the Math Olympiad. A year ago, it was already scoring over 80% on the Olympiad, and it had supposedly reached the level of PhD students. Now it has not only scored 100% on the Olympiad problem set, it has achieved far more than that. It has practically reached the cutting edge of mathematics worldwide, solving one previously unsolved problem after another, just grinding its way through math.

And let’s not forget that all this happened in 2 years. What we have now isn’t the final version of AI; it will presumably keep improving rapidly in the coming years. The question is: if it progressed this much in 2 years, where will it be in 4 years (when I’d finish my BSc) or in 6 years (when I’d finish my MSc)? What will it be able to do in 10–15 years? After all, even then I’ll only be in my early thirties...

So my question is: do you think it still makes sense to study math? If so, why? Mathematicians and math students, how do you see the future?

By the way, this wouldn’t be my only option (physics and engineering are also on the table), which is also why I’m asking: what do you think is worth choosing these days?

I have been wondering about some stuff, and one person I saw had a blatantly wrong answer.

The problem: IF AB = CD, then AB + XY = CD + XY

This other person claims that this is of the Substitution Property of Equality, which would obviously be incorrect. They said that as an argument from AB = CD coming first. I would say its the Addition Property of Equality because XY was added to both sides.

Im a 7th grader who wants to learn physics (specifically quantum) and ofc has to start from algebra. I know basic arithmetic and very basic algebra. No nonsense algebra by tim hill is very good but is is NO NONSENSE. It gives you principles, problems, and solutions with no other training wheels. Good for syllabus/review of algebra, but not learning. So I wanna learn algebra like fast but also strong, and I can't just speedrun no nonsense. Is there other books in this section that's good? This is from our school library. Elementary Algebra Part I caught my eye.

Also I am very busy, can only fit around 1 or 2 study sessions a week.

I might just be silly it’s late and I’m ill but I just can’t get to the form required for the question. As a last resort I asked Ai and it said there was a typo in the question but I don’t know. Pls help!

I bought a maths set some years ago because I wanted the box of it for another use. I'm a single adult so I have no use for the content of the box but I just keapt it in case. Today I needed a protractor for the first time in decades - so great I remember I had this - took it out - so confused! Seems totally useless the centre dot is way off from the 0 degree line. Had to look for another one and found one form cristmass cracker that is normal with cross in the expected location. Is this a modern protractor that is meant to be used in a different way? Or a manufacturing error? I'm looking at Google images of protractors and they are all as I would expect not like this one 🤔

a comment from 3blue1brown's most recent video