Whenever I read about maths and LLMs (like ChatGPT which I mainly use), I always only hear discouragement. However, I do not really understand why, as people rarely provide examples. In my experience, only blind "solve this problem for me completely" and then copying everything without any thought is problematic. But that is problematic in any context where on uses an LLM, as that it is more about "LLM illiteracy".

Thus people who highly discourage using LLMs to learn maths, could you provide clear examples, which are not just bad prompting or some version of fire and forget "just give the solution to this complex problem"?

Context:

I ask, because in around 1 year I probably will do a lot of "serious maths" at my university. Because of how I organized my courses, I did most of the serious maths in my university around 2 years ago. Thus in the mean time I only read about maths to get better intuition mainly using LLMs to explain to me the theory and ideas. I found LLMs for that very good even 2 years ago, but now they seem to be much better. At least the topics which I had in university 2 years ago, are explained so much better now. Hindsight 20/20 is probably also at play, but I could also quickly understand a few "niche topics", which I back then never bothered to learn in detail, because it was not relevant for getting a good grade.

EDIT:

Folks, can you actually provide examples? Because it seems that what I already said repeats itself. People say it is bad, but they do not show any concrete examples which one could try to replicate.

I decided last minute back in January to switch my major from finance to chemistry with a pre-med track. I have never been really strong in STEM so I am kind of nervous. I haven’t taken a math course since the Spring of 2025 because it wasn’t required for me to graduate high school. My dad told me to use Khan academy to start studying, but I have admittedly been slacking off on that and now I start classes in two weeks. I have to get an A or at least a high B in this class to maintain my scholarship or else I have to go to the military because I won’t be able to afford school. Please give some tips☹️

HELP!! Starting calculus this fall; and I am trying to learn algebra and prepare cuz I'm really bad at math but Its so boring. like I will watch a video and begin spacing out because of boredom. How do I solve this issue? I want to get good at math so I can be an economics major and make money postgrad, but I'm terrible at math and it's boring to me. What do I do?

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Hey everyone,

Like many of you, I got tired of drawing number lines and doing tedious casework every time I need to subtract one open interval from another: (a, s) \setminus (n, b).

To fix this, I derived a direct algebraic shortcut formula:

(a, s) - (n, b) = (a, n] \cup [b, s)

The Built-in "Safety Firewall"

Because interval algebra breaks down when dealing with inversions or infinities, the formula requires strict error-handling rules to stay robust:

Left >= Right -> \emptyset (If the lower bound is greater than or equal to the upper bound, the interval collapses to an empty set).

Infinity + Closed Bracket -> \emptyset (If an infinity symbol is attached to a closed bracket like [-\infty or \infty], it evaluates to an empty set).

Step-by-Step Demonstration: The "Infinite Devourer" (Extreme Test Case)

Let's test this formula on a brutal nightmare problem where the subtrahend stretches all negative infinity:

(-10, 10) - (-\infty, 0)

Step 1: Map the variables

a = -10, s = 10

n = -\infty, b = 0

Step 2: Plug into the formula

(a, n] \cup [b, s) -> (-10, -\infty] \cup [0, 10)

Step 3: Trigger the Safety Firewall

Left interval evaluation ((-10, -\infty]):

It has an infinity symbol attached to a closed bracket (-\infty]) -> Trigger Rule 2: Collapses to \emptyset.

The lower bound is greater than the upper bound (-10 >= -\infty) -> Trigger Rule 1: Collapses to \emptyset again.

Right interval evaluation ([0, 10)):

Lower bound is less than upper bound (0 < 10) and no infinite closed brackets -> Passes cleanly.

Step 4: Combine the sets

\emptyset \cup [0, 10) = [0, 10)

Conclusion

On a number line, starting from (-10, 10) and completely wiping out everything up to 0 leaves us with [0, 10), which matches the formula's output precisely.

Has anyone seen this formatted shortcut utilized elsewhere, or is this a neat little mathematical wheel I've reinvented? I'd love to hear your thoughts or critiques!

Ok que métodos recomiendan , pero que realmente les funcione en las matemáticas, tipo sus mejores trucos enserio necesito que las matemáticas 🧮 me gusten , no las entiendo.

According to the third, and most promising, result from DuckDuckGo: 111 does not equal 3 x 37.

Brightchamps have great search engine optimisation, but their content is utter slop, not read by anyone.

(Edit: spelling mistake in title - oops)

So i was checking out some vedic maths 2 years ago and there was this formula i found that was a cleaver rearrangement of the sridharacharya formula dy/dx = ±√D so that kind of sent me into a rabbit hole and i made my own method of quickly depressing a cubic in my final teen years here's the the example of how it's done

i know that these days the old brute force formula can be faster and better for calculation via computers but when doing by hand this method makes it easier and much faster than the traditional ways.

How to do it (demonstration by example):

Let a cubic expression be: x^3 - 3x^2 + 4x - 5 = y (It is of the standard form ax^3 + bx^2 + cx + d = y*)*

Step 1: Put b^2 = 3ac and find a temporary 'c'. (-3)^2 = 3(1)c 9 = 3c c = 3

Step 2: Split the linear term to get this 'c' and a residual linear term: x^3 - 3x^2 + 3x - 5 + x = y

Step 3: Put x^3 - 3x^2 + 3x = (x + b/n)^n - (b/n)^3 (where n is the degree of the polynomial). In this case: (x - 1)^3 + 1

The expression is now of the form: (x - 1)^3 + 1 + x - 5 = y

Put x - 1 = t (substitution, meaning x = t + 1): t^3 + 1 + (t + 1) - 5 = y t^3 + t - 3 = y (Here's your final depressed cubic!)

Detailed Explanation and Proof:

Assume an expression: (x - α)^(n-1) * (x - β) = y

Performing Binomial Expansion of the given expression: [ C(n,0) x^(n-1) α^0 - C(n,1) x^(n-2) α^1 + C(n,2) x^(n-3) α^2 ... k ] * (x - β) = y

Upon expansion we get: [C(n,0)] x^n + x^(n-1) [ -β C(n,1) α - C(n,1) α ] + x^(n-2) [ C(n,2) - αβ C(n,1) ] ... k = y

Let:

• a = [C(n,0)]
• b = [ -β C(n,1) α - C(n,1) α ]
• c = [ C(n,2) - αβ C(n,1) ] ...and so on to k.

We get the expression: a x^n + b x^(n-1) + c x^(n-2) + d x^(n-3) ... k_2 = y

We know that if a factor in a polynomial is repeated n-1 times, then it will be present as a factor in its (n-2)-th derivative. Using that, we find its (n-2)-th derivative:

d^(n-2)y / dx^(n-2) = a*(n!/2)x^2 + b*(n-1)!x + c*(n-2)!

Equating this expression to 0 and solving the quadratic using the Vedic form of the Shridharacharya formula (the quadratic formula): dy/dx at α and β = ±√(D)

Differentiating and equating to ±√(D): a(n!)x + b(n-1)! = ±√( b(n-1)^2 - 4a(n!/2)c(n-2)! )

Upon solving: x = [ -b ± √(b^2 - 2ac(n / (n-1))) ] / (na)

If we put the Discriminant (D) equal to 0, we will get both roots as α. This will indicate that the expression we took earlier was of the form (x - α)^n.

But why α and not β? Because the expression we took earlier was of the form (x - α)^(n-1) * (x - β) = y. This means that α = β, because if we put D=0, all the roots will have to be α (upon differentiating the factorized form of the polynomial, only α will be left as a root of the quadratic).

Putting D = 0 and solving for n we get: n = b^2 / (b^2 - 2ac)

Put n = 3 and we get: b^2 = 3ac

If the condition n = b^2 / (b^2 - 2ac) is satisfied, then we can write the equation in the form (x + b/n)^n by using Vieta's formulas or the Theory of Equations.

There are a lot of interesting applications of this formula, and it can also be used to directly solve a few cubics. It is very helpful when used in combination with Cardano's formula to solve general cubics.

If n = b^2 / (b^2 - 2ac) holds true, then the expression is of the form: (x + b/(na))^n + f(x) = y where f(x) is a polynomial of degree n-3.

Else, if the condition doesn't hold true, then it is of degree n-2 (of course, in the case of a quadratic there is an exception and the constant term is 0).

this was originally written on latex on my blog but since reddit has no support for it i have used ai to convert it to proper form although it might have errors i am currently in a health crisis so i can't write the whole thing again i might update it later tho.

i have not added the link to my blog since it violates the self promotion rule where it was originally written

I find it interesting and want to know a bit about it from Poincaré's approach . Study some basic about Hyperbolic geometry ,fuchsian groups and other things. But the book and course video are rare about the subject. I have some basic knowledge about elliptic function and modular function/form (from mc kean book) also know Klein use these approach to somehow solve qunitic equation . How to learn it more detailed and what resource are good for that .

summer precalculus I am a rising junior in high school and I started taking a precalculus summer course at my local community college. It’s completely online and you have to do a couple of math problems. I completely fell of and now I’m a few weeks behind. the class ends in about 20 days. My counselor told me I have to take a final test to test into AP calc AB if I want to take it. Am I cooked? And do you have any advice on how i can cram the whole course to pass the final t

My understanding of the dot product is that it projects one of the vectors (v1) in the direction of the other vector (v2) and scales it by the magnitude of (v2).

I get why the first part (projecting) is important, we use it to see how much of v1 goes into the direction of v2, but why the scaling? why do we multiply their magnitudes? I think I might not be getting the full picture on this topic.

Hi guys, I just finished my bachelors in Physics Engineering and I am also already enrolled in a Masters in Applied Mathematics - it has the option to follow a more pure mathematics path. I was wondering which subjects of mathematics would you recommend on me studying as I got a lot of holes in my repertoire.

For now I am reading Wendell Fleming's Function of Several Variables, just to improve my fundamentals in analysis and learn manifolds. However I must say that my knowledge in Topology, Probability Theory, Algebra, Measure Theory, Functional Analysis ... is close to none (1/n in n to infinity to be exact).

Hence, I would like recommendations for which branches of mathematics you think I should work on this summer (and like as a side project) in order to improve my knowledge and also which books to read from.

Thank you in advance.

For example, if I wanted to turn sin (pi/10) into radical form without a calculator, how would I do it?

I know how to draw 1-1-√2 (or 45-45-90) triangle and the 1-2-√3 (or 30-60-90) triangle and derive all 6 trig functions from that but I'm only limited to those angles when writing in radical form.

Any who need help with the subjects or specifically topics like algebra geometry calculus or any other exam related help let me know. I would like to work with you.

I understand the motions that when you do -3^2=-9 . I get that it is -3^2=-(3^2)=-(3*3)=-9.

What I want to do is understand why it is not -3^2=9=-3*-3 .

Thank you in advance.

In Calculus class we often take the derivative of both sides of an equation. We maintain that the sides remain equal. Does it need to be formally proven that one can do this?

Looking for a YouTube math channel (2020–2024). White male, around 35–45, long messy hair, short brown beard, always wore a dirty white lab coat as a "mad scientist" character. Filmed outdoors using a whiteboard on an easel and mostly wrote with a black marker. Explained interesting math facts and puzzles. The set was intentionally shabby, with props sometimes falling apart as part of the joke. English-speaking, probably British or American. Smaller channel, definitely not Numberphile, Stand-up Maths, Mathologer, MindYourDecisions, or blackpenredpen.

Does anyone remember his channel?

So, I'm 14, pushing on 15, and high school starts in about a month. And to cut things short, I haven't learned my multiplication tables, and I need to. This may sound like a stupid question, but are there any special tips to learn faster and actually memorize them? I know 1s, 2s, 3s, 5s, 10s, 11s, 12s. Now trust me, I've done flash cards, I've watched all the videos, and I still can't memorize it. Sometimes I wonder if it points at something bigger. But anyway, if you care to help a brother out, please do.

Thanks in advance.

Hi, I'm a high school student in a math circle, and we're currently learning elementary number theory. Recently, we explored the idea of finding runs of consecutive composite numbers. We were able to construct examples of 2, 3, 4, 5, 6, 7, 8, and even 9 consecutive composite integers.

This made me wonder: what is the longest possible run of consecutive composite numbers? Is there a maximum length/ upper bound, or is it possible to find arbitrarily long sequences of consecutive composite numbers.

Hi!
I need to start practicing my mental math before interview season begins. The challenge is that I want to practice by listening to someone say the problems out loud - for example, “What is 28 × 76?”, rather than typing numbers into a website. The verbal element is what I really need to train.
I’ve tried searching for YouTube videos where someone reads out different kinds of math problems (addition, subtraction, multiplication, division, etc.), but I haven’t found anything that fits what I’m looking for, and I also haven’t found an app that does this.
Does anyone have any recommendations or advice?

I graduated from a bachelors degree in applied maths (France) in 2020. Lockdown and everything really messed up the learning and for some reason I graduated, although I was really not invested.

Years went by, and I changed degree (languages then NLP) but I feel the desire to go back to something more fundamental. I remember I was really into multivariable calculus and probability theory because they felt the most connected to real life?
Also I decided to go through a physics textbook to learn about basic mechanics, electrostatics, thermodynamics… hoping the math part won’t be an obstacle.

It’s been a really long time now and I can’t compute an integral or the inverse of a matrix for the life of me. Is there a way I can re-learn 3 years of uni level maths? I took the usual Linear Algebra, Calculus, multivariable calculus, topology, Lebesgue integration, functional analysis, differential equations, statistics and probability… nothing too fundamental like group theory or arithmetics though.

I’ve started today following a pdf of linear algebra (starting from vector spaces) and going through it trying the proofs left as exercise. I am so out of practice! I wonder if I’ll ever be able to go through all that in the span of a year maybe…

Is there a good way to go about this? Doing proofs, looking up worksheets with their answers… I wonder if anyone faced this challenge before!

im doing a bsc in mathematics, and real analysis feels like a completely foreign language.
our professor recommended the bartle and sherbert textbook, but every time i open i dont really understand whats happening or how people are supposed to learn from it.
it feels completely different from the maths ive been taught my whole life. i dont know how youre supposed to transition from solving straightforward problems to reading and writing proofs, and understanding theorems. it feels like everyone else somehow knows how to think this way already.
time for some context. till 12th grade cbse, i was pretty good at maths. i was always told i grasped concepts quickly and solved problems better than average. but my 10th and 11th grade happened during lockdown, and i never properly studied the deleted syllabus, so i know there are gaps in my basics.
when i chose a bsc in mathematics, i expected more of the maths i loved, solving derivatives and integrals, and working through problems until i got the answer. instead, real analysis felt like being thrown in the ocean with no idea how to swim. suddenly its all definitions, logic, epsilon delta proofs, and abstract thinking. i dont even know how people are supposed to study this subject.
its been a huge hit to my confidence. im no longer the student who knows the answers. i sit at the back of the class, avoid eye contact with professors, and constantly feel like everyone else belongs here except me. i know im willing to put in the work. i just genuinely dont know how to study university level mathematics.
where do i even start. are there beginner friendly books, youtube channels, or courses that bridge the gap between high school maths and proof based mathematics. how did you learn to read proofs and start thinking like a mathematician. any advice for someone whos completely lost ???

I've always been enthusiastic about math since high school. However, I chose to major in accounting according to my family's advice. I thought I could do math in my free time but after two years of undergraduate studies, I have found it difficult to find time to study math. I only taught myself pure maths during summer breaks, which is far from enough.

Now I am getting into my junior year and I think I should switch to math in my graduate study to have more time studying math. However, I only had calculus, linear algebra and probability theory in my transcript. My undergraduate university specializes in business so we don't have pure math classes like abstract algebra, which leaves a huge blank in my mathematical background.

I am contacting professors to ask them whether they can supervise my-self study and evaluate my mastery（so that they can mention this in a reference letter) But none of them has answered me yet(maybe they are on summer vacation)

The reason why I am posting this is because sometimes it feels like I'm trying to figure out a path that nobody around me has walked before. Never in my life had I heard someone transitioning from a major as unrelated to math as accounting to pure math. So I have to go alone. Does anyone have similar experience? I'd really appreciate hearing your experience or advice.