I don't know If it's new or not, but i'm a bit proud of this formula. Wanted to share it to see your reaction.

I tried making a triangle of numbers and then marked the primes. I saw that the primes in the left were more frequent than primes in the right. I can also extend it by writing some code but does it ever happen that the primes in the right exceed the primes in the left or do the primes in the left increase their gap against the primes in the right

Here's a mental maths trick I really like.

Want to calculate 75² without pen and paper?

Take the first digit (7), multiply it by the next number (8), and put 25 at the end.

7 × 8 = 56

So, 75² = 5625.

It also works for:

35² = 1225

95² = 9025

And even 115² = 13225.

Does anyone know a simple way to explain why this works, especially to school students?

I'd also love to hear other shortcuts that are useful for teaching maths.

Helloooo, Im a high school student that is currently learning about logarithims,exponential functions and graphing, and in the course my professor started off by saying that he has a Nanotechnology Masters Degree, this got me curious as to what has he seen in math? So I asked him what is the hardest subject he had to learn during his student years, he told me it was Group Theory and just by hearing the word theory I could assume it was a hard topic/subject.

So now I ask, what exactly makes Group Theory so hard to learn and understand or what are your thoughts on it? Of course im only still a mere high school student that has much learning ahead, but I want to know what thoughts everyone has about this topic which is technically my teachers "Nightmare".

Just curious, best of luck to anyone studying for a degree!

En la última viñeta en realidad es distributividad, me confundí al ponerle asociatividad 1.

Requiero saber si ¿estoy siendo lo suficientemente riguroso con el lenguaje matemático y a la vez siendo muy explicativo? ¿Qué puedo mejorar en este procedimiento de solución?

I created the inverse function Eln(y) to solve equations like e^x + In(x) with Taylor Series. At the Bottom you see the approximation for the inverse function. I want to see your reaction, maybe somebody of you needs it to solve an equation ;)

Hi! I’m planning on going to college and I was thinking of majoring in Math because I had enjoyed doing it so much the last time I took a Math class. But I am also interested in getting into the tech sector as I had grown an interest in technology and software in the recent years, so I was wondering if it would be wise to study Math with a minor in CS or should I straight up pursue a CS degree instead? Any advice would be much appreciated. Thank you!

Hi!

So, all my life I've been using this theorem I developed and I thought was common knowledge, but apparently it isn't. So, I came here to check if it really holds up. I know someone else smarter than me must've noticed this before, so I also ask the name of this theorem. Here it is:

To multiply two full numbers that aren't equals and that are either both odd or even, you can, instead, take the number that is equidistant to them and raise that to the power of two, then you subtract from that the distance between one of the original numbers and this equidistant one raised to the power of two.

Examples:

13 x 15. The equidistant number here is 14. So, 14², which is 196. The distance between 14 and 15 is 1. So, I subtract 1² from 196, resulting in 195.

24 x 28. The equidistant number here is 26. So, 26², which is 676. The distance between 26 and 28 is 2. So, I subtract 2² from 676, resulting in 672.

6 x 18. The equidistant number here is 12. So, 12², which is 144. The distance between 12 and 18 is 6. So, I subtract 6² from 144, resulting in 108.

I don't use this for everything, mainly for two numbers that are close.

Thanks in advance!

I decided long ago that I want to learn math. My goal is either applied maths or operational research. I’ve been studying by myself to get better before I start college. As someone who failed pre calculus twice about a decade ago, I am nervous about when to sign up. My plan was to self study all the way to calculus and then sign up just to at least be familiar with the material and not worry too much about being lost in class. Specially since I am going for a full online course because my lifestyle won’t allow me to go in person. Basically prepare myself very well so I don’t have to struggle when the course starts.

Also, I understand that in person is much better and I would love to. But I got too much responsibility, a full time job, and a part time job. So my only option is online.

I've been thinking about what it really means to be good at mathematics.

Some people can calculate incredibly fast but struggle with unfamiliar problems. Others take longer but have excellent logical reasoning skills.

If you were designing a short maths assessment for school students, which abilities would you prioritise?

• Numerical fluency
• Logical reasoning
• Conceptual understanding
• Problem-solving ability
• Calculation speed

Would love to hear perspectives from maths teachers, students and enthusiasts.

Apologies for the rant, I just figured I should ask this sub for input.

I’m currently in my second year of community college and preparing to transfer and start at a 4-year uni in fall. I’ve been pretty scared and honestly felt pretty down. Everyone who majors in math already had an interest in the subject for almost as long as they’ve been alive. I don’t develop an interest until the summer before starting CC.

There’s this one guy in my calculus 3 class, and he always seems to know the answers to the questions. I spoke to him, and he told me he took AP Calculus in high school. I’ve never taken an AP class. Hell I got a 450 on the math portion of the SAT. My first semester started with accelerated precalculus. Even though I got to calculus 3 with A’s, I still feel like I don’t know anything. It’s like I’ve even forgotten basic algebra.

Doesn’t help that I still don’t know proofs or linear algebra. Everyone usually has these courses done their first or second year. I won’t have that finished until my 3rd year (it would be my first year at the university but I would’ve been in college for 3 years).

I know it’s not a race, but it’s sort of discouraging. It doesn’t help that I want to go to grad school, but it’s like I know I’m going to get tripped up by proofs and it could possibly delay my graduation even more.

Don’t know if it’s relevant, but I do have ADHD. I’ve already started treatment for it, and things should hopefully get better. While I’m on that topic, I know medication can give up a bunch of motivation, but I feel like I need to actually narrow down what I actually need to focus on. Any suggestions/ideas?

I’ve been thinking a lot about prime numbers lately and wanted to get some perspectives on this. How hard is it to actually discover a completely new primality test today? Specifically, is it possible that an elementary test—one using just basic algebra or modular arithmetic—is still out there undiscovered?

We already have things like Fermat’s Little Theorem, which is fast but has those annoying Carmichael pseudoprimes. Then there's Wilson’s Theorem, which is perfectly accurate but completely useless for big numbers because factorials take way too long to compute.

But then in 2002, the AKS test was discovered using relatively elementary polynomial math, which shocked everyone. Since that happened not too long ago, it makes me wonder if there are other basic patterns or theorems hiding in plain sight.

Do you think the elementary math options for finding primes are completely tapped out at this point, or is there still a chance a human (or a computer) could find a new simple trick? Love to hear your thoughts.

I was thinking about my real analysis class when I took it. I think it could have been improved in many different ways. More practice problems, more explicit instruction instead of trying to have students figure it all out.

I want to pursue mathematics, I am still exploring whether I enjoy pure or applied more, but throughout all of it, it seems as if I am more interested in the proofs of statements than anything.

The caveat is that I have been roped into engineering (Mechanical First Year) and it acts more as a hindrance due to poor scheduling (literally an 8-6). Alongside, I don't want to stay completely stuck in books forever, I have other non academic hobbies that I want to at least maintain alongside. Apologies for the tangent.

Though I am a first year that has no formal education past highschool for mathematics and that any entrance exams (instance IITJAM, GRE etc) for higher education I can pursue are only possible if and only if I take an engineering or a science degree, I have already taken action and am learning Real analysis, I wish to diverge and also pick up linear algebra and group theory (the latter seeming more appetizing) alongside RA.

But for now, I do not have a proper timeline for how I should take these fields on, as I don't have available formalised courses that deal with these subjects (being restrained to engineering faculties, which is a big "if", books and online resources) and that my prep timeline is 4 years long, from my tangent, it's clear that I do not want to face academic burnout by studying both engineering and undergrad Mathematics and forsaking all my time for anything else. But I do not want to step away from Mathematics, would it be mentally and academically safer if I pursue Mathematics closer to a hobby for the first year or so and also develop other interests (that I might later monetize in some way) and engineering academics? And thereafter I can start putting more effort into it than engineering (given I can maintain my grades)?

Outside this rant, can someone recommend online lectures and resources for the content you'd find in an undergrad Mathematics course?

Watched a lot of Michael Penn videos on RA, what he uses in most of the proofs is kinda questionable... he takes a functions back propagates it to reach a certain value in terms of variable in scratch work then writes the formal proof assuming the scratch work ...

Is it a good practice to write proofs that way?

What were the point of proofs in an area of math that involves shapes? Why were proofs even made part of this type of math? Everyone please be respectful, just asking a question. Great answers so far.

Hi guys im currently a first year doing bachelor in math honour and wondering what kind of jobs I can get with it other than teacher/professor. I chose the degree cause I was good with high school math but now have no idea what kinda jobs I can get with it. If I were to switch to smth like acturial sciences, statistics or anything of the sort id have to add a year onto my studying which I dont rlly wanna do

I’m a sophomore studying nuclear engineering and minoring in math. I’ve always been interested in mathematical modeling and chose to do engineering instead of mathematics because there are more job opportunities with an engineering degree. However I’m at a point where I’m not finding nuclear research opportunities because all the nuclear classes are offered next year. What should I be doing now so I can guarantee myself a research position next spring or next year? Or is it possible for me to do math research as well??

Hi everyone what the best way to study these subjects for my university exam (keep in mine I have not studied math in like 2.5years)?

If the aim of constructing number systems is to explain the geometric line as a set of points, wouldn’t ZFC + (V=L) be a natural choice, perhaps even the best one? In this framework, analytic geometry, differential geometry and topology all work just as they normally do, without the need to grapple with metamathematical questions such as the continuum hypothesis. (Moreover, this rules out measurable cardinals, large-cardinal phenomena and similar feverish pies in the sky, but for the purposes of describing the continuum, that seems a reasonable price.)

I have always found it a little surprising that popular mathematics books rarely discuss Gödel’s set-theoretic universe, which seems to offer such an intuitive and straightforward foundation for mathematical analysis.