For 2^x the derivative has an extra constant of about 0.693, and for 3^x it's about 1.099. So somewhere between 2 and 3 there has to be a base where that constant is exactly 1, and that's e. Honestly this made way more sense to me than just "it's 2.718 and it shows up everywhere." Is this how you were taught it, or did it click differently for you?

Hi, I’m in my 30’s and I have been trying to start a degree on mathematics. At this age, responsibilities are everywhere and the schedule is tight. I have been doing some research to accommodate my studies in my schedule. First I went for a night program, very few unis offer it, then weekends programs, just to find even fewer options, and lastly online programs. After all the research, I came across Open University and uniDistance, but it’s really frustrating not having accessible options.

I’m not going to deceive myself, I know math isn’t the most popular degree and that throughout the course there is a high percentage of dropouts, but are there any other reasons why colleges do not offer online pure and applied math programs? Oxford and the MIT make their courses resources already public, it makes me wonder

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?

Hello, I am a master’s degree student specializing in algebra. I have begun studying homological algebra, and I need to develop an understanding of category theory.

During my undergraduate studies, I took courses such as abstract algebra, basic topology, group theory, ring theory, module theory, tensor algebra, and Lie groups. Currently, alongside the courses I am taking for my master’s degree, I am also working through a textbook on homological algebra—specifically, the one by Rotman—but I am struggling to grasp the concepts of category theory.

I am not entirely sure whether my undergraduate background is insufficient, if I should study another subject before diving into homological algebra, or if I am simply having trouble with the language used in this particular book.

I would welcome any advice, as gaining a solid understanding of category theory is essential for me.

I want to learn math intuitively, ie: understanding how it actually works and where it's applied and not just how to solve the equation but there is virtually NO website that does this, for any subject. tbh im shocked that this is an issue, I wasn't able to find any books either, they start by explaining intuitively but then its like they give up or they forget the reader can't read their minds. DONT say brilliant or khan academy because they do NOT teach intuitively. they only teach you how to solve an equation/ forget IDK what they're explaining like some sort of language gap. When I studying on my own by grasping at what little intuitive information im given and piece it together with real world examples I see that math is really easy, as easy as reading, it is just reading and has nothing to do with being smart or not. however there's no websites or books that already provide this way of learning which doesn't make sense because math has been a thing for way too long....

Context: 2nd year pre-graduate on an engineering track. I'm currently taking differential equations and linear algebra and did pretty well in my calculus courses overall.

When working problems for these classes, I often find myself having forgotten a technique and having to look it up again or find myself taking a long time to reach a solution that someone else did with a shorter method. This is 90% in regards to my algebra (which isn't bad, but I wouldn't call it good) and more specifically trig. This is also where most of my errors occur when it actually matters.

I'm already going over my algebra from the ground up along with basic trig identities, I'm wondering where I can find more rigorous problems (or some helpful techniques that might be less taught in high school). I want to get to the point where I "own" these skills and can spend more of my efforts tackling the actually new stuff being taught in my higher level classes.

TLDR: Where can I find more of/learn how to solve the difficult algebra problems that I might find in my courses. I want to find and fix the holes in my math before it comes up on an assignment or exam.

I'm just curious about what I would need to know for a general chemistry class if I ever go back to school again. Here's the description of the course.

The course covers fundamental principles of modern chemistry, including problem-solving techniques. Topics include atomic and molecular structure, chemical nomenclature, stoichiometry, chemical bonding, properties of gases, liquids and solids, and solutions. One year of high school chemistry and a working knowledge of elementary mathematics, including algebra, is recommended.

However, I don't know the specific algebra. So I would like some advice on what to go over please.

I’m 20 and was taken out of traditional schooling in 6th grade for medical reasons. I’m currently rebuilding my academics, especially math, through an intensive remedial course during my gap year. After that, I plan to start community college and eventually apply to transfer to a strong university.
I’m planning to take the SAT in about two years, and my goal is 1500+. I know that’s ambitious given my starting point, but I’m committed to putting in the work.
How would you recommend preparing over that time? Should I focus entirely on my foundations for now, or introduce SAT-specific practice along the way? I’d especially love to hear from anyone who started with significant math gaps and eventually scored well. What helped you most?

I'm a little embarrassed at this post tbh. I've never hit a wall like this before with math.

I'm a first year Mathematics student in the UK and taking my very first proofs module. I am struggling with translating mathematical statements into predicate logic using quantifiers. I can barely rewrite the most simple statement into predicate logic.

I guess what I'm wondering is if anybody has any good resources for this specific topic such as youtube videos or specific textbooks? I know all I need to do is practice and practice again. The best possible resource in my case would be an excercise book with answers. I just seem to be struggling to find resources.

Thank you all :)

Hey guys! I have a math test in IB Math AA SL tomorrow, and this problem is worth eleven marks. Our teacher did not show us how to solve this type of problem, and math is not my strong suit. Could I please have help on how to solve this kind of problem? Thank you!

I only have an explanation of what the problem is:

There are four diagrams (A, B, C, D). The first diagram has the box split into four, and one fourth is shaded. In the second diagram, one fourth is shaded, and then one of the fourths is split into four smaller parts, and one fourth of that part is shaded.

So, you have one fourth shaded and then one sixteenth shaded. The pattern keeps going, with each new shaded area being multiplied by one fourth.

The question asks for the area of the box that is shaded in diagrams B and C, and then to write the geometric sequence. I think the starting value is 1/4, and the common ratio is 1/4. Then, you have to find the sum of the infinite geometric series.

My explanation is really scattered, sorry about that!

Hello i am an adult and i need help finding good math books to learn from the beginning up until linear algebra and calculus i know i said books right but any media format is welcome

My math skills are pretty weak, and I want to improve them from the basics. I don't have a strong math background, and I'm not focusing on any particular area. I just want to get better at general math.

Can someone recommend any good books, courses, or other resources for a dummy like me?

Same as heading.

I like to study everything whether it's pure or applied. Topology is my favourite subject overall. On the basis of first semester marks in masters, we were given options to choose our thesis supervisors and I chose someone who specialised in mathematical physics and cosmology. I did have options of choosing some supervisor specialising in Topology but I had heard they aren't too accommodating with their students. Anyway I completed masters with a good cgpa but thinking if my thesis would come in my way of pursuing PhD in a pure mathematics subject.

I am doing my research essay on maths and I am thinking of using Lotka-Volterra Model or one more model.

However, I don't now anything about it nor how to use it what it does, I am not sure if I should do further research on it?

Hey guys, I am a freshman in college rn studying computer science and I admit that I havent been bright when it came to math, I didnt excel in anything that was taught in high school and I just assumed that I was no longer a math person like I was before in elementary.

But ever since I found out that I had calculus and higher math courses that I will be taking in 2nd year I got to work by teaching myself pre-algebra at the start of June (which was still summer break). I utilized Khan Academy as my roadmap and other resources to explain topics Khan couldnt.

I started with the defintions of prime and composite and this week I just learned how to graph quadratic functions and now I am moving on to Algebra 2.

But one area that I truly have been weak in since pre-algebra was always word problems, when I look at it I just have no clue what to do, I do what everybody tells, I write out the values, what happens in time according to the problem, and seperate the reading from the solving but I just get stuck which leads me to frustration and mental breakdowns which always ruins the rest of the day or evening for me.

Ever since those bad episodes, I have had an instinct to avoid or not to focus much on them which I know is bad so does anybody here have any tips for me? A lot of it would really help.

Hi, so I'm a high school senior, and my sophomore year I didn't do any of the homework, and I got a B-, leading me to have to take college algebra instead of pre-calc. When I started to understand that I want to study Econ in college, I locked in, got an A in College Algebra, which was very easy, and then I took Pre-Calc Trig to be eligible to take Calc AB. Now, after two tests, limits and derivatives, I have a 69 in the class, and I got a 64 and a 65 on both tests. I don't know what I'm doing wrong. I do the homework, I do the classwork, and I understand it, and then it's test day, and I do badly. What should I do to succeed in Calc AB?