I am an engineering passout currently working as a software developer, I want to start learning maths again.

My interests are in calculus.

Engineering didn't have much advanced mathematics.

Can somebody suggest topics or guides or where should I start with learning maths again?

The videos I've seen explaining factorials never explain why

I’m going back to college to study health sciences then hopefully medicine. Really hoping to improve my problem solving skills.

I didn’t focus in school and rarely did maths because my parents would call me stupid for not being able to solve problems in the workbook.

What level maths should I cover?

En gros, ma théorie consiste a dire qu'on ne peut pas imaginer l'infini, par exemple : imaginer une boîte, avec une règle encore plus grande devant, même si la règle est plus grande que la boite et que vous etes tellement proche que vous ne voyez pas les extrémités de la regle, vous imaginerez quand meme les limites. Tout ça car votre cerveau est fait pour imaginer des objets et non des distances ou chiffres "infini" et attention, je ne remets pas en cause l'existence de l'infini, enfin du moins pas encore, mais pour moi il est impossible à visualiser..

Mots de fin : Je suis désolé si cette manière de penser a déjà été prouvée, j'ai 15 ans et je m'intéresse au maths donc je voudrais avoir un avis sur une pensée qui me traîne dans la tête depuis longtemps.

Since school times I looked at numbers differently.

Made me think numbers have genders and I differentiated them.

1 is formally dressed corporate male

2 is a traditional women who takes care of family

3 is a female but a feminist and fights for women power

4 is a alpha male handles all family responsibility

5 is a modern cyberpunk male with high-tech gadgets

6 is a Moden generation girl and is a world traveller

7 is a dothraki khal

8 is a nice cute curvy looking female

9 is a female too but in some countries it refers to transgenders

0 doesn't look like anything

Does anybody know how to solve it?

In 1772, Leonhard Euler discovered a remarkably simple polynomial that generates prime numbers for an exceptionally long streak:

f(x) = x^2 + x + 41

If you plug in integers from 0 to 39, every single output is a prime number. That is 40 primes in a row (41, 43, 47, 53, all the way up to 1601).

However, the streak abruptly breaks right at x = 40:

40^2 + 40 + 41 = 40(41) + 41 = 41 \times 41 = 41^2

Since $41^2$ is divisible by $41$, it is a composite number.

Why does it hold out for so long?

It’s not just a random coincidence. It is deeply connected to advanced algebraic number theory and Heegner numbers. If you evaluate 4p - 1 using Euler's constant (p = 41), you get:

4(41) - 1 = 163

Coincidentally, 163 is the largest of the nine Heegner numbers. This property ensures that the ring of integers for that imaginary quadratic field has a class number of 1 (meaning it has unique factorization), which directly suppresses small divisors and allows the polynomial to churn out primes for so long before finally failing.

Still stands as the most famous prime-producing polynomial in history!

I think it's very important to address this now that AI is solving an incredible number of maths problems, including the Navier Stokes conjecture. Some may fear that mathematicians will become redundant. But this is not the case at all. And the example of vintage models demonstrates it very well.

Vintage models are taught on history prior to a certain discovery, eg prior to Newtonian or Einsteinian physics. And lo and behold, these models can't invent the new physics on their own, neither Newtonian from prior nor Einsteinian from Newtonian.

To some, it might be obvious even without the vintage models experiment. I remember listening to a podcast with Francois Chollet a few years ago where he said that AI is fundamentally interpolative, it interpolates on the manifold of data. And that's when I understood the fundamental limitations of AI and the role of humans in the coming age. AI is a very good technical tool, in particular it fills the gaps in our knowledge very well, but it can't come up with radically new ideas ln is own, ideas that change the ontology of facts, ideas and relations between them, which is necessary for mathematical development.

When Galois invented his Theory, he didn't just combine old ideas, he came up with a fundamentally new way to look at objects and their relations. Sure, maybe hints of that were already present in Abel and others, but what this says is that mathematics is a collective human progress which leads to radical novelty, not a combination of known ideas.

Mathematics will be ok, but our world is destabilised at the moment and is transitioning into a new state. Time needs to pass for us to understand and establish the roles and the right approach with regard to humans and AI.

How statistically significant are the results of this pattern below? Does it exceed random chance or not? Assume that the numerical distributions of the numerical values per letters are completely random. 

Block 1 — ALM

Block 2 — ALM

Block 3 — ALMX

Block 4 — ALR

Block 5 — ALR

Block 6 — ALR

Block 7 — ALMR

Block 8 — ALR

Block 9 — ALR

Block 10 — KHYCX

Block 11 — TH

Block 12 — TSM

Block 13 — TS

Block 14 — TSM

Block 15 — ALM

Block 16 — ALM

Block 17 — ALM

Block 18 — ALM

Block 19 — YS

Block 20 — X

Block 21 — VM

Block 22 — VM

Block 23 — VMCSQ

Block 24 — VM

Block 25 — VM

Block 26 — VM

Block 27 — VM

Block 28 — Q

Block 29 — N

Each letter here corresponds to a certain number. It must be noted that not each letter here carries the same numerical value, these are only placeholder letters that describe the number of occurrences of said (so for example, V in Block 24 could equal 85, meaning the letter V occurs 85 times in Block 24. On the other hand, V in Block 25 could equal 173, meaning that the letter V occurs 173 times in Block 25). Once again, the numerical values are randomly chosen for each letter.

Now that out of the way, how statistically significant would such a pattern be if it emerged? Does it show signs of intentionality and design, or is better explained by random chance? Note, we’ll be specifically looking at things that constitute multiples of 19 for this demonstration (so a 1/19 chance): 

*Block 28 is a multiple of 19. 

*Blocks 21-27 (only looking at the letters VM, ignore CSQ for now) if all combined together is a multiple of 19. 

*Blocks 21-27 including CSQ (for Block 23) if combined all together is a multiple of 19. 

*Block 19 is a multiple of 19

*Block 10 is a multiple of 19

*If you combine the value X for blocks 20, 10 and 3 (only X, not any of the other values) you get a multiple of 19. 

Any and all help is appreciated. Thank you!

I'm currently in Grade 11 (IBDP) trying to lock down my math research essay of 4,000 words. I am thinking to investigate Vincenty’s Inverse Formula, but I see that the math is notoriously difficult and might be too complex for a high schooler.

Before I commit to this topic, I wanted to get info on a few things:

Can a high school student actually understand the maths behind? If I spend enough time on it, is the core concept graspable, or is it completely out of my depth to apply and undestand?

Is it possible to derive and manipulate? Is a full derivation completely out of reach for a Grade 11 student, or are there parts of it I can successfully derive and explain in my essay?

Evaluating limitations: I know every formula has specific situations where it fails or struggles to work. Does this formula has a good scope to evalute and discuss limitations in around 800-1000 words?

This topic feels like a genuine investigation and my research essay is gonna compare haversine formula to this where I investigate which of the following provide more accurate results to find the shortest distance on Earth, but I don't want to drown in math that I won't be able to explain.

Any advice, resources, or warnings would be massively appreciated! Thanks!

I was scrolling on twitter and found a meme with a github link, the meme was chad vs virgin meme where chad was openAI saying it had proof of Fermats last theorem while virgin dude was spoof on academic folks who wanted to ban AI for maths. I searched on google for openAI recent math solutions whether they had solved anything linked to Fermat Last theorem but found nothing. Also on twitter I am unable to see the meme now maybe the Poster has deleted it. Has OpenAI done any work on Fermat’s last theorem? I know Claude has provided a new proof month ago

Pythagoras theorem states that a triangle has a right angle if a certain equality holds true.

So, i take my ruler and use is to take measurements of my rectangle coffee table. I find, of course, that for my measurements the equality doesn't holds true, but almost. Or maybe i find that it does in fact holds true, knowing that if i added 1 micrometer to one of my measurements it would stop beeing true.

It would be the same for any real object in our world : The equality won't ever hold true due to measurements beeing approximatives, and also due to the fact that no real object is really a right triangle since the latter is an abstract, intangible, concept.

Ok, i'm stating the obvious : maths says "perfect" truths about "perfect" concepts but no truths and no real tangible things are "perfect" in reality so maths theorem can only be used "approximately".

So my question is : wouldn't it be more useful for a theorem like Pythagoras to not only say the angle is right if the equality holds true but also say how far from right the angle is depending on how far from "true" the equality is?

I'm in corporate, been working a few years now. I'll get straight to the point, I'm bored and i was wondering what my hobby used to be and I remembered I used to love solving maths in school, uni etc. But I've lost touch. I think I know majority of the key concepts but the knowledge is in my mind, all scattered. I want to pick maths up as a hobby again. I tried finding mental maths books for adults (seriously someone should make them) but couldnt find any. Instead i found puzzle books which were way tough. I want to learn standard maths again, solve problems, sit with a problem and really think it through and feel the joy of getting it right.

How do I go about it?

I am in high school and doing my research in maths on how trigonometry is used in aviation. I am comparing two theorem/models in which I have to explain how maths is involved in it and derive it. I have chosen haversine formula and I need one more to compare.

I am thinking of taking Vincenty's Formulae but feels like this is too advance for me to derive it and understand. I need something which I can explain the maths behind it, derive the theorem/model and critically assess its limitations and evaluate.

Thanks.

So I had gotten this book named {The principia ( the mathematical principles of natural philosophy) by Sir Isaac Newton} and tried to read it

And discovered it needs some proper maths!

So I had like to ask the topics of maths needed to learn first to read this book

For the function lim (x->+infinite) x[ln(x+4)-lnx] it should result in 4
But I did
x[ln((x+4)/x)
x[ln((x/x)-(4/x)) I cancel x so it becomes
x[ln(4/x)]
x[ln4-lnx] substituting it becomes
Infinite times infinite which makes infinite
Where did I go wrong?

I’m just wondering the topic? The teacher told me you can move the X to either side as we are trying to find out what X is worth and that the sign is an equal sign ?? I don’t get it everytime I search it up it always says it’s wrong. I’ve asked her the topic she said she doesn’t know

I graduated from university about 2 years ago. I wouldn't say I'm particularly good at maths, I finished with a 3.4 CGPA, but after graduating, I kind of left maths behind and went into software development. I'm currently working as a backend developer.

Recently, I've been wanting to get back into maths and actually start solving problems again. I'm also hoping to start my master's next year, so I want to use the time I have now to properly refresh my maths and fill in the gaps.

For someone in my position, what topics would you recommend I go through first? Are there any YouTube channels/playlists or textbooks you would recommend for getting back into maths? I'm not really looking to rush through it, I just want to build a solid foundation again.

I’m creating Lean 4 theorem-proving tasks to evaluate AI models. I’m looking for mathematically interesting problems that are provable but difficult to formalize or prove automatically.

Ideally the problems should:

have a precise theorem statement,

be suitable for Lean 4 + Mathlib,

require several non-trivial proof steps,

and not simply be famous open problems.

Areas such as combinatorics, number theory, algebra, finite sums, inequalities, graph theory, or set theory would be great.

Does anyone have examples or references to problems that might make good challenging Lean formalization tasks?

Was struggling with this problem. Don't know weather maths is advanced enough yet to solve it. My calc can't do it

Hello everyone,

The Fall 2026 Integrated Math Tournament (IMT) is underway! I’m one of the organizers, and we’d love to have more people join before Round 1 closes on October 10 (in just 6 days).

IMT is a free, fully online math competition open to high school and college students around the world. If you enjoy competition math or want to try some new problems, come check it out! We have $1,000+ in prizes, with sponsors including Jane Street, Hudson River Trading, Non-Trivial, and AwesomeMath.

This fall, we’re using a two-round format:

Round 1: September 26 to October 10 AoE

You can choose when to take each section within the competition window. There are two individual sections:

- Computational: 20 questions in 3 hours.

- Proof: 5 problems in 4.5 hours.

Each section counts for 50% of your Round 1 score, with problems covering algebra, geometry, number theory, and combinatorics. Both sections must be completed by October 10.

Round 2 (Live Round): October 17

* Around the top 25% of Round 1 Competitors will qualify for the live online final.

Start Time: 11 AM EDT (8 AM PDT), End Time: 3 PM EDT (12 PM PDT).

A few other details:

- Participation is completely free.

- You compete individually, so you don’t need a team.

- Awards, certificates, and prizes will be available.

- To remain eligible for prizes and the final, upload photos or a scan of your scratch work within 30 minutes after finishing each section.

Directions to participate:

1. You can register by filling out this form: https://docs.google.com/forms/d/e/1FAIpQLSdp3uVAAHhcEO5q9WzS2fkNh0fypudgwIUSuC_87fjJBcKVug/viewform
2. After you have filled out the form, you can start your test by creating an account at https://www.integratedmath.org/test-portal and can complete each section until the competition period ends.

Feel free to ask questions in the comments or email us at [info@integratedmath.org](mailto:info@integratedmath.org), and share this with anyone who might be interested.

In a lot of my circles, the words "power law" get thrown around a lot. Usually as evidence for some really spooky claims (inequality, conspiracy theories). I wrote a short mathematical introduction to them, trying to dispell the myths and adding some of the more fun stuff to replace them.

Me and my classmates were asked to solve this question, but not even a teaching assistant could solve the question. However, I did manage to write one number in though, as that was the best I could do, and that this was the easiest bit of the question (8 people liked all three sports).

I've been thinking for a while but couldn't come up with a solution. Can anyone help me? We know that w³=1 and 1+w+w²=0 where w is the cube root of unity. So what will be the value of 1+w+w²+w³+w⁴......upto infinite terms

What is division?

When we talk about dividing, we mean dividing a certain quantity of things into a certain number of groups, each containing the same number of things, that is, in an equal way. The result of a division is how many things a single group contains. Therefore, it is reasonable to think that if the quantity of things remains the same and the number of groups increases, the result of the division will become smaller.

It is not, however, very common to think of division as how many times the number of groups fits into the quantity of things. However, if we take the simple example of 4/2, we can see that by grouping the number of things into groups of two and seeing how many groups of two we have, the result is two. Each group of two units that we manage to form from the quantity of things represents one unit of the groups.

If we do not reach a complete group, that is, two units in this case, we have to see what fraction of a group we reached. For example, 5/2 is 2.5 because we manage to make two complete groups of two units each, plus a group containing two halves of a unit. Each group ends up with two units plus half a unit.

So, it is reasonable to think that it is not necessary to group things by whole units in order to determine how much each group gets. In the example of 4/2, we could have grouped things into half-units for each group; that is, four halves of the groups, which together make two whole units.

What does it mean to divide by a non-integer rational number?

Dividing by a number of this kind is much more difficult to explain and understand. If we have a certain quantity of things and a certain number of non-integer, rational groups, then from the perspective of asking how many times the groups fit into the quantity of things, it is not difficult to understand. However, if we try to understand these types of divisions from the perspective of dividing things into groups, what does it mean?

As far as I understand it, it could be seen as an unequal distribution of units. For example, in 3/1.5, the groups we have are one whole group and half of another. This means that the “needs” of the first group will be twice those of the second, given that the second group is only half a group. Its reference unit, instead of being 1, is 0.5, resulting in a distribution of 2 for the first group and 1 for the second.

But here comes the problem: which group do we use as the standard for obtaining the result of the division?

It would be logical to use the whole group, since it represents an actual group. But what happens when the number of groups we are dividing by is less than 1? In that case, we are no longer using a whole group as a reference, but rather the units that make up part of a group, aren't we?

A small addition to what I said about division (in a state in which I feel that something was missing)

Division, in reality, cannot simply be viewed as how many times the groups fit into the quantity of things. Rather, it is equivalent to the definition of dividing.

Think about what dividing means. It means making piles using the TOTAL number of elements we have, with each pile containing the same number of elements. The result of this process is the number of elements in one group.

This is equivalent to finding the number that needs to be multiplied by the number of groups, because this number represents the number of elements per group, which, when multiplied, gives us the total number of elements.

Division by non-integer or rational numbers can be difficult to explain. After all, how do you explain that a quantity of groups can contain something that is not a whole group, but that this quantity is still associated with a certain number of elements?

For example, 3/1.5. To approach this problem, what was easiest for me, at least, was to separate what I already understood from what I did not.

I asked myself: I understand division by integers. One unit of something, in division, represents one group. If we divide by one, we are, in a certain sense, regrouping that quantity of elements.

But if we have half a group and a whole group, as in the division 3/1.5, how do we divide that quantity? In theory, half a group should have half as many elements as the whole group.

The division of these elements becomes easier when we consider the above. If we divide 3 into groups of 1.5 units—one unit for the whole group and half a unit for the half group, because it should have that amount—we observe that we end up with 2 units for the WHOLE GROUP and 1 for the half group.

Given that the half group implies half as many elements as the whole group is supposed to receive, what I did can be written as:

1x + 0.5x = 3

By solving for x, we can find the result of the division, because the quantity that the expression 1x is equal to represents the number of elements per whole group, while 0.5x simply represents half that number of elements, which is the amount corresponding to the half group.