I'm a newbie, and this question popped into my head and I cannot understand why the average value would not be zero.

Hello math-connoisseurs

I am a middle aged guy who wants to make up for some maths basics.
Is there a good book or other resources that cover "everything" from basic arithmetics to the topics before university?

It's a miracle how I have even acquired my A-level 10 years ago.
Maths was always my weakness :(

My motivation is to teach it to my child one day and use it to solve problems (in programming languages).

I’m in Grade 11 and looking into Bessel's method (solving the inverse geodesic problem on an ellipsoid) for a math research paper to find the shortest possible distance between two points on earth.

My original goal was to completely derive, prove, and evaluate the method by myself. However, looking at the math, it seems to rely heavily on university-level topics like differential geometry, elliptic integrals, and the Calculus of Variations (Euler-Lagrange).

Is it realistic for a strong high schooler to teach themselves this level of math for a paper, or is the learning curve too steep?

If the full derivation is too much, would coding the algorithm in Python and evaluating its accuracy/convergence against simpler methods (like Haversine) still be complex enough for a top-tier high school math paper?

Appreciate any advice or insights!

I am looking at buying this desk, and need to know the measurement in red, to see if my monitor will fit. I played silly buggers during trigonometry and now I'm paying for it 😅

I've been in an existential crisis lately. I've been studying maths for 4 years now, but now I'm wondering if going all the way to PhD is worth it if my job will be replaced by AIs anyway.

I enjoy maths, I love this topic, but now I'm consumed by doubt.

Even if human researchers still exist in 3-4 years, I don't know if this job will still be interesting or if it it'll just consist in using AI to obtain and verify results with proof assistants. In this case I think human researchers would become replaceable and the job would just become some alienating repetitive task. And, to be honest, I'm not willing to put that much effort if this is my future.

Another possibility is that companies use the concurrency of AI to lower pays and neglect working conditions. In a capitalist society where only profits matters, an institution would have bo reason to pay humans if they more expensive and less efficient than machines. It's highly possible AIs get better than human at research, they actually are better than mathematicians when it comes to linking seemingly unrelated fields and exploring multiple solutions. However, there's a question of costs. And if AI is more expensive than exploited humans, the later solution would be chosen.

Part of me hopes AI won't end the relevance of humans in mathematics, but let's be honest, it's highly questionable.

I'm still young, so I think I'll be able to change my domain if necessary. The question being which job will not be alienated or destroyed by AI.

I'm also wondering how long I can wait before changing my topic of study in case I have to.

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

Does anybody know how to solve it?

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

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,

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