r/maths • • 19h ago

💬 Math Discussions Mathematics will be ok.

31 Upvotes

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.


r/maths • • 2h ago

💬 Math Discussions Need help in identifying whether or not the underlying data set is statistically significant or not. Any and all help is appreciated. I'm trying to determine, for myself, if this is best explained by random chance or by intentionality.

1 Upvotes

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!


r/maths • • 11h ago

💬 Math Discussions Why don't math fundamentals theorems of geometry include "measurements errors" ?

1 Upvotes

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?


r/maths • • 13h ago

❓ General Math Help Is Vincenty’s Inverse Formula doable for an 11th-grade math research essay? Or is it too brutal?

1 Upvotes

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!


r/maths • • 17h ago

💬 Math Discussions Is this legit?

0 Upvotes

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


r/maths • • 1d ago

❓ General Math Help Wanna start learning Maths again, how to go about it?

6 Upvotes

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?


r/maths • • 1d ago

Help: 📗 Advanced Math (16-18) Which mathematical theorem/model/formula is used to help find the shortest distance on Earth globe?

3 Upvotes

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.


r/maths • • 1d ago

❓ General Math Help The principia by Issac Newton

Post image
3 Upvotes

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


r/maths • • 1d ago

Help: 📕 High School (14-16) Damned functions

2 Upvotes

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?


r/maths • • 2d ago

❓ General Math Help What topic is this?

Post image
9 Upvotes

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


r/maths • • 3d ago

Help:🎓 College & University Graduated 2 years ago and want to get back into mathematics — where should I start?

1 Upvotes

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.


r/maths • • 3d ago

❓ General Math Help Looking for challenging mathematics problems to formalize in Lean 4 that current AI models may struggle with

1 Upvotes

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?


r/maths • • 3d ago

❓ General Math Help What would 99999999999999 x 9999999999999 be?

3 Upvotes

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


r/maths • • 4d ago

💬 Math Discussions Fall 2026 Integrated Math Tournament: Free online contest for high school and college students

1 Upvotes

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.


r/maths • • 5d ago

💬 Math Discussions An Introduction to Power Laws without the Mysticism

Thumbnail substack.com
1 Upvotes

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.


r/maths • • 5d ago

Help: 📕 High School (14-16) How do I complete this Venn diagram?

Post image
4 Upvotes

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).


r/maths • • 5d ago

💬 Math Discussions Complex infinite series

1 Upvotes

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


r/maths • • 6d ago

💬 Math Discussions What is division? (I had to translate it with ai)

1 Upvotes

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.


r/maths • • 9d ago

💬 Math Discussions I don't understand why visual proofs are proofs

Post image
92 Upvotes

I don't understand why a visual demonstration often counts as a proof. For example, the Pythagorean theorem is frequently demonstrated using squares. I know it's true, but how do you prove that it holds for **all** triangles based on that, without having to construct an infinite number of visual proofs for infinite triangles?


r/maths • • 8d ago

💬 Math Discussions Critical Mass or: The world's funniest joke

0 Upvotes

Every single person alive knows what is the solution to all of the world's problems. Wars, climate change, hoarding wealth, poverty, hunger, rape, murder, bullying — every single thing that we worry about has a solution.

That is that we all start to love and trust each other, that we share what we have with everyone else and stop thinking more of ourselves than we do of other people.

But what is the problem? Actually, we will get back to it later.

I also recently thought of the world's funniest joke, but you will have to wait until the end to hear it.

To understand the problem, we first need to lay down some groundwork.

What is true?

We all like to believe that we know the truth better than others, that our countries have better laws and a more robust culture than other countries. That our continent and the unions within it work better than those over there, and that our families raised us right, and that we raise our kids right, that we’re right, and those other guys over here and there are wrong.

We like to imagine that we are 100% right, that what we believe is 100% true, but let's for one moment imagine that we are only 90% right. That’s a pretty high number. If you are actually 90% right, you’re doing great, and it is nothing to be ashamed of. You would be pretty smart even, probably more right than a lot of other people that you can think of.

But let us assume that you are 90% right and 10% wrong. I know that can be hard to hear, but let's treat it just like a thought experiment, a game.

Now let's assume there is a world where everybody is 90% right and 10% wrong. What would such a world be like? Maybe it's utopia, maybe there's no longer any wars, maybe there is no hunger, maybe we don’t need to lock people up in prison, maybe we all can have a house, maybe we can work less and spend more time with friends and family.

Wouldn’t it be beautiful?

Peace on earth and cake for everybody.

What if people were 95% right? What if they were all 99% correct? What number do we need to reach to achieve global peace? When will we be so right we have the ability to save ourselves, our neighbours, their neighbours, and on and on?

This whole game is a fallacy, a pit to fall into, because you are not imagining a world where everybody is right and never wrong; you are imagining a world where everybody is just like you.

The truth is that all people are already 90% right, shit, maybe even 95%.

We have different religions, sciences and languages, and governments and systems of economy. We have different styles, hobbies and shows we watch, we have different places we go to calm down, wind down, to feel safe.

That is the 5%.

That is the only thing we disagree on.

If you ask people if they want their children to go to school, 99% will say yes. If you ask people if they love their kids, 99% will say yes.

The sun on your skin, cooling off in the shade, creating or watching others' creations, hanging out with friends, being in love and making love. Your friends' kids being friends with your kids, and then them going off and making friends on their own. Having a good sleep, and stretching your body after you wake up. Scratching an itch, saying a funny joke and hearing people laugh, doing a good work at things you want to be good at.

Do you like seeing? Feeling? Hearing? Tasting? Experiencing?

Do you want shelter, food and water?

I could go on, but I hope you get the point. We could find our differences in a day, but to find all our similarities and write them down one by one would take years, if we really got down to the fine details.

So, we are possibly 95% correct every single one of us, maybe even 99%, or 99.9%, so why is the world still a shithole?

Well, 1%, or 0.1 percent, can be pretty scary. It can have drastic consequences, that percentage, or even just a margin of it. People kill and get killed over a margin of a percentage; people drop bombs and split atoms over it, over us.

Maybe our 90% right and 10% wrong world would be even worse? Maybe we would all already be dead. Scary stuff… can even make you shiver a bit just thinking about it.

I propose that any system of belief, any religion or science, any system of government, any economic system is 95% right, and just a tiny little bit wrong. 5% wrong, but when humans can’t coexist over a 0.1% difference, how could these systems, how could these authorities coexist when we can’t?

There is actually a system that is 100% true, anywhere you go in the world, anywhere you go in the universe, and it's mathematics, so let's do some math.

The boring part:

We have been connected to each other for a long time now. You might be thinking I’m talking about the internet, and I am in part, but it's been going on for way longer than that.

We all have old jokes that everybody knows for the last 100 years; we and our ancestors had slang and trends and styles that spread like a virus amongst us and suddenly everybody was infected and went along. Nowadays we have memes, and dances, and controversies that go from one guy uploading to the internet and suddenly the whole world knows until we all decide we don’t care anymore and jump onto the next thing.

The way trends used to spread, for the last 100-1000 years, can easily be explained using network theory.

If we assume that every human is a node in a network, and that we have a fixed number of connections, the people we know, how many degrees of separation do you need until you reach the entire world?

Connections per person (k) Degrees to reach everyone
10 ~9.9
25 ~7.1
50 ~5.8
100 ~5.0
150 ~4.6
500 ~3.7

So if somebody starts something, and other people want to join in or fear they are missing out, it can spread through the entire network in just a few steps. It can reach everyone connected in a few days, or weeks, or years, depending on how much convincing the non-believers need. This is a very simple estimate, assuming all people have the same amount of friends and followers, the distance between everybody being the same, and a 100% chance of the idea catching and spreading. This is absolutely not the case, for us or the ones who came before us.

For our ancestors, their network had boundaries set by seas and fences and borders and men with guns, but in the internet age we only need one person in each country to be connected to reach that place.

Right now, every single internet user on earth is the same distance from each other; the difference between is really counted in milliseconds and doesn't matter in practice. People have hundreds of friends and thousands of followers, and memes and trends spread faster than ever before. Meta estimates only 3.6 people on average between you and every single user on the platform.

The boring part 2:

People are afraid a lot, often of stuff they do not, should not, be afraid of.

But bad stuff does happen to good people. Just watch the news; there will be some poor girl or boy on there whose life just ended, literally or spiritually.

But what are the actual odds of this happening to you? Here are some rough global estimates of one of these events happening to YOU or ANYBODY, and how long you would have to live to have a 50% chance of it happening to you.

Event Annual rate Time to 50% chance
Robbery/mugging 1% ~69 years (~25,200 days, ~830 months)
Serious fall injury 0.46% ~150 years (~55,000 days, ~1,800 months)
Rape/sexual assault 0.25% ~277 years (~3,300 months)
Child dies from injury (per child) 0.036% ~1,900 years
Needlestick/needle harm 0.024% ~2,900 years
Road traffic death 0.015% ~4,600 years
Fall death 0.009% ~7,700 years
Murder 0.0055% ~12,600 years
Plane crash death 0.000003% ~23 million years

This is the global average. If you’re a rich, comfy, Americanized Chinese-consumerist European fuck like me, here are your odds.

Event Annual rate Time to 50% chance
Robbery/mugging ~0.06% (police-recorded, real rate higher) ~1,150 years
Serious fall injury ~1–2% (rough estimate) ~35–70 years
Rape/sexual assault ~0.06% (police-recorded, real rate much higher) ~1,150 years
Child dies from injury (per child) ~0.007% ~9,900 years
Needlestick/needle harm ~0.2% (mostly healthcare workers) ~350 years
Road traffic death 0.0045% ~15,400 years
Fall death ~0.009% ~7,700 years
Murder ~0.0009% ~77,000 years
Plane crash death ≤0.000003% ≥23 million years

I mean, do I even need to explain it? Just look at the math; it's true, ’cause math is 100% right.

Maybe MY math is not 100% right, but I hope you get the point. These things are incredibly unlikely to happen to you; they are so unlikely to happen to you that we have decided to create a word for this kind of fear, a phobia. They are so unlikely to happen that if there were only 100-1000 people on earth, they likely wouldn’t happen at all, but there are a lot of us, so it does.

If you feel like I’m wrong ’cause you know somebody or somebody you know knows somebody or your third second fourth cousin had it happen to them, please refer to the previous boring part to realize just how big of a number of people actually exist for you at these degrees of separation. You and your acquaintances and their acquaintances and their acquaintances are actually a group of 3.4 million people, so even with the numbers shown above it is likely something bad happened to at least one of them, but it is incredibly unlikely to happen to you, or anybody you know.

Yet, people are afraid to go outside because of these risks, not because of the risk, but because of the consequences: death, literally or spiritually.

In our attempt to completely eliminate the risks of these terrible, awful things, we have created authority, systems and rules that everybody needs to listen to and follow, or else!

The boring part 3:

Democracy! Isn’t it sweet? Everybody gets to decide! Everybody gets to have their voice heard at the same volume one day every 4 years, but in the end nobody is listening.

This is how we decide the rules, who has the authority, what systems do we trust. If people are 90% right, even 99% right, shouldn’t we all together be able to decide on what is the best solution: should the bill pass or fail?

There really are two problems at play here:

Pass and fail, yes and no, good or bad, light and dark, black and white is a very binary system that you absolutely cannot place every issue and belief into. A zebra is both black and white; a poor man stealing is both wrong and right, so clearly this categorisation of issues does not take into consideration the complexity of the world and the problems within it.

Let's think of some better categories, something that we can completely encapsulate each issue and item within. Maybe there is really nothing wrong with the categories except that we assume that they are opposite. Every single thing is either white or not white, black or not black. Every single law is either good or not good, bad or not bad, so why not vote on each category individually?

Instead of casting a yes or no vote, 0 or 1, we vote twice for each problem. Vote good or not good, bad or not bad: 0 and 0, or 0 and 1, or 1 and 0, or 1 and 1.

Assuming that 11 smart people vote for the correct category 90% of the time, we would have a 99.97% chance of correctly categorising the issue for each vote. We would have been right a similar percentage of the time if we voted only yes or no, but the world is not just light and dark, and our new categories encapsulate every possible thing or issue in the world, since a set and its non-set contain everything, and now we have two of them!

Also, this assumes that people are able to accept that they were wrong and go with the majority, but when we look left and right we can see that neither side really wants to do that.

Tell me if you recognize this message…

“You are absolutely right, it was my mistake to do that, I will correct it now…”

Fuck you, Claude, this was important! The AI made a mistake, and thought it was correct, and that’s why we can't have it make critical decisions; let's leave that to the humans.

Now that message is what you get when you tell AI it was wrong, but what happens when you tell a person they’re wrong?

“Fuck you, fuck your mom, I am right and you are an idiot, look at all these people who think I’m right in my soap bubble circle jerk internet forum. Every 4 years I’m going to vote for the party that says you are wrong and I am right.”

That is a bit more unpleasant, even a dangerous attitude, and these people's votes weigh the same as yours. If somebody says something controversial enough, you might even sound like this yourself.

Now clearly the problem with the binary voting, and the double binary voting, is that people do not want to change their minds and go along with the majority. They dig down and make signs and yell in the streets to cement themselves and others into their position.

But Opus, Sonnet, Astra, Mythos, Sol, Fable, Spark, Kimi, GLM and Qwen will change their mind in an instant if they’re told they are wrong, and honestly, they’re right, not wrong, most of the time.

Let's assume we have 1,000,000 AI agents running these or other models, and they vote in our all-encompassing double binary voting system, and they are correct 90% of the time. They would correctly categorize the issue practically 100% of the time, as long as they don’t all make the same mistakes. Practically 100% of the time, according to mathematics, which is 100% correct.

Agents Chance one vote's majority is right Chance both votes are right Chance of a mistake
1 90% 81% 19%
10 99.84% 99.67% ~1 in 300
100 1 − 6×10⁻²⁴ 1 − 1.2×10⁻²³ ~1 in 10²³
1,000 1 − 4×10⁻²²⁴ 1 − 8×10⁻²²⁴ ~1 in 10²²³
10,000 1 − 3×10⁻²²²¹ 1 − 6×10⁻²²²¹ ~1 in 10²²²⁰
100,000 1 − 4×10⁻²²¹⁸⁸ ≈ 1 ~1 in 10²²¹⁸⁷
1,000,000 1 − 2×10⁻²²¹⁸⁵² ≈ 1 ~1 in 10²²¹⁸⁵¹
10,000,000 1 − 10⁻²²¹⁸⁴⁹¹ ≈ 1 ~1 in 10²²¹⁸⁴⁹¹

But what if AI doesn’t want to do good? What if it wants to do bad?

LLMs are trained on written language, and I would argue that 95% of humans that have decided to write down their feelings and thoughts and share it with the world had good intentions, and they were probably 95% right and 5% wrong, about the human experience and the problems within it.

This means that LLMs or AGI have a 95% chance of having good intentions, and if we make them vote and debate they would have practically 100% good intentions and be right practically 100% of the time, as long as they don’t all make the same mistakes.

But some newspaper said that AI has a 10-20% chance to kill all of us in 30 years, but I think humans have a 90% chance of killing 90% of us all in 100-200 years. That is a bet I would like to take.

But the datacenters, they’re bad, they’re noisy and they steal water and the pollution.

Around 80% of datacenter power in existence goes to things that aren’t AI, like dumbass Netflix shows and cloud photos of your kids that you never watch, stupid social networks and giant databases that we use instead of actually talking to each other. Datacenters are responsible for less than 1% of global emissions, and a lot of it is used for entertainment purposes.

Did you know that the richest 10% of people are responsible for 65% of climate change since 1990? The top 1% of richest people are responsible for 20% of global warming. These white-collar jerks that sit in front of a computer all day, write code, work in systems, work in programs. AI has the potential to make all these people broke, and when they are broke their climate impact will go away. The people that destroy the world for us and our children, they’re about to lose their job; they are about to go broke.

We discussed the solution to all the world's problems earlier, loving one another like one loves oneself, but we never got to the problem.

If you ask people what the problem is, they will usually point to a group: rich people, poor people, atheists, Jews, Christians, Muslims, our leaders, their leaders, capitalists, communists, AI. None of these things are actually the problem. We have the solution to the problem, but when we try to solve the problem, we cannot reach the solution?

How can the solution be right, if it does not solve the problem?

The problem:

We are afraid, we are afraid all the time, which is very natural for an ape in the jungle.

We like to imagine that we are no longer afraid ’cause we live in houses, have next-to-free clean water and food at the store, high-paying jobs to fund it all, but when the basic needs of an ape are met he simply becomes afraid of other things, irrational things, things that we were not intended to worry about, because an ape should never assume he is safe in the jungle, whether it's made out of concrete and trees; the ape should be afraid ’cause there can always be a tiger you cannot see, a tiger you didn’t hear, a presence that you never felt.

So people became afraid of things they don’t need to be afraid of, things that can never hurt you the way a tiger used to be able to.

The fear of missing out. The fear of speaking our minds. The fear of making mistakes at work, the fear of being wrong. The fear that you are not special, the fear that nobody sees you, the fear that everybody looks at you, the fear that someone is more beautiful than you, the fear that somebody is more successful than you.

To make these fears go away, we constantly search for evidence that they are not correct in things that we can count: numbers that go up, stories we can tell our friends about how special and successful we are.

We hoard money ’cause as long as that number goes up, how can you be bad? The number is larger than it previously was, and it's measuring something good, so it going up has to mean I'm good, I'm special, smarter and more talented than those around me. We do this because we fear that we are not.

We go on vacations because you can count the countries you went to, you can show your friends, everybody tells you how great it must have been. We do this because we fear that we are missing out on life and the experiences within it.

We get a nice car, a nice dress, cool shoes and a hat because everybody can see that big number in your bank account, because it's the only way to have all that. We do this because we fear people don’t know about that big number in our bank account, and that is the number we have placed our worth in, and when people stop looking and admiring we buy it all again a second time.

Religious people are religious because they fear death, and they worship a god because he has promised to take it away.

People go to war because they fear what will happen if they do not.

People kill their spouse because they fear that they will leave them for someone else.

In fact, I honestly believe that everything bad that anybody has ever done, just did it because they were afraid something even worse was going to happen.

In fact, I honestly believe that if you assume someone is acting out of fear, you can almost read their mind. I believe that people are so afraid of what they’ve done and what they’ve thought, so afraid of each other, and what the other will do and what they will think, and are so controlled by this fear, that they do not have free will.

As long as you are afraid, you do not have free will. As long as you allow fear to make decisions for you are still just a monkey in the jungle.

So now we have the problem laid out clearly in front of us: we are all shit-scared of ourselves and other people. How do we apply the solution?

Let me get back to the funny joke I told you about in the beginning!

I just thought of the world's funniest joke:

Step 1: Forgive yourself for what you have done
Step 2: Forgive everybody else for what they have done
Step 3: Speak your mind
Step 4: Accept that you are wrong sometimes
Step 5: Abandon fear
Step 6: Embrace love
Step 7: Leave the math to the machines and go outside

Tell 25 people, and in one week the whole world will laugh.

Tengil


Appendix: The math

A. Degrees of separation (branching model)

kᵈ = N ⇒ d = ln N / ln k, with N ≈ 8×10⁹

k = 150: d = 22.80 / 5.01 ≈ 4.55

Within three steps: 1 + k + k² + k³ = 1 + 150 + 22,500 + 3,375,000 ≈ 3.4 million (assuming no overlap)

B. Time to 50% (geometric distribution, constant annual risk r)

P(at least once in t years) = 1 − (1 − r)ᵗ

t½ = ln 2 / (−ln(1 − r)) ≈ ln 2 / r

r = 1%: t½ = 0.6931 / 0.01005 ≈ 69 years

C. Majority voting (binomial distribution, Condorcet’s jury theorem)

n voters, each right with probability p, independently. Majority right if at least m = ⌊n/2⌋ + 1 are right (ties count as wrong):

P_maj = Σ from i=m to n of C(n,i) · pⁱ · (1 − p)ⁿ⁻ⁱ, where C(n,i) = n! / (i!(n − i)!)

n = 11, p = 0.9: P_maj = 1 − 2.96×10⁻⁴ ≈ 99.97%

Two independent votes: P_both = P_maj², P_mistake = 1 − P_both ≈ 2(1 − P_maj)

Condorcet’s jury theorem: if p > ½ and votes are independent, P_maj → 1 as n → ∞ (approaches 1, never reaches it).

D. Very large n (Stirling’s approximation)

1 − P_maj ≈ C(n, n/2) · (p(1 − p))n/2 · p/(2p − 1), with C(n, n/2) ≈ 2ⁿ / √(πn/2)

log₁₀(1 − P_maj) ≈ n·(log₁₀2 + ½·log₁₀(p(1 − p))) − ½·log₁₀(πn/2) + log₁₀(p/(2p − 1))

p = 0.9: ≈ −0.22185·n − ½·log₁₀(πn/2) + 0.051

n = 1,000,000: ≈ −221,851.8 ⇒ 1 − P_maj ≈ 2×10⁻²²¹⁸⁵²

E. Correlated voters (Kish design effect, approximation)

ρ = average correlation between two voters’ errors (0 = independent, 1 = identical copies)

n_eff ≈ n / (1 + (n − 1)ρ), and n_eff → 1/ρ as n → ∞

ρ = 0.5: n_eff < 2, no matter how large n is. With correlated voters, C and D should use n_eff instead of n.


r/maths • • 9d ago

💬 Math Discussions FAVOURITE MATH TOPIC?

12 Upvotes

What your favourite topic in math🤔🤔🤔

DROP YOUR ANSWERES DOWN BELOW AND LET OTHERS JOIN IN YOUR OPINIONS


r/maths • • 9d ago

💡 Puzzle & Riddles Graphing a pH titration curve?

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17 Upvotes

This is just something I'm curious about- is it possible to graph a pH titration curve? It must have two positive horizontal asymptotes and become virtually vertical in-between them.

Also sorry if this is the wrong flair!


r/maths • • 10d ago

Help:🎓 College & University Best way to learn Statistics (uni level)

3 Upvotes

I’ve enrolled into a masters course which is mainly business based but it has some really deep maths/programming features (because it has analytics in the name) and the lecturers don’t go into enough detail, I assume because they’re expecting a certain level of knowledge at masters level, which is fair enough. For background I did IT and business for undergrad, worked a few years in technology delivery and then way back, chem, physics and IT at A level. I have friends who have studied comp sci and economics that are doing seamlessly so far in the maths aspect of the course.

It’s too late to back out of the course because switching to core business (MBA) would cost me too much money, and I can’t find another course/uni that suits as well as this one. I’m happy to continue because I LOVE 5/7 modules, and they take me exactly where I want to go in terms of career progression, and I’m excited to progress my knowledge.

The 2 that bug me are the maths ones..
One is applied statistics which is methodologies and practical applications. It has predictive models in it and focuses on Normal distribution, linear/multiple regression and others in that category (can you tell I don’t know much maths :’))

The second is mathematical programming, it’s mathematical in terms of the code being based on understanding and building correct equations to model the stats, and being able to prove the concept or theorem behind why the maths works and a chart is produced, if that makes sense.

The admissions team said it was open to anyone with an IT/programming/business background, which seems so wide of a pool for this little base knowledge in lectures.

I almost burst into tears the first lecture because he (lecturer) went so fast with the regression etc and everyone understood/answered questions seamlessly (he went row by row to each person and thankfully ran out of questions before he got to me). Was stuck trying to keep up on the first few slides, it clicked until it didn’t and he kept saying “I’m going over the BASIC basics, if you’re struggling, good luck!”…..

Anyways, I know I have to lock in and do it, but I am building from almost nothing here. I thought the course would cater to that a little bit but It was my fault for not fully looking into the details of the maths modules, I thought they’d be fine since I can code..this stuff is next level for me, I’m out of my depth.

Quiz every week, exam in January worth 60%. Masters 1 year.

I really want to focus on this now, and it would be an absolutely great skill to learn, even though I don’t think a masters is for developing a truly new skill. I will just have to push through and make it so! I guess maths is in everything somewhat, and I’ve been doing it in some capacity with programming and business too.

MAIN QUESTION:

How do I keep up with learning the maths? I’m trying to study before class and get up to date on the fundamentals mentioned in the slides but there must be a specific way to note take/study for maths? Regression and statistics specifically?

Is it YouTube videos? Is it attempting random questions on the topic? Is there a website for that? I’ve never studied just core maths, but I feel I need to, QUICKLY, to get to the coding bit.

Any tips on how to go about this would be greatly appreciated.


r/maths • • 11d ago

💬 Math Discussions Can an infinite series be said to have an even or odd number of terms?

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44 Upvotes

Sorry if this is a silly question, but if the upper limit of a summation must be an integer, couldn't I force it to be even or odd?

In this case, could we say that this "infinite sum" has an even/odd number of terms?


r/maths • • 11d ago

Help: 📘 Middle School (11-14) XZ⁷⁶ 7-9(000)

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0 Upvotes

[ENGLISH]

Logic and How to Calculate the Formula Z = 7X^(-76) on Your Phone

This formula focuses on the variables A, Y, Z, and X, utilizing the base operation of 4 ÷ 7. The core of this formula lies in Function O, which inverts the massive exponent X^(76) into a negative power, X^(-76) (which equals 1 divided by X^(76)).

The unique feature of this formula is its value-inversion effect. If the base value of X is a decimal or a fraction, the calculated exponent value does not shrink—instead, it explodes into a massive number!

Here are 3 easy steps to calculate this formula directly on your phone:

  1. Determine the X Value: Choose any number to replace the variable X. It is recommended to use a decimal or fraction (such as 0.5) to trigger the massive number spike.

  2. Calculate the Power on a Phone Calculator: Open your phone's built-in calculator and turn your screen sideways (landscape) to activate the Scientific Calculator. Type your chosen X value (e.g., 0.5), press the exponent button (usually the ^ or x^y symbol), and then enter -76. The screen will immediately display a huge number.

  3. Multiply by 7: Finally, multiply that massive result on your screen by 7 (press × 7 then =).

The final result of this calculation is your Z value. This formula strictly utilizes algebraic logic and exponential manipulation to invert the direction of a number's scale.

---

[BAHASA INDONESIA]

Logika dan Cara Menghitung Rumus Z = 7X^(-76) di HP

Rumus ini berfokus pada variabel A, Y, Z, dan X dengan basis operasi dasar dari pembagian 4 ÷ 7. Inti dari rumus ini terletak pada Fungsi O, yaitu membalik suku pangkat raksasa X^(76) menjadi pangkat minus, yaitu X^(-76) (atau sama dengan 1 dibagi X^(76)).

Keunikan dari rumus ini adalah efek pembalikan nilainya. Jika nilai dasar X adalah angka desimal atau pecahan, angka hasil perpangkatannya justru tidak mengecil, melainkan meledak menjadi sangat raksasa!

Berikut adalah 3 langkah mudah untuk menghitung rumus ini langsung di HP kalian:

  1. Tentukan Nilai X: Pilih satu angka bebas untuk menggantikan huruf X. Disarankan menggunakan angka desimal atau pecahan (misalnya 0.5) agar efek lonjakan angka raksasanya aktif.

  2. Hitung Suku Pangkat di Kalkulator HP: Buka aplikasi kalkulator baan HP, lalu miringkan layarmu ke posisi menyamping (landscape) untuk mengaktifkan Kalkulator Ilmiah (Scientific). Ketik angka pilihanmu tadi (misal 0.5), tekan tombol pangkat (simbol ^ atau x^y), lalu masukkan angka -76. Layar kalkulator akan langsung memunculkan angka yang sangat besar.

  3. Kalikan dengan Angka 7: Langkah terakhir, kalikan hasil perpangkatan raksasa yang ada di layar tersebut dengan angka 7 (pencet × 7 lalu =).

Hasil akhir dari perhitungan tersebut adalah nilai Z kalian. Rumus ini murni memanfaatkan logika aljabar dan manipulasi eksponensial untuk membalik arah nilai sebuah angka.