#math community

[xyymath]

Why the Number Zero Changed Everything

Zero: a concept so foundational to modern mathematics, science, and technology that we often forget it wasn’t always there. Its presence in our world today seems obvious, but its journey from controversial abstraction to indispensable tool has shaped entire civilizations.

1. The Birth of Zero: A Revolutionary Idea

The concept of zero didn't exist in many ancient cultures. For example, the Greeks, despite their advancements in geometry and number theory, rejected the idea of a placeholder for nothingness. The Babylonians had a placeholder symbol (a space or two slashes) for zero, but they didn't treat it as a number. It wasn't until Indian mathematicians in the 5th century, like Brahmagupta, that zero was truly conceptualized and treated as a number with its own properties.

Zero was initially used as a place-holder in the decimal system, but soon evolved into a full-fledged number with mathematical properties, marking a huge leap in human cognition.

2. The Birth of Algebra

Imagine trying to solve equations like x + 5 = 0 without zero. With zero, algebra becomes solvable, opening up entire fields of study. Before zero’s arrival, solving equations involving unknowns was rudimentary, relying on geometric methods. The Indian mathematician Brahmagupta (again) was one of the first to establish rules for zero in algebraic operations, such as:

x + 0 = x (additive identity)

x × 0 = 0 (multiplicative property)

These properties allowed algebra to evolve into a system of abstract thought rather than just arithmetic, transforming the ways we understand equations, functions, and polynomials.

3. Calculus and Zero: A Relationship Built on Limits

Without zero, the foundation of calculus—limits, derivatives, and integrals—wouldn’t exist. The limit concept is intrinsically tied to approaching zero as a boundary. In differentiation, the derivative of a function f(x) is defined as:

f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

This limit process hinges on the ability to manipulate and conceptualize zero in infinitesimal quantities. Similarly, integrals, which form the backbone of area under curves and summation of continuous data, rely on summing infinitely small quantities—essentially working with zero.

Without the concept of zero, we wouldn’t have the means to rigorously define rates of change or accumulation, effectively stalling physics, engineering, and economics.

4. Zero and the Concept of Nothingness: The Philosophical Impact

Zero is more than just a number; it’s an idea that forces us to confront nothingness. Its acceptance was met with philosophical resistance in ancient times. How could "nothing" be real? How could nothing be useful in equations? But once mathematicians recognized zero as a number in its own right, it transformed entire philosophical discussions. It even challenged ideas in theology (e.g., the nature of creation and void).

In set theory, zero is the size of the empty set—the set that contains no elements. But without zero, there would be no way to express or manipulate sets of nothing. Thus, zero's philosophical acceptance paved the way for advanced theories in logic and mathematical foundations.

5. The Computing Revolution: Zero as a Binary Foundation

Fast forward to today. Every piece of digital technology—from computers to smartphones—relies on binary systems: sequences of 1s and 0s. These two digits are the fundamental building blocks of computer operations. The idea of Boolean algebra, where values are either true (1) or false (0), is deeply rooted in zero’s ability to represent "nothing" or "off."

The computational world relies on logical gates, where zero is interpreted as false, allowing us to build anything from a basic calculator to the complex AI systems that drive modern technology. Zero, in this context, is as important as one—and it's been essential in shaping the digital age.

6. Zero and Its Role in Modern Fields

In modern fields like physics and economics, zero plays a crucial role in explaining natural phenomena and building theories. For instance:

In physics, zero-point energy (the lowest possible energy state) describes phenomena in quantum mechanics and cosmology.

In economics, zero is the reference point for economic equilibrium, and the concept of "breaking even" relies on zero profit/loss.

Zero allows us to make sense of the world, whether we’re measuring the empty vacuum of space or examining the marginal cost of producing one more unit in economics.

7. The Mathematical Utility of Zero

Zero is essential in defining negative numbers. Without zero as the boundary between positive and negative values, our number system would collapse. The number line itself relies on zero as the anchor point, dividing positive and negative values. Vector spaces, a fundamental structure in linear algebra, depend on the concept of a zero vector as the additive identity.

The coordinate system and graphs we use to model data in statistics, geometry, and trigonometry would not function as we know them today. Without zero, there could be no Cartesian plane, and concepts like distance, midpoint, and slope would be incoherent.

[kimblestudies]

would anyone be interested in an upper level mathematics discord? I know there's math and hw servers out there but I was thinking it may be nice to help each other with let's say everything past precal ?

[inkskinned]

you were raised in comparison.

it wasn't always obvious (well. except for the times that it was), but you internalized it young. you had to eat what you didn't like, other people are going hungry, and you should be grateful. you had to suck it up and walk on the twisted ankle, it wasn't broken, you were just being a baby. you were never actually suffering, people obviously had it worse than you did.

you had a roof over your head - imagine! with the way you behaved, with how you talked back to your parents? you're lucky they didn't kick you out on your ass. they had friends who had to deal with that. hell, you have friends who had to deal with that. and how dare you imply your father isn't there for you - just because he doesn't ever actually talk to you and just because he's completely emotionally checked out of your life doesn't mean you're not fucking lucky. think about your cousins, who don't even get to speak to their dad. so what if yours has a mean streak; is aggressive and rude. at least you have a father to be rude to you.

you really think you're hurting? you were raised in a home! you had access to clean water! you never so much as came close to experiencing a real problem. sure, okay. you have this "mental illness" thing, but teenagers are always depressed, right. it's a phase, you'll move on with your life.

what do you mean you feel burnt out at work. what do you mean you mean you never "formed healthy coping mechanisms?" we raised you better than that. you were supposed to just shoulder through things. to hold yourself to high expectations. "burning out" is for people with real jobs and real stress. burnout is for people who have sick kids and people who have high-paying jobs and people who are actually experiencing something difficult. recently you almost cried because you couldn't find your fucking car keys. you just have lost your sense of gratitude, and honestly, we're kind of hurt. we tell you we love you, isn't that enough? if you want us to stick around, you need to be better about proving it. you need to shut up about how your mental health is ruined.

it could be worse! what if you were actually experiencing executive dysfunction. if you were really actually sick, would you even be able to look at things on the internet about it? you just spend too much time on webMD. you just like to freak yourself out and feel like you belong to something. you just like playing the victim. this is always how you have been - you've always been so fucking dramatic. you have no idea how good you have it - you're too fucking sensitive.

you were like, maybe too good of a kid. unwilling to make a real fuss. and the whole time - the little points, the little validations - they went unnoticed. it isn't that you were looking for love, specifically - more like you'd just wanted any one person to actually listen. that was all you'd really need. you just needed to be witnessed. it wasn't that you couldn't withstand the burden, but you did want to know that anyone was watching. these days, you are so accustomed to the idea of comparison - you don't even think you belong in your own communities. someone always fits better than you do. you're always the outlier. they made these places safe, and then you go in, and you are just not... quite the same way that would actually-fit.

you watch the little white ocean of your numbness lap at your ankles. the tide has been coming in for a while, you need to do something about it. what you want to do is take a nap. what you want to do is develop some kind of time machine - it's not like you want your life to stop, not completely, but it would really nice if you could just get everything to freeze, just for a little while, just until you're finished resting. but at least you're not the worst you've been. at least you have anything. you're so fucking lucky. do you have any concept of the amount of global suffering?

a little ant dies at the side of your kitchen sink. you look at its strange chitinous body and think - if you could just somehow convince yourself it is enough, it will finally be enough and you can be happy. no changes will have to be made. you just need to remember what you could lose. what is still precious to you.

you can't stop staring at the ant. you could be an ant instead of a person, that is how lucky you are. it's just - you didn't know the name of the ant, did you. it's just - ants spend their whole life working, and never complain. never pull the car over to weep.

it's just - when it died, it curled up into a tight little ball.

something kind of uncomfortable: you do that when you sleep.

[cannibalisticdespair]

So, humanity is at over eight billion people. Time for a bit of statistics education for y'all, because I feel like it.

Okay, take a group that's around 1%. At least officially, it could possibly be higher. So like,

BPD: 1.6% officially

DID: 1.5% officially

Trans: 1.14% officially

Schizophrenia: 1.1%

These are American statistics, but presuming that overall none of these have some sort of strong cultural cause, they should be representative of the norm of humanity. Now, let's get the raw number estimate out of this. What we're going to need to do is multiply 8,000,000,000 by 0.016, 0.015, 0.0114, 0.011 respectively.

128,000,000

120,000,000

91,200,000

88,000,000

So, this a rough estimate for the number of people in each category respectively. Bit bigger than you might assume when you hear "approximately 1%", right? When you hear "approximately 1%", you're liable to think something is super rare. And in proportion, yeah, sure.

But plot twist, I'm discussing misinformation and bad propaganda. Did you know the internet allows disparate groups of small populations to connect and form larger communities than was ever possible offline due to how irl populations are distributed? Now, imagine a community of just 25% of trans people. Using the prior information, you can do this calculation yourself.

Done it? Did you get 22,800,000 people? Good job. If not, the calculation should have been 91,200,000 x 0.25. Now, imagine a community online of 22,800,000 people. That's a pretty damn big community online, right?

And this here shows how false claims of the level of visibility of various groups online being the result of "fakers" and "trenders" is. Those claims rely on your inability to understand that even 1% of humanity is 80,000,000 people. You aren't seeing anywhere close to 80,000,000 different people posting about it. You aren't even seeing 1,000,000 people posting about it. You are seeing a tiny fraction of a tiny fraction of humanity posting about it. Social media just enables that itty bitty bit to find each other and interact.

[purposeastro]

High Sex Drive| Vedic Astrology ( 18 + )

These Combinations and Aspects indicates a Higher Sexual Drive in a Person

If your Mars is in 1st 5th , 7th, 8th and 12th house aspected by Venus or in Venus Nakshatra then it gives native a very high sexual drive.

GEMINI MARS and SCORPIO MARS especially have higher sex drive.

GEMINI MARS aspected by Venus will get attracted to multiple partners and different types of sexual activities.

SCORPIO MARS is more on the hidden side deep and intense relationship with someone who noone knows.

MARS + VENUS in LIBRA and GEMINI shows Higher Sex Drive

RAHU + MARS in 5th House aspected by Venus

RAHU VENUS and MARS in 8th 7th or 12th houses can get agressive in sex and can harm themselves

This combination in 8th house with debilated planet can make the person into Rap*s, Extra Marital Affairs and Criminal activities.

MOON RAHU aspected by VENUS person will think about ssex sexual thoughts whole day. Involvement of Rahu will get into Porn. All the ONLY F@NS community and other things which are digital have Rahu energy in them.

VENUS SUN RAHU clearly shows extra marital and are mostly in prostitution and they can earn money alot due to VENUS SUN combination and rahu is online so through media.

Afflicted PISCES VENUS can make a person have higher sexual drive and more into these activities.

100 drops of blood = 1 drop of semen

1 drop of semen = 500 million to 700 million sperms and this is the nutrition for your brain as well.

Excessive masturbation can cause hair thinning, fuzzy vision and other issues as you're loosing your brains nutrition.

I'm doing Vedic Readings. Please Donate 👇👇👇🙏🙏

Radhey Radhey 🪷🪷🪔🪔🪷🪷

[anim-ttrpgs]

"Arithmomaniac," investigator Trait from Eureka: Investigative Urban Fantasy. Every investigator has 3 to 6 Traits!

[floralfractals]

so id say my tumblr network (as in, the people who tend to see/interact with my posts) is pretty mathy. i wanted to see how people interact w math and how they like to learn about it :) (and: maybe do something with that on my blog!!! wouldnt that be fun)

polls have a limited amount of characters i can add per option, so ill clarify some concepts here:

informal education is learning via a coordinated effort by an instance/expert outside of school system (e.g. voluntary lectures, social media posts, museum visits, youtube videos or similar). by informal i dont mean "its school but the teacher is chill" or independent research!!

formal education is learning through a school system (usually mandatory/with a teacher or professor present)

i refer to any education you do without making use of coordinated programmes as independent research, so that would be just you picking up an advanced math book to educate yourself, or perhaps scanning wikipedia, or emailing math profs with questions

when i talk about reading math in a general context, i mean that the material discusses math for a broad audience, so it doesnt talk about super niche specific mathematical concepts, and doesn't contain any complicated formulas/proofs/math speech

please do elaborate in the tags!!!

[graham-tails]

Tiktok is gone. I’m going back to my roots.

[cyanophen]

giantleongiantleongiantleon-

[divinit3a]

[xyymath]

The Math of Social Networks: How Social Media Algorithms Work

In the digital age, social media platforms like Instagram, Facebook, and TikTok are fueled by complex mathematical algorithms that determine what you see in your feed, who you follow, and what content "goes viral." These algorithms rely heavily on graph theory, matrix operations, and probabilistic models to connect billions of users, influencers, and posts in increasingly intricate webs of relationships.

Graph Theory: The Backbone of Social Networks

Social media platforms can be visualized as graphs, where each user is a node and each connection (whether it’s a "follow," "like," or "comment") is an edge. The structure of these graphs is far from random. In fact, they follow certain mathematical properties that can be analyzed using graph theory.

For example, cliques (a subset of users where everyone is connected to each other) are common in influencer networks. These clusters of interconnected users help drive trends by amplifying each other’s content. The degree of a node (a user’s number of direct connections) is a key factor in visibility, influencing how posts spread across the platform.

Additionally, the famous Six Degrees of Separation theory, which posits that any two people are connected by no more than six intermediaries, can be modeled using small-world networks. In these networks, most users are not directly connected to each other, but the distance between any two users (in terms of number of connections) is surprisingly short. This is the mathematical magic behind viral content, as a post can be shared through a small network of highly connected individuals and reach millions of users.

Matrix Operations: Modeling Connections and Relevance

When social media platforms recommend posts, they often rely on matrix operations to model relationships between users and content. This process can be broken down into several steps:

User-Content Matrix: A matrix is created where each row represents a user and each column represents a piece of content (post, video, etc.). Each cell in this matrix could hold values indicating the user’s interactions with the content (e.g., likes, comments, shares).

Matrix Factorization: To make recommendations, platforms use matrix factorization techniques such as singular value decomposition (SVD). This helps reduce the complexity of the data by identifying latent factors that explain user preferences, enabling platforms to predict what content a user is likely to engage with next.

Personalization: This factorization results in a model that can predict a user’s preferences even for content they’ve never seen before, creating a personalized feed. The goal is to minimize the error matrix, where the predicted interactions match the actual interactions as closely as possible.

Influence and Virality: The Power of Centrality and Weighted Graphs

Not all users are equal when it comes to influencing the network. The concept of centrality measures the importance of a node within a graph, and in social media, this directly correlates with a user’s ability to shape trends and drive engagement. Common types of centrality include:

Degree centrality: Simply the number of direct connections a user has. Highly connected users (like influencers) are often at the core of viral content propagation.

Betweenness centrality: This measures how often a user acts as a bridge along the shortest path between two other users. A user with high betweenness centrality can facilitate the spread of information across different parts of the network.

Eigenvector centrality: A more sophisticated measure that not only considers the number of connections but also the quality of those connections. A user with high eigenvector centrality is well-connected to other important users, enhancing their influence.

Algorithms and Machine Learning: Predicting What You See

The most sophisticated social media platforms integrate machine learning algorithms to predict which posts will generate the most engagement. These models are often trained on vast amounts of user data (likes, shares, comments, time spent on content, etc.) to determine the factors that influence user interaction.

The ranking algorithms take these factors into account to assign each post a “score” based on its predicted engagement. For example:

Collaborative Filtering: This technique relies on past interactions to predict future preferences, where the behavior of similar users is used to recommend content.

Content-Based Filtering: This involves analyzing the content itself, such as keywords, images, or video length, to recommend similar content to users.

Hybrid Methods: These combine collaborative filtering and content-based filtering to improve accuracy.

Ethics and the Filter Bubble

While the mathematical models behind social media algorithms are powerful, they also come with ethical considerations. Filter bubbles, where users are only exposed to content they agree with or are already familiar with, can be created due to biased algorithms. This can limit exposure to diverse perspectives and create echo chambers, reinforcing existing beliefs rather than fostering healthy debate.

Furthermore, algorithmic fairness and the prevention of algorithmic bias are growing areas of research, as biased recommendations can disproportionately affect marginalized groups. For instance, if an algorithm is trained on biased data (say, excluding certain demographics), it can unfairly influence the content shown to users.

[study-diaries]

Math Tips

(Pictures are not mine)

Well, let me tell you, we all have this love-hate relationship with this subject, right? The worst part is that when you don't know what the heck is going on, so, as a girl who studied maths (2 Volumes/textbooks) on her own during the year she was homeschooled, here are some tips and tricks that I did to get an A+ in my math finals!

Get your syllabus together

In the beginning I had no damn idea what was going on and it was just confusing. I had to do the first thing I did was taken my index/table of contents and mark the chapters which i knew very well and the ones I had no clue about. And then i arranged them with the marking scheme, like which one carries the most marks etc etc and study accordingly.

Complete lessons/chapters that you already know

When you finish off the things you already know then that's gonna give you the confidence you need even if you know only 1-2 chapters, learn it throughout and make sure that you'll get the answer no matter how twisted the sum is. If you're doubtful about the whole textbook like any normal person.... Start with the easy ones. (I know there are literally really no "easy" chapters, spare me)

Harder chapters need hard work

Most chapters like Trigonometry proofs, Geometry proofs, Algebra, Graphs, Mensuration and Calculus etc need more than minimum effort but here's a trick, what is the common thing in this? Yes, they're all formulae and theorem based which goes to my next point. These chapters are completely based on how much you've understood your basics.

Formulae and theorem cheatsheets

Make a list of all formulae and the theorem used in the book, write them chapter wise and no printouts or digital notes. Take a paper and write it down, no excuses. It helps you while you're practicing, revising and in the last minute review, it helped me damn much. Remember, maths is a sport. The basic formulae must come to you like reflexes.

YouTube is your best friend.

For every single chapter, go and watch the basics and how a sum is done step by step. A recommendation for this is Organic Chemistry Tutor who literally is one of the reasons i passed. He has videos from basic geometry, trigonometry, statistics to calculus. Search for your own YouTubers and be clear with concepts.

Math is fully memorization

Memorize formulae and theorems with the back of your hand, you should be able to recall them within seconds. Be thorough.

Memorize basic math values (if calculator isn't allowed)

Do this if you have a majority of chapters like Statistics, Mensuration, Profit/loss calculation etc, where large numbers are concerned. Memorize the first 10 square, cube, decimal and multiplication values. It may be dry but there are literally songs available for these things, I'm serious, i learnt the first 10 cube roots by listening to Senorita xD Search for rhymes and they'll definitely be many!!

Work it out!!!!!!

Can't stress this enough, atleast 30-40 mins is the minimum for maths. I'm serious, work out each sum, don't ever think it's a waste, you'll see the results. Practice makes perfect. Work out every single sum, from examples to exercise ones cause let's be honest, our examiners love to take problems from every nook and cranny of the book.

Whiteboard method

So, I made this up and it actually works, if you have a whiteboard or anything else, once you completed a chapter, take a random page and whatever sums you have on those two pages, you need to complete within a given time limit. It helps you to identify your weak points and where the hell you're losing both time and effort and not to mention that it gives you confidence boost up.

Hope this helps :))

[catscomputerscreativewriting]

I need to start a collection of "math things that really, really sound like wizard and/or cleric things."

[purposeastro]

What Saturn wants you to sacrifice? 🪐

Saturn in 1st House : Sacrifice to make your body Fit.

Saturn in 2nd house : Sacrifice food. Fasting.

Saturn in 3rd house : Sacrifice dictating people. Do your work on your own with your own hands.

Saturn in 4th house : Sacrifice emotional feelings.

Saturn in 5th house : Sacrifice fruits of life just do work without thinking about the results.

Saturn in 6th house : Sacrifice being not in routine.

Saturn in 7th house : Sacrifice pleasures of marriage.

Saturn in 8th house : Sacrifice not being loyal. Lots of sacrifices needed in this house.

Saturn in 9th house : Sacrifice your freedom.

Saturn in 10th house : Sacrifice irregularities in life. Eg : working regularly.

Saturn in 11th house : Sacrifice your friendship.

Saturn in 12th house : Sacrifice being Lazy.

Add on : currently Saturn will go in Pisces on 29 March. There'll be a huge change in people and more will become lazy. Many Natural calamities related to water bodies will happen. We've very few time left now!!

[egotisticaleaderr]

Drawing two struggling at doing basic math question bc I hate math