Due to the properties of the number 25, we'll get some notable mathematical holidays this year

Square Root Day - 5/5/2025

Pythagorean Theorem Day - 7/24/2025

Square Sequence Day - 9/16/2025

Summary: If I have middle school level of mathematics and I want to qualify to the AIME and I only have 4 years, would it be possible?

Explanation: Hello, I am in seventh grade and have no experience with any competition mathematics and did not know about the AMC/AIME until like last week. It is 3 years until I take the AMC 10 and in 4 years, I am hoping to have enough knowledge to qualify to AIME. Any advice for pure beginner on books to read, courses to do, etc. that would get to a level of qualifying to the AIME in around 4 years and the AMC 10 in 3 Years

What do you think are the best places to study Differential Geometry, both for a masters degree or a PhD?

What are your thoughts?

So, I broke my leg twice during my junior and senior years in hs. I was still going to school during this time and I had to move around to get to places such as the cafetaria, music rooms, auditorium, etc. So, I was wondering if there was a way to mathematically solve for the optimal position to place my classroom (which is basically where all my lessons take place and therefore where I would have to inevitably come back to after each trip) so that I can minimize my distance of travel.

Is it possible to solve for this mathematically? If so what concepts must i use to do so and how is it done? Also, I was wondering if I can weigh in the frequency of visits to each place too, in the calculation.

(Btw, my school has 4 floors and multiple ways to get to one place. Given this, is the calculation still possible?)

So...there's an obvious reason for this, right? (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)^2 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3

I just completed the multiple integral part of calculus 3, and I found myself doing the same things from calculus 1, and it kind of seemed uninteresting. It was fun to learn about derivatives and integrals for the first time and understand the justifications behind them, but now it seems it's just about rates and volumes, etc. So, I ask you what is something that I don't seem to see and what else I can hope in future topics to know that there is more than rates and volume in calculus.

Let's say there's a roulette wheel with numbers 1-36 plus a green zero, but the payout for any type of bet is based on what would be fair odds if there was no green zero. This means the house's advantage is 1/37 (or, your expected return for any money you put on the table is -1/37 per dollar you bet)

But why are you playing roulette? I assume you want the excitement of a chance to win big money. In this case, you are much better off taking a long shot bet (like putting $30 on a single number) rather than putting $540 on an even money payout like red/black or odd/even

Both of these cases give you the chance to walk away with $1080, but the former has a better expected return because you're putting less money on the table (though it's still negative). Even if you decided to repeatedly bet $30 till you either won or ran through the full $540 you brought with you, you will still lose less on average because if you win early then you've put less on the table (you can do the math to check. An easier example is if someone has $10 they put on 18/37 chance of doubling, his expected return is worse than putting the first $5 at 12/37 and the next $5 at 9/37 if he hasn't won yet, even though both options give him the opportunity to walk away with $20)

This makes me wonder if, in situations where a bookie is setting the odds (like sports gambling), should he / does he deliberately make the long shots worse to encourage people to choose big safe bets rather than smaller bets? Is there a name for this?

To summarize / put a different way, if we psychologically think about our bets in terms of how much we stand to win, but the house makes money on how much we actually stake, then the player should prefer long odds with small stakes

Im almost at college (currently 4th year JHS) and i want to enroll for a Bachelor of Science Major in Mathematics degree but i dont know what to do about it. I love math and is good at understanding it but math jobs are a pretty niche topic in my area so any suggestions please? I cannot decide since there are a really lot of suggestions in google so if anyone has a BS math degree here feel free to spread some word of advice and how your jobs went!!! (⁠⊙⁠_⁠◎⁠) + Btw i live in a residential community but going far to the big city here in our country is not a problem for me!:}

[logic joke; delete if not allowed]

...to fail at least one of my future New Years' resolutions.

I hope I fail again this year.

Hi! I am writing on this topic I came up with: “how do the fractal dimensions of fractal-like shapes in nature compare to calculated fractals?” I plan to compare by taking pictures of spiral shells and fern branches and lining them up with similar pictures of fractals to the best of my ability to get similarly sized printed images, then I will lay a few clear laminated sleeves with differing grid sizes over the pictures to use the box method using the number of inches the individual side length of a box on the grid as the box size to calculate their fractal dimension, then I will use my results to come up with a conclusion. Would this be mathematically “allowed”? It seems sketchy to me with all the eyeballing and approximations involved, but I figured I should consult someone with more than 1 week of experience in the subject. Thank you for reading, I hope I made it understandable😭

I have to take this class as a requirement for my applied math major and im honestly not too confident that i can pass this class. I've had a combinatorics class that was 1/4 proof based and i totally sucked at doing them. I can only do weak induction at most. This is my final semester and im honestly scared it will delay my graduation.

What do you think made your application stand out? Why do you think you got accepted? And which schools did you get accepted to, where did you end up at?

I know white holes are a big one. The math checks out but we haven't observed any so far. Anything else?

Happy New Year lovely mathematicians 🤓

So I was reading the news and read about some guy just found the next prime number and was a bit confused, thought we actually had a formula, any hooooow I thought well it would be a bit of fun to just see what I could do with a bit of code and basic formula so I started with the gaps between the primes because Ive always enjoyed patterns... my results however are intresting enought to see it keeps growing...

Range 1 - 1000

Pattern Positions:

Position 10: [31, 37, 41, 43] → [6, 4, 2]

Position 17: [61, 67, 71, 73] → [6, 4, 2]

Position 20: [73, 79, 83, 89] → [6, 4, 6]

Position 36: [157, 163, 167, 173] → [6, 4, 6]

Position 57: [271, 277, 281, 283] → [6, 4, 2]

Position 73: [373, 379, 383, 389] → [6, 4, 6]

Position 83: [433, 439, 443, 449] → [6, 4, 6]

Position 110: [607, 613, 617, 619] → [6, 4, 2]

Position 129: [733, 739, 743, 751] → [6, 4, 8]

Position 132: [751, 757, 761, 769] → [6, 4, 8]

Pattern Frequencies:

6,4,2 occurs 4 times

6,4,6 occurs 4 times

6,4,8 occurs 2 times

then the next range and I did this for each range

Range 1001 - 2000

Pattern Positions:

Position 41: [1291, 1297, 1301, 1303] → [6, 4, 2]

Position 74: [1543, 1549, 1553, 1559] → [6, 4, 6]

Position 91: [1657, 1663, 1667, 1669] → [6, 4, 2]

Position 106: [1777, 1783, 1787, 1789] → [6, 4, 2]

Position 115: [1861, 1867, 1871, 1873] → [6, 4, 2]

Position 131: [1987, 1993, 1997, 1999] → [6, 4, 2]

Pattern Frequencies:

6,4,2 occurs 5 times

6,4,6 occurs 1 times

now I cannot post ever single one as there are a lot.

but I can see it keeps repeating, this was up to 1 000 000.

Overall Analysis

Total Pattern Frequencies:

6,4,2 occurs 303 times

6,4,6 occurs 380 times

6,4,8 occurs 178 times

6,4,12 occurs 168 times

6,4,14 occurs 159 times

6,4,18 occurs 148 times

6,4,20 occurs 115 times

6,4,24 occurs 76 times

6,4,26 occurs 75 times

6,4,30 occurs 33 times

6,4,32 occurs 22 times

6,4,36 occurs 26 times

6,4,38 occurs 20 times

6,4,42 occurs 8 times

6,4,44 occurs 5 times

6,4,48 occurs 4 times

6,4,50 occurs 1 times

6,4,54 occurs 2 times

6,4,56 occurs 3 times

6,4,60 occurs 1 times

6,4,62 occurs 1 times

6,4,72 occurs 2 times

6,4,74 occurs 1 times

6,4,98 occurs 1 times

I notice that every group with → [6, 4, 2]

the numbers ends in 1 7 1 3 or 7 3 7 9

examples

Position 52: [14551, 14557, 14561, 14563] → [6, 4, 2]

Position 0: [9001, 9007, 9011, 9013] → [6, 4, 2]

Position 81: [11821, 11827, 11831, 11833] → [6, 4, 2]

I then went and picked another random group → [6, 4, 14]
the numbers end in 3 9 3 7 or 7 3 7 1

Position 60: [25633, 25639, 25643, 25657] → [6, 4, 14]

Position 6: [27067, 27073, 27077, 27091] → [6, 4, 14]

Position 4: [62047, 62053, 62057, 62071] → [6, 4, 14]
Position 11: [80167, 80173, 80177, 80191] → [6, 4, 14]

so since you guys are the experts I can only code a bit, what would you recommend next?

I didn't have any interest in math in high school and for some reason I decided to study physics just to see how it was like. I did well in the beginning, but one thing that that unmotivated me was an analytic geometry and linear algebra test that had some tricky questions that were in the exercise list but that I didn't do. Even though I got an A on the other tests I ended up with C in total, calculus 1 and 2 I found easy but I made some silly mistakes and ended up with two Bs. Even though my grades were not bad in my view considering how much effort I was doing, I felt in a way very behind my colleagues because they were mostly people that were always interested in stem subjects, I just didn't know many things that they knew. After a year I dropped out for many reasons and started studying to try to do entrance exams not sure exactly for what course, but I became obsessed with math, and started doing it creatively, finding identities with generating functions, I found my own proof of the zeta Euler product, of the non constant part of Stirling's approximation, a relatively precise lower bound for the sum of reciprocals of primes, I rediscovered specific cases of Abel Summation and Lambert Series, I discovered a combinatorial proof that the coefficients of the recursuon of the partitions are given by the difference between the numbers of partitions in odd and even numbers of parts, and other things, but I feel like a crackpot given that I don't have any contact with any serious mathematicians and even if I had I'm usually too shy to talk to them. I tried reading some papers and I get small parts of some, I tried doing some Putnam questions and I usually do fine in the more basic ones, I could do 3 questions of the 4 doable ones (How I call A1 A2 B1 B2) of the Putnam 2024. But I don't know any great mathematician in modern history that didn't have any interest in math until the age that I started studying. I feel like I may be condemned to mediocrity, like I will never be a real mathematician. Do you think that I lost the train for serious math?

I recently tried creating a formula but can't find a website to find a website to check the output for first 100 primes. If u know any one please tell

Just a simple thought of 1 game control plus one more equals 2 controllers.

2 isn't anything new, it's just a term used to simplify 1+1 this when you're saying 1+1=2 you're really saying is just 1+1=1+1.

Thus how 1 is used is always 1=x and every other number besides 0 is just more 1s. But this quickly gets in to imaginary numbers.

1/2 isn't possible since 0.5 is imaginary. It's only imaginary since 1 is the smallest. Tho let's say 1=6 than we can be 1/2=0.5 since the true number would be 3.

In other words a decimal is only possible when 1 doesn't represent the smallest possible thing.

I also want to touch upon real and imaginary numbers. All imaginary numbers are is what's possible with 1=0 while real is 1=x. Let's say I divide 1/2 for 1=0 it's half of nothing with is still nothing, while for a cake it's half of a cake. If 1+2 that means I added 3 nothings together or 3 cakes in to a group. From 1=0 we get the idea of infinity allowing for the numbers between 1 and 2 to be infinite, but nothing to our knowledge can fit that idea thus imaginary.

We also can get in to a number so big we can't exist. In other words write the largest number you can on paper with just 1s, let's say 600 1s. Thus that's the limit of what's real, when we go to 601 and not and not 601 1s than we get in to imaginary numbers. But this is to say if there is a limit to what can exist, that is unknown.

So this makes me think what is 1, the true one. Would can have said matter in the past, than atoms or quarks, but with quantum mechanics things get even more messier. But ultimately 1 is what ever is the smallest thing to exist.

Would be grateful for anything - books, works, your own perspectives

Don't want a modern proof

Since, we can understand the integer power by multiplication(i.e. 2^2 = 2*2).

Is there a way to interpret the faction powers as divisions. I know there is a method of finding the roots using division, but I am asking that how on the earliest day this method of finding the roots was developed.

I want to understand and feel that division gives the value of roots.

So i'm currently in undergrad studying finance with minors in math/stats. I realized a little too late that my true passion and interest lies in math so I'm curious what possibilities there are for higher education past undergrad. For reference I've been able to stack my schedule with math/stats courses(i listed some below). The ones I have listed below are ones I've either taken or will have taken by the time I graduate. I've mainly been looking at financial engineering masters programs but any pure math programs is also of great interest to me. Is that possible and if so what are my best options?

Linear Algebra 1/2, Multivariate calc, Diff Eq, Partial Diff Eq Stochastic Processes ,Analysis( for my school this is just a slightly easier version of real analysis) ,Probability theory(grad level) ,Statistical Theory(grad level) ,intro fourier analysis ,financial engineering ,intro stochastic calculus

Hello, I’m currently in my undergrad doing finance. In my country, you can’t change major once you enter a university. So, I wanted to chase my dream of studying math, either as master or phd. Is it possible to change? Does taking classes with credit in math help? Or as a last option go and do another bachelor? I was planning to move to USA since I’m an American. Thanks a lot.

Recently sparked interest in Math. I work as a software engineer but my math is terrible. However, I want to learn math and go into a research career. Any suggestions on where to start from the beginning? I am thinking of learning pre-algebra, algebra, linear algebra, statistics, Calculus

What made you interested in mathematics, and how do you deal with limited support in your country? (Except for ex-USSR countries as you guys have good math).

For example, I am from southeast asia , the education system here is downright bad, extreme brain drain, and generally a more religious society which does not put emphasize science and math. Our rate of math/physics students plummeted to almost being the lowest in the southeast asia region. There are no initiatives for math and physics in my country. My county depends on importing techs from the west and japan/china, so there are no big initiatives for science here.

What made me interested in math is that I am interested in how people solve problems. The curiosity came to me when I was put in a super religious boarding school, where people were not allowed to think "out of the box." Ironically, I belong to the same religion as the devout mathematician who discovered how to solve polynomial. Reading stories about our "golden age" really made me question. Cause the school seemed to really prevent us from pursuing "secular subject," but at the same time, there were devout religious people who contributed to the field of mathematics some hundreds of years ago.

My path had been rough but in the end I dropped from the school and pursue math-physics related degree in Russia (they have really good education system when it comes to logical thinking, math, physics and chemistry, first semesters have been really tough). I couldn't do it in my country because they don't really teach deeply and enough.

I have a general understanding of math topics like integrals, sets, and other concepts, but I want to dive back into studying and solving problems. My main focus is finding resources, such as books or courses, that emphasize exercises while teaching concepts in an easy-to-understand way, as I plan to self-study.

I'm particularly interested in algebra, discrete mathematics, and calculus. I’m not looking for dense academic textbooks but rather something more approachable and practical. Could anyone recommend good resources or courses for this? Thank you!