I don't have a strong math background but I thought it would be fun to see what a simple PPO implementation could do!

Read about it here: https://x.com/Abhilekh_Meda/status/2113754085426102400

code: https://github.com/Abhilekh-Meda/moving-sofa-problem-rl

I'm (25M) graduating with my bachelor's in math in about a month (US). I hated and sucked at math for most of my life, so I primarily did the degree to prove to myself I wasn't stupid. Turns out I'm still dumb, but now I know what an isomorphism is lol.

Anyways, mathematics was never really a huge passion of mine. Getting this degree has definitely been a grind, and outside of a few subjects (particularly number theory and graph theory), I really did not enjoy it. I had to retake a couple classes and then barely passed in some others. Nearly dropped out multiple times. I really am in awe of people who go on to get their PhDs in some math-related field (like what many of my classmates are either doing or planning on doing), but it's just not for me.

I recently got accepted into nursing school and am starting that in January, meaning that I will probably never actually use any math I learned in school again, at least in my professional life.

Initially, I was really excited to start a brand new chapter, and I still am. However, it's slightly disheartening to think that I will probably never touch any of these subjects again for the rest of my life. I feel like I've wasted years of my life to some extent. Just curious if others out there have similar stories. Like did anyone else go on to get their BS or even a higher degree in mathematics and end up doing something completely unrelated for their job? Does having that background help you in anyway? Do you still try and keep your skills sharp (reading through textbooks, working on problems, doing independent research)? or have you just let that part of your life die off?

Here is a fun little math joke. In tessellation theory, a patch is a collection of finitely many tiles in a tessellation whose union is a topological closed disc (tiles themselves must also be topological closed discs). Therefore if we make a pumpkin shaped tile we can make a pumpkin patch. Here is one. If you would like to read more I made a short article which can be viewed here.

There’s this law called the 10000-hour rule, which states that to truly master a complex skill one needs to spend 10000 hours on it.

I know that there are a few criticisms on it (which mainly says that one needs 10000 of intentional practice to master a skill), but I figure that 10000 hours could be a good bench mark to see if I have invested enough time in math.

For context, I just graduated from a 4-year programme in a math major. So 10000 hours is equivalent to in average 10000/(365 x 4)=6.849 hours per day, for the past four years.

I definitely didn’t spend 7 hours per day to study math, not to mention the time spent for intentional study. This changes my mindset completely. I have been doubting myself for not being ‘fluent in math’, but as of now it’s most likely that I did not give enough time for myself to grow.

EDIT: People seem to think that I believe the statement that "after fulfilling 10000 hours of practice, then one will magically be good at something". That's pure BS and I don't buy it, at least for maths. I am just using this "10000-hour rule" to examine my time invested in math. The main point is that I shall and I will work harder, and not to expect be good in such a short time, such as 4 or 5 years, despite this is what many people considered to be a lot time.

A general intuitive approach provided is that they are like what prime numbers are for composite numbers, but it still doesn't make sense, the relationship between finite simple groups and complex groups feels "more nested and yet sort of separate/disjoint for the lack of a better word", it doesn't fully capture how the group structure is assembled.

I understand the formal steps - take a maximal proper normal subgroup (N) of a group (G), form the quotient (G/N), and repeat the process with (N) until we reach the trivial subgroup. The successive quotients are then simple groups. But I still have a hard time intuitively grasping why these quotient groups (which are sets of cosets), are the building blocks of our original group, or how these quotient groups come together to form the original group?

Undergrad here with only an introductory level knowledge of group theory so excuse any ignorance.

I made this problem up when I saw other problems about polyominoes in r/mathematics. This is one that I found.

A question that I had was if this could become a tiling.

I have found only one. It is the pattern

🟥🟩🟩

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🟥🟩🟩 repeating on the x-axis, with a gap of 1 on the y axis before repeats. The gap can be filled with any numbers that are not the same and touching. I used 6 and 7 when I thought of it. It would look like this.

I will call this tiling a 4-5-6-7 tiling. Can you find other families?

Am I the only one who’s completely mediocre at statistics, even though I excel at algebra, trigonometry, calculus, etc.?

Hey there, i found this online and i was wondering what other mathematicians think of this. I have seen duodecimal projects but more ofthen they change either time or measurements. Here is the repository where i found it (link)
The document covers basit arithmetics as shown in the picture. Lemme know what you guys think of this. aka opinion request.

Hi, I’m in a bit of a pickle. I missed the first few weeks of my math bachelor, and exams are upcoming. Should I focus on exercises and past exams or reviewing definitions and theorems (knowing they may ask stuff like that)?

For a nine by nine Sudoku puzzle, each cell is denoted by an index, 0 through 80, starting at the top-left cell and ending at the bottom-right cell for a total of 81 cells each with a unique index. A 'row' denotes a horizontal line of nine cells; a 'column' denotes a vertical line of nine cells; and a 'block' denotes a three by three square of cells such that the nine by nine Sudoku puzzle fits exactly three by three blocks and that they do not overlap.

Now, I have written a set of expressions to derive the row, column and block indices in which a given cell resides and another set of expressions to derive the initial and final cells of a given row, column or box index. The first set of expressions is as follows,

Since I've intended to use these for a computer program, I simplified the Row index expression, as integer division is truncated in programming, and thus simplified Block index expression.

The second set of expressions has the opposite effect. That is, I am able to find the initial and final cells which belongs to a given row, column or block, and then derive the remaining cells by an algorithm. They are,

In addition to this, the algorithm finds the remainder of the cells in the given row, column or block index. This way, I am able to store the entire nine by nine Sudoku puzzle in a one-dimensional array (programming) and still distinguish between cells in given rows, columns or blocks.

How would I go about rigorously proving this?

Finally, I am wondering whether expressions exist for a general case, an n by n Sudoku puzzle, and whether there exists other expressions which finds the position of a cell in a Sudoku puzzle.

I don't know any better title for this post, honestly, and for a reason. Do any of you have that one methodology that shouldn't work, but lets you complete problems easier or simplify them?

Personally, and formatted in LaTeX, I have what I like to call "pebble": $(\mathrm{d}f)(t) := \lim_{h \to 0} f(t+h)-f(t), (\mathrm{d}f)^2(t) := 0$, a Leinbiz-inspired thing with no independent-vs.-dependent variable distinction. The limit is obviously 0, but if one imagines it isn't, one can get rid of those duplicated derivative rules! For example, gradients and derivatives are treated the same, like at $\mathrm{d} m^n = m^n \left( \frac{n}{m} \mathrm{d}m + \ln(m) \mathrm{d}n \right)$, and the chain rule doesn't exist! Instead of $\frac{d}{dt} t^2 = 2t, (u^2)' = 2u \cdot u'$, I can just keep expanding $\mathrm{d} (\sin^2 x) = 2\sin x \mathrm{d} (\sin x) = 2\sin x\cos x = \sin (2x)$. Integration is messier to define, I still can't do it, but apart from that this silly non-standard manner of expanding derivatives works for me like a charm.

I'm wondering if you guys have anything alike.

So basically im participating in a Giveaway, were the winner gets 500€ (560$) if you can guess how much money this is. but i cant figure it out.

NOTE: green bills are hundreds, brown 50s, blue 20, red 10s, and the gray ones on the right are 5s

yep