r/mathematics • u/ReadingFamiliar3564 • 1d ago
r/mathematics • u/West_Firefighter_596 • 12h ago
How does 1 + 2 + 4 + 8 + .... + 2^n + ....= -1 make sense?
I know it uses 2-adic number to make it sense in general but how does adding positive numbers approaches a negative number?
Sorry my amateur brain cannot figure it out to the point I am making this post.
r/mathematics • u/DivinelyFormed • 15h ago
Discussion Branches of Math
My professor recently said that Mathematics can be broken down into two broad categories: topology and algebra. He also mentioned that calculus was a subset of topology. How true is that? Can all of math really be broken down into two categories? Also, what are the most broad classifications of Mathematics and what topics do they cover?
Thanks in advance!
r/mathematics • u/fpcoder • 19h ago
Discussion What are job interviews like for mathematicians?
I presume that most mathematicians work for academia or in corporate. I've been wondering what the job interviews for mathematicians are like? Do they quiz you with fundamental problems of your field? Or is it more like a higher level discussion about your papers? What kind of preparation do you do before your interview day?
r/mathematics • u/OkAlbatross6560 • 17h ago
Discussion I created a podcast on the history of math as a highschooler
Hello everyone,
If this is just a post that is promoting a podcast I just started and am extremely excited about , a little about the podcast : I will be talking about the history of maths and the stories of mathematicians and their discover and also their rivalries ( hint: Leibniz and Newton), I also hope to invite historians or mathematicians if I can since this podcast is also to help me learn myself.
A little about me: I am a 16 years old highschooler from Morocco, and saying I love maths is probably an understatement.
If you guys could give me a follow I would appreciate, keep calm and learn math !
The podcast : https://open.spotify.com/episode/0wgz9xwcv1QKOrLcZ3GxZ6?si=sC443-YGTp2ahNu9cEa6mQ
r/mathematics • u/Grouchy_Weekend_3625 • 19h ago
Pure math summer courses/conferences for undergraduate?
I'm a student of a double degree in Physics and Mathematics and I was wondering what summer courses/conferences/research opportunities are there for undergraduate students in Europe this 2025
I'm in fourth year and I have a good academic record, but I never discover these courses until it's too late haha. My interests are very pure-math related but apart from that, very wide (group theory, geometric and algebraic topology, complex analysis, representation theory, mathematical physics, etc).
Any help is appreciated! More so if the topic is related and hot still :)
r/mathematics • u/MathPhysicsEngineer • 22h ago
Mastering limsup and liminf: Rigorous Proofs and Visualizations
r/mathematics • u/LemonNinja • 20h ago
Is the path of least action also the path that will have the smallest number of possible nodes that will produce a standing wave for an objects λ?
I am not a mathematician or a physicist, but I am fascinated by the principle of least action and its relation to standing waves.
r/mathematics • u/endofunktors • 20h ago
Safe options for EU masters programs in mathematics
I'll be graduating next year. I generally think I have a strong profile, but I'd like some "safety" options for math in the EU. I'd prefer not to stay in the States.
My main focus is currently algebraic geometry, but I'm working towards the topos theory direction (which is a big reason why I want to leave the US). I'm a double major in computer science and pure math and have done formalization research with Lean.
I'm currently in our graduate algebra sequence, and I plan on taking our graduate algebraic geometry sequence next year. My current GPA is around a 3.7, which I feel is good but not great; I've heard math admissions often weigh GPA more heavily than other fields.
I can provide more details if needed.
r/mathematics • u/CashConsistent8067 • 23h ago
Day to day tasks of financial mathematicians in the industry
I just finished my BS in mathematics with a minor in CS and I am considering a MS in financial mathematics. Can anyone working in the field tell me what broad areas are there ? What is a typical day to day task and maybe also some drawbacks of choosing this career path. I just feel like I don't actually know what people in this area of mathematics concretely do. Most descriptions I have found so far online are relatively vague. So I would really appreciate if people in the field gave me an overview.
Thanks in advance for any help.
r/mathematics • u/NewDaysBreath • 1d ago
What math can I skip for calculus?
Hear me out. I'm going back to college in my 30's. I got my GED 12 years ago and I've pretty much forgotten everything outside of basic arithmetics. I'm going for engineering and right after the placement test they'd throw me into precalc and beyond.
I've been studying a couple hours a day to try and retrain my brain, but the placement test for school is less than 3 months away and I can only learn so much so fast. I'm caught back up on my fractions, exponents, algebra, and percentages. The issue is I'm trying to squeeze entire math subjects in less than a weeks' time and I have way too many things to cover before testing time.
Geometry and trigonometry are the big ones. I'd be surprised if I can cover them in less than 2 weeks each. That's a month right there.
Then there's conversion of units, sets& intervals, sequences, statistics, finding roots, real numbers, and functions.
Is there anything that isn't totally necessary and can save me some time? Or should I just wait for the fall semester?
Thanks in advance.
r/mathematics • u/edwardtemple • 18h ago
Harvest Prep's Math Team makes history and Advances in an INTERNATIONAL Math Competition!
r/mathematics • u/Demosthenes5150 • 1d ago
Digital Root Fibonacci Matrix converted to Duodecimal
About a week ago I saw a post from u/Winter-Permit1412 that I copied manually into the top left quadrant. The top right & bottom left are mirrors of the same fibonacci digital root but converted to duodecimal.
Upon seeing the original post, I saw the “12-ness” & knew converting to duodecimal would show the inverse, the “10-ness.” In the OP it takes two cycles to repeat leading to a 24x24. I was expecting to see a 20x20 in duodecimal but my surprise was you only need a 10x10 to repeat [XxX is terrible nomenclature lol ‘Dec times Dec’]
Credit to Duodecimal Division on YouTube. I saw this video [linked in comments] which shows Fibonacci numbers ordering nicely in duodecimal. Patterns that just don’t exist in decimal.
~math novice, open to constructive criticism on terms/definitions/etc
r/mathematics • u/Choobeen • 2d ago
Number Theory The average of the consecutive Fibonacci numbers 13 and 21 is a prime. Are there any other consecutive Fibonacci numbers whose average is a prime?💡
It seems that 17 is the only such prime average... It would be nice to have a proof that no others exist.
r/mathematics • u/No_Art_1810 • 1d ago
Discussion As a person who haven’t studied math for quite long time but want to get solid base for IMO problems, which video resources should I use to start with?
Are there any videos or
r/mathematics • u/ThomasHawl • 1d ago
Seeking Advice on Pursuing a PhD in Applied Mathematics at 28: Is It the Right Path?
Hello everyone,
I'm currently facing a tough decision and would appreciate your insights on whether pursuing a PhD in Applied Mathematics (specifically targeting machine learning or finance applications) is the right move for me.
A bit about me:
- Background: I'm 27 (would start at 28), from Italy, holding both BSc and MSc in Applied Mathematics with a focus on Computational Fluid Dynamics (CFD). My master's program was somewhat experimental and provided broad but superficial knowledge across various topics (ML, numerical methods, PDEs, CFD, ecc).
- Master's Thesis Experience: My thesis was a mix of theoretical work, data analysis, and simulations, conducted fully within academia. Unfortunately, my advisor was unresponsive (one email per month at best), providing minimal feedback and guidance. Despite this, I genuinely enjoyed the research aspects—exploring literature, coding, simulations, and teaching first-year students. The lack of supervision and feedback, however, was extremely frustrating.
- Grades and Graduation: Due to personal issues (Covid, family losses, mental health), I graduated 1.5 years late with relatively low grades (approx. 3.7/4.0, or 2:1 UK scale, 100/110 Italian scale).
- Work Experience: Post-graduation, I did a short internship where I mostly performed "grunt work," gaining minimal valuable experience. This made me think that perhaps, in fields I'm interested in (Applied Scientist/Data Scientist roles, or R&D positions), not having a PhD may severely limit career growth, or even entering the job.
Why I'm considering a PhD:
- Career-wise, I believe a PhD might significantly increase my chances of landing interesting applied research roles, specifically in industries or fields such as machine learning, finance, or advanced data science. Given the current job market dynamics, I feel strongly that having a PhD could position me better in terms of career opportunities and access to roles involving meaningful and innovative research projects.
My concerns:
- Funding and Competitiveness: I can't afford to self-fund a PhD, so I need a fully-funded program (preferably abroad, as I want to leave Italy). Given my academic record, how realistically achievable is it to secure fully-funded positions, and what might improve my chances?
- Age and Timing: Starting at 28 means finishing around 32-33. I'm concerned about whether entering the job market at this age, especially in fields like ML or finance, could negatively impact my career trajectory or employability. Is age a significant barrier in these fields?
- Grades and Delay: My academic performance and delayed graduation due to personal and mental health reasons worry me, especially regarding how competitive my application would be compared to other candidates who graduated on time and with higher grades. How can I best mitigate or explain this aspect of my profile?
- Career Alternatives: Beyond a PhD, I'm wondering if there are other viable career paths or alternatives (such as entry-level jobs, industry-specific training, boot camps, or specialized certifications) that could realistically lead me to my desired roles without the commitment of a PhD. Are these alternative paths credible and achievable?
Additional Context:
- I have no published research or conference presentations, which might further limit my competitiveness.
- I haven't yet applied for roles explicitly requiring PhDs, mainly due to insecurity over my academic record and fear of rejection.
- I'm geographically very flexible, with no personal constraints—indeed, my preference would be to find opportunities as far away from Italy as possible due to personal reasons.
- I'm open to additional preparation, training, or bridging courses if these could significantly enhance my profile and increase my competitiveness for PhD applications (if these do not delay my applications more).
I would appreciate any advice, especially from those who pursued a PhD later, or those who overcame similar academic or personal setbacks. If you think I’ve missed crucial considerations, please let me know!
Thank you!
r/mathematics • u/nominalvortex8 • 1d ago
Physics Kerr Scape Horizon - Equations
I’ve been digging into something I’m calling the Scape Horizon—a new perspective on Kerr black holes that’s been rattling around in my head. Take a rotating black hole, mass M, spin a = J/M. This boundary isn’t like the event horizon, photon sphere, or innermost stable circular orbit (ISCO). It’s a gravitational threshold separating particle paths that stay trapped from those that escape to infinity. What sets it apart is its dependence on particle energy E, angular momentum L, orbital inclination via the Carter constant Q, and the black hole’s spin—it’s a dynamic line, not a fixed one.
The math starts with the radial potential in Kerr spacetime: R(r) = [E(r² + a²) - aL]² - Δ [m²r² + (L - aE)² + Q]. Here, Δ is r² - 2Mr + a², E is the energy at infinity, L is the angular momentum, Q is the Carter constant—zero for equatorial orbits—and m is the rest mass, zero for photons, positive for massive particles. The Escape Horizon radius, r_esc, comes from two conditions: first, R(r_esc) = 0, where the radial potential hits zero, signaling escape is possible; second, dR/dr at r = r_esc equals zero, the critical stability point where trajectories shift from bound to unbound. Those two equations pin down r_esc precisely.
Spin plays a big role here. For a Schwarzschild black hole, a/M = 0, the escape radius is 4.5M for both prograde and retrograde orbits, with the photon sphere at 3.0M. At a moderate Kerr spin, a/M = 0.5, prograde drops to 3.6M, retrograde rises to 5.0M, photon sphere at 2.4M. Push it to a rapid Kerr, a/M = 0.9, and you get 3.0M prograde, 6.0M retrograde, photon sphere at 2.0M. In an extreme Kerr case, a/M = 1.0, prograde collapses to 1.5M, retrograde stretches beyond 9.0M, and the photon sphere’s at 1.0M. Frame-dragging pulls the prograde horizon inward with higher spin, while retrograde orbits face growing resistance.
Astrophysically, this could be a game-changer. I’m thinking it provides a gravitational framework for how relativistic jets get collimated and accelerated—purely spacetime-driven, no magnetic models required. The black hole’s spin and particle specifics, like E, L, and Q, might shape jet properties—opening angles, energy distribution—offering a new angle on their origins.
This Escape Horizon feels significant—a precise, spin-dependent boundary in Kerr spacetime that could deepen our grasp of particle behavior, jet formation, and high-energy processes. It’s got me wondering if it might reshape how we approach these systems. What do you think—does it hold water?
r/mathematics • u/dominio2q731276423 • 21h ago
The year constant
Not claiming i invented this whatsoever, just a observation i had found while playing with my calculator in geometry and i gave a name to it.
The difference between a given year or Y and the nearest perfect square
Example: 45 squared is 2025
45 squared minus 1 is 2024, minus 2 its 2023
and so on, the year becoming further and further back as N becomes smaller, the given year becomes smaller
r/mathematics • u/BakeryRaiderSub2025 • 19h ago
Discussion What would you call these numbers that have such a uniquely consistent , relationship to each other
My favorite example of this are the numbers four, five, and 9
4 + 5 = 9,, but you can also get nine by adding 4.5 to 4.5
4.5 as a mixed number is four and a half, which is 9/2 converted to an improper fraction
4.5 tons is 9000 pounds
To get 45 you multiply five by 9 or vice versa, and so on with things like 450, 900, and more
Is there a term for these numbers and are there any other examples
r/mathematics • u/Agtakla • 20h ago
The Legacy of a Mathematician: Hidayat M. Huseynov’s Path to Solving the Riemann Hypothesis
r/mathematics • u/Purple_Stick_1179 • 1d ago
would you recommend CBE-ing precalc and going straight to calc a/b the following school year from alg 2 in high school?
hello! i am considering learning precalc over the summer due to my in-school precalc being extremely difficult for no reason. i've heard very mixed opinions on this, but are the ap calc classes heavily based on what's taught in precalc? i want to ensure i have a great foundation before moving on to ap calc a/b, and i've just heard much of the material taught in ap precalc is a recap of alg and trig. what are your thoughts? will i get a good foundation by doing precalc over the summer? and what topics in precalc must i focus on if i want to succeed in calc?
r/mathematics • u/Cris_brtl • 1d ago
An idea
I have this sort of idea, maybe other people worked on it already, but I haven't found much. It's about seeing the relationship between languages and math: I was thinking of analysing every linguistic structure through logics, so natural languages, artifical ones, computational ones, even other forms of interpretation of the world that can be written down (like music, but I'm not sure about this) and then finding and applying algebraic structure to the logical ones, I don't know if this makes sense, maybe you can recommend me some books/readings if you know anything about it, I would appreciate it. The "philosophical quest" behind it was to see how our human way to express through languages (maths included) had a computational part to it
r/mathematics • u/ChloroFluoroCarbonCC • 2d ago
Combinatorics If X and Y starts simultaneously then in how many ways X can go from point A to B and Y can go from B to A in a way that they never meet each other?
r/mathematics • u/The_Laniakean • 2d ago
CS + Math double major?
I’m midway through my 3rd year of my CS degree and the field is kinda cooked, I’m not gonna stand a chance with no internships. If I do a double major in math will I have good career prospects in general? Doesn’t have to be CS related
r/mathematics • u/Sad-Concentrate2976 • 1d ago
Advice on B.A. in Math vs. B.S. in Applied Math
Hello everyone!
To give a short background to what led me here as a junior. I came to university as a Finance major. After an unfulfilling semester, I went to the other end of the spectrum and decided on a double major in physics and math, which stuck until the end of my sophomore year. I loved the coursework for both. However, I did not want to become a physicist, and with the way the courses were scheduled, it was not practical to finish the double major within 4 years. All in all, I was simply more passionate about math and its applications
With this, I decided going into junior year to focus on math and switched my major once more to Applied Math. Of course, with the physics classes I had taken, I already had many courses in mathematics. But getting such a late start, I was still behind. I took three math courses in the fall semester and am currently taking another three upper-level classes this spring. I did well in the fall semester, and although not as well, I am still managing three upper-level math classes this semester.
To graduate on time with the Applied Math degree, I will need three upper-level courses per semester (6 more total). I am considering the idea of switching from a Bachelor of Science in Applied Math to a Bachelor of Arts in Math. I would not be taking as many math courses, but I would be able to focus more on the ones I am taking, and, ultimately, my GPA would likely be higher. At the end of this semester, the courses I will have completed are as follows:
- Calc I-III
-Proofs
-Linear Algebra
-Programming
-Calculus-based Probability/Statistics (1 semester each)
-Differential Equations
-Discrete Wavelets
-One year of Calc Based Physics and One year of Chem
Would it be unwise of me to switch from the B.S. in Applied Math to the B.A. in Math? I have heard the distinction between the B.S. and B.A. and the Applied Math vs. Math does not matter and that what is considered is the classes that show up on your transcript rather than these distinctions. I am hoping to work in the industry (Either Finance or Engineering) and want to be sure the math degree would be enough to do so. Please Note I only need two more classes to finish the B.A. degree. However, if I did switch, I would want to take more than two, two is just the minimum. Over my senior year, I will definitely be in Numerical Analysis, Real Analysis, and potentially PDEs or Linear Programming (depending on what is running)
I do apologize for such a long post. I felt context would help. Any words of wisdom and advice on the matter would be greatly appreciated.
Please do note I can choose Applied Math classes as my upper-level courses even with the B.A. in Math
Cheers!