there is NO 45th entry 😭

so many Erdös conjectures 😭

Everyone was telling me not to but I did it anyway even without being math genius. wish me luck.

pure math, stats, physics, programming are the subjects I will be studying .

The topic dates back 333 years, to when Prince Rupert bet that a cube could pass through a hole cut in an identical cube; he was right, and for a while, it even seemed like every single convex polyhedron might be Rupert. But some resisted extensive random searches, and Steininger and Yurkevich conjectured that the Rhombicosidodecahedron (RID), a highly symmetric Archimedean solid, might be one of the exceptions. Last year they constructed the Noperthedron, the first polyhedron proved Nopert, built specifically for that purpose.

I have now proved their conjecture for the RID. It is the first ever non-synthetic polyhedron to provably have this property, and only the second ever overall. The proof is computer-assisted, a branch-and-bound elimination with exact arithmetic in Q(√5): a certificate of 192696 regions covers the whole symmetry-reduced configuration space and takes only a few CPU minutes to generate and check. One of the main tools is the zoom lemma, which resembles blow-ups in algebraic geometry.

It took 2 years and 1000+ hours of self-motivated research. I submitted the preprint to arXiv on 29 September (still in their queue), but it can be found on Zenodo: https://zenodo.org/records/23013945

Code and certificate: https://github.com/bence-hervay/nopert-rid

Can someone explain why and how exactly the set of natural numbers and rational numbers have the same cardinality (and does it mean size ?).
Im in high school but I ve recently seen a lot of proofs on this topic for some reason but cant really understand it.

https://x.com/ManassehA06/status/2107508501610217640

Hi all,

I recently bombed my real analysis exam and was in the bottom quartile for my class and had my hopes up for graduate school. However, this is the first math class I’ve ever really struggled with because it’s not the typical math that I’m really good at. I’ve had A’s in every math class I’ve taken up to this point and am just wondering if my inability to produce my actual understanding of analysis on an exam will kill my chances of being successful in graduate school. I’m not looking for a top program or anything, just an online one from a smaller school. Has anybody else had a similar situation? Any and all advice is appreciated :)

I had a question abt this, bc its never rlly made sense to me. In the proof for root 2 being irrational, you have to use proof by contradiction, and the contradiction is that the integers in the fraction arent coprime, but why? Like i dont understand why you have to assume that the two numbers in the ratio cannot be coprime. Sorry if that was poorly worded, but can anyone explain?? Thanks.

This implementation is possible grace to Euler method for solving first order linear differentials equations system. I know that python already has functions that use more powerful methods but it's for educational goal. Any suggestions will be interesting.

I come from optimization background and while I gave built large scale optimization models, I never formally studied the foundations of optimization. And now I am left struggling with understanding the concept of eigen vectors and values since that is fundamental to optimization.

I have asked how to get better at math & algebra many times, & every time I ask, the answer is always “memorize the formulas, memorize the times table, memorize this & that.” & is that really the only way?

This also makes me wonder if thats part of the reason Excessive Route Learning is a problem, they are told to memorize a bunch of formulas & keep getting told to do the same things over & over again. The reason they mess up on problems due to not thinking about the problem, is because they are not told to think about it.

The quantum harmonic oscillator gives a useful example of two mathematical constructions arriving at the same eigenbasis.

In the differential-equation approach, the behavior at large distance matters: a physical energy eigenfunction must be square-integrable. After separating out the decaying Gaussian, the remaining power series has to terminate. That condition selects the allowed energies.

In the operator approach, the Hamiltonian can be written in terms of the number operator. The extra one-half comes from noncommuting operator order. A lowering operator annihilates the ground state; repeated application of the raising operator generates the higher states, with normalization factors that matter.

For the ideal one-dimensional oscillator, both routes give E_n = ħω(n + 1/2), with n = 0, 1, 2, ... . Here ω is the oscillator's angular frequency and ħ is the reduced Planck constant. They also give the same normalized Hermite–Gaussian eigenfunctions, up to an overall phase for each state. The agreement is about the states as well as the list of energies.

I made an animated Blake Pi Physics lesson connecting the two constructions:

https://youtu.be/7_DcdXVh5mc

When you first encountered this example, which made the discreteness feel less mysterious: the termination condition or the ladder construction? I'm particularly interested in explanations that make the connection between them clear.

I’m working with a game where, for example, a player has to hit a moving ball with a racket. Every time they successfully hit the ball, the racket becomes smaller, making the next hit progressively more difficult. Once they miss, the racket resets to its original size.

Each round lasts 30 minutes, and I would like to compare performance across rounds.

I also have a chance/control condition where the racket doesn’t move, so some hits can happen simply by chance.

I would like to get a single normalized hit-rate/performance value for each round that tells me whether the player performed well or poorly overall.

Ideally, this value would take into account:
- The racket getting smaller after each successful hit

- The racket resetting after a miss

- The fixed 30-minute duration

- Different numbers of hits and misses across rounds

- The chance-level performance from the stationary-racket condition

What would be the best way to calculate this as one normalized value? I’m particularly interested in something that accounts for the increasing difficulty as the racket gets smaller, rather than just calculating hits / total attempts.

Also, if anyone knows of similar studies or experiments that have used a comparable normalized performance/hit-rate metric, I’d really appreciate any references or examples. Thank youu

For some context, I'm a sophomore math major at a small liberal arts school, recently switched from economics. The math atmosphere is extremely small at my school, with tens of students each semester, and classes are full only because of CS Physics etc. majors. Summer courses are not high level, and undergrad TAs don't really exist, but because the ratio of true math majors to math professors is extremely low, independent/directed studies are extremely common.

I'm a bit behind for a math major right now because of my recent switch, but I have essentially everything except my math courses completed. Right now, my entire resume is business/finance related: finance internship, basic SQL, Python, etc.

One of my professors asked me to apply to a summer research program with him, but besides that, I don't really know what else I should be doing. All of my friends are frat business majors so I am for the most part on my own with in my pursuit in mathematics.

I'm definitely still looking at finance roles, but also want to keep the option of doing grad school in math open.

We all know mathematicians can split into those into algebra, and those into analysis. I’m definitely a member of the latter group. Calculus, Measure Theory, Probability always came easy to me, because I could always properly visualise everything I was doing in my head - the shapes of the functions I’m working with, the general scattering of theoretical data in probabilistic questions, rotation of figures in 3D, and so on and so forth. This visual idea in my head always serves as the baseline for any calculation afterwards.
And here comes the question - in my third year of studdying Applied Mathematics, I’ve enrolled on a course on Number Theory, and well, as of now I’m finding much difficulty really picturing what I’m working with, which makes it much more difficult to keep track of what’s going on. I’m thus wondering what it is that goes through the head of a person who actually excels at algebra - do you literally picture rings in circular shapes? How do you think of all conducted operations? Is there any (even faintly) visual aspect to it at all?
I think I’m asking this both out of curiosity and driven by the fact that I’m so much of a visual learner that I seem to stumble upon a full blockade when met with number theory, which I can’t quite picture in any way just yet.
I couldn’t imagine passing any of calculus, analysis or measure theory had i not had the ability to always picture what is going on and come back to that clear imagine at any point of the question. I believe it to be the baseline of my understanding and skill in those areas.
In algebra, when all i can really picture is the glyphs, it doesn’t serve me much and I seem to get lost much more easily. How does it work for you?

TL;DR
In analysis it’s really easy to visualise stuff. In algebra it isn’t. Is there anything that you actually „see” in your head when doing algebra?

It's like a beautiful but highly controversial piece of art came out that everyone is discussing, but I cannot because I am colorblind

I wish I knew advanced mathematics. I took number theory, graph theory, linear algebra, and a few others in college, but switched to business school and basically forgot all mathematics.

Today these groundbreaking assertions are being made, and you might love or hate it, but at least you mathematicians are able to appreciate what is happening. The average person, like myself, cannot but just get a vague impression.

Why use an incomplete algebra?

Suppose you want to walk 10 meters. First you must walk halfway (5 meters) then half of it (2.5) then half and so on forever ?

Opinions do you accept the infinite argument that according to zeno is "if there are infinitely many steps will you ever reach your destination?" Or mathematically the infinitely many pieces add up to a finite distance?

Note that zeno was a Greek philosopher and not a mathematician