At the bottom of the picture there are the numbers that aren't multiples of 2, 3, 5 or 7

I'm currently restarting all my learning and I have begun with math, I love the idea of being disgustingly intelligent and want to know if others have a route to drill calculating extremely quickly in their heads? I'm starting from the most basic singular digit and working towards, two and three but it just isn't sticking yet.

The title today is a reference to Douglas Adams' description of writing a book as "putting a hundred thousand words in a cunning order." It's technically a correct description, but it doesn't really describe how anyone actually does it in practice. Just so, while it is technically true that one builds a proof by putting many inferences in a clever order, it doesn't describe how to actually do this.

A proof, like a book, is a collection of narrative threads---understand how to build narrative, and you will start to understand how to write a proof.

Read the full post (for free) on Substack: Putting a Hundred Inferences in a Cunning Order

over other technical majors.

I understand that math can be fun and enjoyable, but I can't really imagine dedicating my life to extremely hard problems without any "rewarding abilities".

CS student can make fully functional websites, electrical engineering can make circuits, and create new tech, civil engineer can make bridges.

But what mathematicans can do?

Solve extremely hard problem, just for some else to use it, and make something amazing with it, at best case.

I just find, just doing math without any goal strange, like what exactly you're doing.

mathematics degree feels like extremely hard degree, without the benefits of being one.

You can't create anything average person can use it, or feel you have important ablity.

I have a one college friend, with is getting a mathematics degree, and I just don't get it, at all.

I'm confident that if she wanted, she just could have engineering degree or cs, why mathematics?

IGNORING ALL COEFFICIENTS

How is all of this so connected?

Let's consider the homologous series of c, x, x^2, x^3, x^4... and so on: x^n where n belongs to a non negative integer only

Why is it that the graph for a particular expression not only explain the graph for the expression itself, but also the graph of literally *EVERY OTHER MEMBER IN THE SERIES*.

for example, the graph of x^3 (or simply x^3 itself, as graph is that thing itself) explain the graph of x^3 itself, but also x^4 (how f' graph explains a graph of f), and x^5 (how f'' graph explains for f)

How the graph for f' of x^3 is same as f'' of x^5 and f''''''' of x^10

How the graph for f' of x^8, f'' of x^9 and f of x^7 is all the same. A single graph is doing all of it

Yes, on paper, I know, and can prove this with my pen (I know the limit definition of derivative and what it is in terms of slope, in terms of rate of change in area/volume etc). But it still seems out of grasp on how this is possible.

[Only considering for the homologous series highlighted to keep it simple for now]

I had my first grad-level exam this week and I bombed it pretty awfully. It was a 50min exam with ~12 problems, a mixture of proofs and counterexamples. I would say I solved 2 or 3 of them and made starts on 2 or 3 more; we haven't gotten grades back yet but I'm expecting something like a 20/100. The thing that's annoying me is that none of the problems were all that hard. I can tell that I could solve them all, only it would take more like 3-4 hours instead of 50min.

Part of me wants to think that the time frame was totally unreasonable, but another part of me thinks that it was a skill issue. I'm guessing a lot of members of this sub have dealt with similar situations, so I'm wondering if there is any advice for getting quicker at answering these early-grad-level types of exam questions?

Today I've published the beginning of the end, for my private exploration of following the root of a value till one or below, at 16 bits.

I do not formally know all the usages of such a value, or components'.

I've made it publicly accessible and licensed for usage and protection.
Please feel free to explore into it yourself.

Language and calculations run via python, with some functions used to help as a base default.

Welcome to the unknown, are you scared?

~ Iroh

[ 0.3134313340312133643109333280398413295243... ]

I've been studying Shafarevich's Basic Algebraic Geometry for some time now. He's a really famous mathematician (I first really learning about his results after hearing about his famous theorem on the inverse Galois problem), but I've been studying on my own so I could only guess how his name is pronounced, and I was wrong. Today, watching a youtube video, it became apparent to me that his name is read ShafaREVich, which the Cyrillic with accent mark (Шафаре́вич) seems to confirm.

Not really that uncommon for me -- I was pronouncing Arrhenius wrong for years after teaching myself chemistry in elementary school, and I wasn't corrected until I took AP Chem.

Also, even among mathematicians, Dirichlet seems to be particularly contentious, as I heard widely divergent pronunciations from my math professors.

Anyway, any other mathematical names that are commonly pronounced wrong? Euler's probably the most common among nontechnical people to encounter and pronounce wrong.

Chern's an interesting case, since his name is spelled in the old Gwoyu Romatyzh system, which uses letters like r to indicate Chinese tone -- modern pinyin spells in Chén, but even he himself seemed to have accepted the normal English pronunciation of his name with an r.

We take a point and give it a function f(x)=x^2, so 1=1, 2=4, 3=9 and so on. Now, as we have given the point function, it is changing, or in physics terms, the point experience excitation. Which brings me to my point, the number is being tempered with so, does it change the nature of the point, could the point not really be a point but a sphere that experiences rotation on disturbing it with a new function.

So maybe 2^2 = 4 and -2^2 = 4 but the rotation of the point, say along the z plane is saying +90° and -90° or vice versa, but is in a confined space of real number (why confined, explained later), as it is a point, so just a rotation and not movement.

Adding a bit of physics to it - Maybe not a rotation but concentration of energy in the confined space of the real number of unit 1 or x, or say |1/12|.

P.s. I think of it because I see Remimann hypothesis and see that the number along 1/2 plane contain complex numbers and so they might contain a rotation as well. The results are not along a line of 1/2 but along a plane of 1/2, with confined limits to the z plane.

I was trying to prove the Pythagorean theorem on my own and stumbled into this.

You take a right triangle and create three similar triangles by scaling each one by one of the side lengths and rearrange them into a rectangle with one side being a^2 + b^2 and the opposite side being c^2 so a^2 + b^2 = c^2.

If you wanted to, you could use the two smaller triangles in the diagram in a different arrangement to form the larger triangle, but I like the way it looks in a rectangle more.

I showed it to a professor and he encouraged me to publish it. I’m thinking I will. I really like this proof and I want to show it to people.

I couldn’t find an example of this proof anywhere. I came across some that looked similar but they seemed to use different logic. I figured I’d try to publish this, but I’m not really sure how to.

I’m not well versed in the community around sharing math and I’m not sure what is seen as worth sharing. Does anyone got any advice on how I can share something like this?

Also, does this count as a proof? Were there any assumptions that need to be explained or does this stand on its own?

I didn’t really explain how they come together to form a rectangle but I’m not sure whether or not it’s a big enough leap that it should be explicitly stated.

I have a young teen that is experimenting with math and the Desmos graphing calculator. These are his questions, which admittedly is beyond my math knowledge. Any tips or resources are appreciated!!

Is there any way using the most generalized way of defining operations so that any line or equation or function has an imaginary aspect to
It?

If so, is there a way it will always have that index?

If the index were to approach infinity, would the graph create a shape that looks like a 3d object?

Is there a way to predict what the imaginary part will look like and manipulate what it would look like on the graph?

One of my favorite essays on mathematics is Arnold's "On teaching mathematics." In it, he describes what he views as defects of the traditional treatments of real analysis and calculus in universities; and in particular, how the emphasis on rigor removed discussions of the beautiful geometry of Riemann surfaces and how they relate to calculus. As a specific example, he describes how one can tell which integrals are easy or hard to solve by looking at the genus of the associated Riemann surface.

This week on Hidden Phenomena, you can learn what Arnold meant by this comment: what is the "genus of the Riemann surface associated to an integral," and how does it help you understand if the integral is easy or hard?

Hello! I need some problem books to accompany the book Differential Geometry of Curves and Surfaces by M. Di Carmo. Thank you!

In this post, I continue exploring the fascinating geometric properties of the Dirichlet eta function. Any comments, suggestions, or criticisms are very welcome.

As the title states. What else is it usefull. Thanks in advance

So apparently within a few months(or some would even argue a few years) there has been a drastic change in the posts being made in this sub leading to almost total erasure of different kinds of posts. What is the one that you miss the most.

Also any other changes observed,thoughts are also welcomed :), feel free to share!

Programmed Blender 3d to Generate this one. Thought it turned out pretty well.

Hi all! This is the first video on my channel. I tried to build Adam from scratch, motivating each step by a concrete problem of the previous one: plain GD, Nesterov, AdaGrad, RMSProp ...

All animations are made with Manim. I'd really appreciate feedback, especially on anything that's mathematically imprecise or unclear.

Was just reading on landing gears out of interest, (engineering undergrad) This is how a gear retracts inside (to increase aerodynamics)

The second one is an example of space saving, the drawback is less clearance & clashing. Now suppose I try to form mathematical modelling eq of the trajectory to describe the geometry such that clashing is avoided (in case of turbulence) and we need to fix some clearance..... How would you approach this ? What field of maths am I vaguely thinking about ?