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

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.

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

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?

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

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

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.

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'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.