Weaving Stereographic Projection

mathematicians, constantly: god I’m so tired of people telling me how much they hate math whenever i mention what im into

me: yeah it’s fucked up. i do probability theory, what about you

them: oh man I hate probability theory

When banned from using "trivially" in a proof...

“Hello all. In a fellow mathposter's topology class they were not allowed to use the word "trivially" or any synonym thereof his proofs. The person presenting his work then crossed out "trivially" and wrote instead "indubitably." This inspired him to write a program that will insert condescending adverbial phrases before any statement in a math proof. Trivially, this is a repost. Below is the list--please come up with more if you can!

Obviously

Clearly

Anyone can see that

Trivially

Indubitably

It follows that

Evidently

By basic applications of previously proven lemmas,

The proof is left to the reader that

It goes without saying that

Consequently

By immediate consequence,

Of course

But then again

By symmetry

Without loss of generality,

Anyone with a fifth grade education can see that

I would wager 5 dollars that

By the contrapositive

We need not waste ink in proving that

By Euler

By Fermat

By a simple diagonalization argument,

We all agree that

It would be absurd to deny that

Unquestionably,

Indisputably,

It is plain to see that

It would be embarrassing to miss the fact that

It would be an insult to my time and yours to prove that

Any cretin with half a brain could see that

By Fermat’s Last Theorem,

By the Axiom of Choice,

It is equivalent to the Riemann Hypothesis that

By a simple counting argument,

Simply put,

One’s mind immediately leaps to the conclusion that

By contradiction,

I shudder to think of the poor soul who denies that

It is readily apparent to the casual observer that

With p < 5% we conclude that

It follows from the Zermelo-Fraenkel axioms that

Set theory tells us that

Divine inspiration reveals to us that

Patently,

Needless to say,

By logic

By the Laws of Mathematics

By all means,

With probability 1,

Who could deny that

Assuming the Continuum Hypothesis,

Galois died in order to show us that

There is a marvellous proof (which is too long to write here) that

We proved in class that

Our friends over at Harvard recently discovered that

It is straightforward to show that

By definition,

By a simple assumption,

It is easy to see that

Even you would be able to see that

Everybody knows that

I don’t know why anybody would ask, but

Between you and me,

Unless you accept Gödel’s Incompleteness Theorem,

A reliable source has told me

It is a matter of simple arithmetic to show that

Beyond a shadow of a doubt,

When we view this problem as an undecidable residue class whose elements are universal DAGs, we see that

You and I both know that

And there you have it,

And as easy as ABC,

And then as quick as a wink,

If you’ve been paying attention you’d realize that

By the Pigeonhole Principle

By circular reasoning we see that

When we make the necessary and sufficient assumptions,

It is beyond the scope of this course to prove that

Only idealogues and sycophants would debate whether

It is an unfortunately common misconception to doubt that

By petitio principii, we assert that

We may take for granted that

For legal reasons I am required to disclose that

It is elementary to show that

I don’t remember why, but you’ll have to trust me that

Following the logical steps, we might conclude

We are all but forced to see that

By the same logic,

I’m not even going to bother to prove that

By Kant’s Categorical imperative,

Everyone and their mother can see that

A child could tell you that

It baffles me that you haven’t already realized that

Notice then that

Just this once I will admit to you that

Using the proper mindset one sees that

Remember the basic laws of common sense:

There is a lovely little argument that shows that

Figure 2 (not shown here) makes it clear that

Alas, would that it were not true that

If I’m being honest with you,

According to the pointy-headed theorists sitting in their Ivory Towers in academia,

We will take as an axiom that

Accept for the moment that

These are your words, not mine, but

A little birdie told me that

I heard through the grapevine that

In the realm of constructive mathematics,

It is a theorem from classical analysis that

Life is too short to prove that

A consequence of IUT is that

As practitioners are generally aware,

It is commonly understood that

As the reader is no doubt cognizant,

As an exercise for the reader, show that

All the cool kids know that

It is not difficult to see that

Terry Tao told me in a personal email that

Behold,

Verify that

In particular,

Moreover,

Yea verily

By inspection,

A trivial but tedious calculation shows that

Suppose by way of contradiction that

By a known theorem,

Henceforth

Recall that

Wherefore said He unto them,

It is the will of the Gods that

It transpires that

We find

As must be obvious to the meanest intellect,

It pleases the symmetry of the world that

Accordingly,

If there be any justice in the world,

It is a matter of fact that

It can be shown that

Implicitly, then

Ipso facto

Which leads us to the conclusion that

Which is to say

That is,

The force of deductive logic then drives one to the conclusion that

Whereafter we find

Assuming the reader’s intellect approaches that of the writer, it should be obvious that

Ergo

With God as my witness,

As a great man once told me,

One would be hard-pressed to disprove that

Even an applied mathematician would concede that

One sees in a trice that

You can convince yourself that

Mama always told me

I know it, you know it, everybody knows that

Even the most incompetent T.A. could see,

This won't be on the test, but

Take it from me,

Axiomatically,

Naturally,

A cursory glance reveals that

As luck would have it,

Through the careful use of common sense,

By the standard argument,

I hope I don’t need to explain that

According to prophecy,

Only a fool would deny that

It is almost obvious that

By method of thinking,

Through sheer force of will,

Intuitively,

I’m sure I don’t need to tell you that

You of all people should realize that

The Math Gods demand that

The clever student will notice

An astute reader will have noticed that

It was once revealed to me in a dream that

Even my grandma knows that

Unless something is horribly wrong,

And now we have all we need to show that

If you use math, you can see that

It holds vacuously that

Now check this out:

Barring causality breakdown, clearly

We don't want to deprive the reader of the joy of discovering for themselves why

One of the Bernoullis probably showed that

Somebody once told me

By extrapolation,

Categorically,

If the reader is sufficiently alert, they will notice that

It’s hard not to prove that

The sophisticated reader will realize that

In this context,

It was Lebesque who first asked whether

As is tradition,

According to local folklore,

We hold these truths to be self-evident that

By simple induction,

In case you weren’t paying attention,

A poor student or a particularly clever dog will realize immediately that

Every student brought up in the American education system is told that

Most experts agree that

Sober readers see that

And would you look at that:

And lo!

By abstract nonsense,

I leave the proof to the suspicious reader that

When one stares at the equations they immediately rearrange themselves to show that

This behooves you to state that

Therefore

The heralds shall sing for generations hence that

If I’ve said it once I’ve said it a thousand times,

Our forefathers built this country on the proposition that

My father told me, and his father before that, and his before that, that

As sure as the sun will rise again tomorrow morning,

The burden of proof is on my opponents to disprove that

If you ask me,

I didn’t think I would have to spell this out, but

For all we know,

Promise me you won’t tell mom, but

It would be a disservice to human intelligence to deny that

Proof of the following has been intentially omitted:

here isn’t enough space in the footnote section to prove that

Someone of your status would understand that

It would stand to reason that

Ostensibly,

The hatred of 10,000 years ensures that

There isn’t enough space in the footnote section to prove that

Simple deduction from peano’s axioms shows

By a careful change of basis we see that

Using Conway’s notation we see that

The TL;DR is that

Certainly,

Surely

An early theorem of Gauss shows that

An English major could deduce that

And Jesus said to his Apostles,

This fact may follow obviously from a theorem, but it's not obvious which theorem you're using:

Word on the streets is that

Assuming an arbitrary alignment of planets, astrology tells us

The voices insist that

Someone whispered to me on the subway yesterday that

For surely all cases,

Indeed,

(To be continued)

My favorite example of girl math is when David Hilbert and Albert Einstein couldn't solve how energy conservation worked in general relativity, so Hilbert asked Emmy Noether about it and she solved it for them.

doing (basic) algebraic topology in this context feels like going to that jungle and saying you know what bring this thing down we are building a city here. everything is a CW complex, everything is euclidean, and compact or paracompact if it must, all of this so that we can forget about sidestepping around topology and do algebra in peace lmao

Measure theory and topology both have this great flavor where you give the most minimal possible definition for the thing you want and then you get all the nice properties, except no, your definition is soft enough to allow crazy nonsense counterexamples hiding behind everything that you have to carefully sidestep around. It's like doing math in a jungle

ok now i might have some kind of super memory??

a week ago i played chess with bf and we didn't finish, so now i arranged the board as i remembered it and i got 13 out of 14 pieces correctly

i mean wow i didn't know i am capable of something like this

might be autism i suspect i might have

anyway now i want to know everything about human memory and take advantage of that

4-5 VIII 2021

did much topo and walked

sleep: weird. 5 hours. woke up at 3:30, at least right now it seems i might finally fix my circadian rythm

concentration: not good. too little sleep

phone time: good

almost done with operations on topo spaces and did some measure theory today. i love it so much, it's so new and yet so intuitive

tomorrow gonna take a peek at some art probably and possibly finish the operations on topo spaces, hoping to jump right into connected spaces and maybe do some more measure theory. kinda gave up with multivar calc boring af lol

maybe a littel late for Real’s Math Ask Meme 18, 6 and 3, please?

hi, thanks for the questions!

3: what math classes did you like the most?

tough choice! for the content itself I'd say abstract algebra, commutative algebra, analytic functions and algebraic topology. for the way the class was taught, a course on galois theory I took last semester was probably the best. the pace of the lecture allowed me to learn everything on the spot, not too fast, but not so slow that my mind would wander. the tutorials were also great, because the teacher found the perfect balance between explaining and showing the solutions, and engaging us to think about what should happen next. the courses I mentioned above were also taught well, but the galois theory one was absolutely perfect

6: why do you learn math?

I enjoy the feeling of math in my brain. I can spend hours thinking about a problem and not get bored, which doesn't usually happen with other things. when I finish a study session I feel tired in a good way, like I spent my time and energy doing something valuable and it's very satisfying

18: can you share a good math problem you've solved recently?

given a holomorphic line bundle L over a compact complex manifold, prove that L is trivial iff L and the dual of L both admit a non-zero section

this problem is quite basic, in a sense that you work on it right after getting started with line bundles, but I believe it to be a good problem, because it forces you to analyze the difference between trivial holomorphic bundles and trivial smooth bundles, so it's great for building some intuition

26 III 2023

I had a lot of headaches recently, idk why. probably something to do with muscle tension, because my back, neck and jaw just lock up sometimes to the point that every movement hurts. I need to see a doctor about it, maybe I injured something or there is some other underlying cause

I wasn't very strict with studying this week, because a lot of stuff we did was a review of what I already knew but obviously it needs a refresher. if I keep ignoring it, I will end up in a situation where I won't know what's going on at all

I picked up some side hustles along the way, one of which is reading the extra topics from hatcher. one of the lecturers recommended a book to me, about galois theory in the context of covering spaces, I'm reading it right now, seems pretty good

tomorrow I'm seeing my advisor to discuss my progress with solving the problem for my thesis. I think I found the basis for the module, at least I proved that the set I chose generates all the other elements, remains to show that it's linearly independent. the second part of the question is the rank of the module, which is how an algebraic topology problem turned into a nasty cominatorics problem eh

today I completed the first "serious" task for my IT job, which was translating the code from java to python. I have never seen java before, but it looks a lot like c++, so I managed. I wrote 500 lines of code but I haven't tested it yet so debugging might be very painful. lol I guess that means I shouldn't say I completed the task

I am wondering if I should go to a conference, I have until the end of the month to submit a presentation. I am not sure if I can handle a trip to another city, it would be in a month, so there is no way to predict how I'll be feeling. this week I am giving a presentation about some knot theory (skein modules, bracket and jones polynomial) and it's a good pick for the conference too, which makes it a really touch choice as the hardest part will already be done. idk I guess I'll toss a coin, like I did about the IT job lmao

other than that, big thanks to everyone who interacted with my post about book recommendations! there are many great suggestions, it turned out much better than I expected tbh, I thought I would get like 2 or 3 notes. I will post a list of the books mentioned in that post, so it will be easier to find for anyone interested

eigenvalues are just the TLDR for a matrix