Their purpose really is to let the authors show off how smart they are, impress their peers, and advance their careers. The other properties derive from that.

;-)

edit: I don't want to disparage research in general, BTW, but specifically, the scientific paper redaction process.

I know you were being sarcastic, but I think you are also being a bit unfair. Publication is necessary these days at perhaps an unfortunate rate, I agree.

However at least most research mathematicians publish largely to share ideas. After all, that's the best part of the job. Certainly this is true of the vast majority of them in my experience, and the ones weren't motivated by this tended to be very focused on teaching and very good at it.

e.g. redaction in german means editing

And then it's basically (paraphrasing with reckless abandon) just the probably of your event divided by the total probability space. Lots of words and jargon and theory given in countless papers and articles, and it pretty much just boils down to intuitive addition, multiplication, and division.

And our aimbot detector actually worked pretty damn well! Just gather some data points to determine probabilities, plug them into the simple formula, and it was always correct in our test cases.

Or does it? After all, probability is one of the very first mathematical tools to be divised, but a rigorous theoretical underpinning for probability and statistics had to wait until measure theory, millenia later. And this was not for want of trying.

Part of what makes things "boil down" to the simple and intuitive is years of hard work. Reading Newtons original work on the calculus is painful and convoluted, it took many hands to polish it to the point you might have seen it in.

If we've done our jobs well as mathematicians, eventually the essence of an idea will be easy to understand an apply. If you really want to understand it though, you may have to dig into some much deeper work. And often, as with many thing is in mathematics, human intuition will just tend to be wrong about it (e.g. the Monty Hall problem).

I was incredibly proud when I noticed, just through algebraic manipulation, without reading it anywhere first, that you should be able to extract the public key used to create an an ECDSA signature. Schnorr signatures don't have this property. This is kind of sad in a way becaue it's trivial, but you have no know how the primitive functions and the difference between a field and a group.

https://news.ycombinator.com/item?id=4112327

Unambiguous? I wish! The notation in most fields is way more ambiguous than code; you're expected to resolve the ambiguity by the norms of whatever research community it's for. Code isn't necessarily clear, but at least all the information is there to be decoded.

An example of trying to do better: http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/boo...

In other words, the purpose is primarily tenure and advancement.

This may be a problem.

As a simple explanation, consider the difference between explaining the Monty Hall problem - which might seem to be philosophical, open to interpretation - and coding it up. The moment you code it up --- go ahead, code up a monte carlo simulation that compares the two alternatives of switching doors or maintaining the same choices, and spits out a running count of which is what percentage correct. I'll wait while you code. ---

the moment you do that, you see two lines in your code that make the explanation 100% irrefutable and completely obvious.

That is why papers are written this way. Intuition can go both ways.

A good mathematical author must be guarding against both of these selection biases.

That's actually a pretty brilliant way of explaining it. With numbers like that the answer becomes much more intuitive.

Well, obviously, you should - with a million doors, it becomes obvious that you have just a 1 in 1,000,000 chance of having picked it.

But thing is - that "obvious" thing 'should' be just as obvious with 1000 doors, 100, 20, 5, or...3....

It's a matter of degree - not kind.

So appealing to a way of intuiting it that is a lot more 'obvious' - while in fact having the exact same format of question, just goes to underscore how fickle intuition can be.

That said, taking individual variables to ridiculous extremes is a great way to thought experiment and an awesome way to get intuition to work better.

It's easy, pick a door, then the host discards 98 doors in which the car isn't. Do they still think that the probability of the other door left is the same than the one they picked? I want to play gambling games with them!

    Pick a door, the host discards 98 doors
    where the car isn't.  There are now two
    doors left, so it's 50:50.