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I don't expect non-math people to relate or even care. If you open a textbook on algebraic topology and you've never studied even the most mundane calculus, you won't understand anything.

Somehow, this infuriates people.

The same people would have no problem admitting that they should probably not read specialized literature on law that requires readers to have gone through 8 years of law school before they can make sense of the content.

Mathematical literature is not meant for casuals. Its impossible to express advanced concepts concisely, in such a way that people who don't know the material can understand them.

This is like asking someone for an explanation on how to walk and then throwing a fit when they reply with "well, place one foot on front of the other in such a way that you dont fall over". You don't expect them to discuss activation levels in skeletal musculature resulting from biochemical processes in the nervous system. But in Math, thats what you want. Clear and concise language that inspires and is fun AND fully describes the problem at the same time.

Not going to happen.

You still don't get it... You are arguing against something I did not say!

Theres no elitism in math. We just require you to write proof in such a way that it is actually a proof, and not just some idea you've had.

In order to do that, you need to study math. Not because we are elitists but because you need to learn how to prove something. You need to learn the tools.

The same way a mason expects you to learn his craft before he takes you seriously. If you don't have a clue about masonry, you can still semi reliably build a brickwall in your backyard. But not a cathedral. Obviously, you dont expect anyone to allow you to work on a cathedral. But you expect mathematicians to take your thoughts on math seriously.

Its like a bootcamp idiot trying to piss all over a big software project. Just because they know how to vomit on a keyboard doesnt mean they get to make decisions.

you STILL dont get it!

Posting that opinion in this thread was bound to generate confusion, but I get your point. That's usually called divulgation or public awareness. The problem is that it's often quite hard to do, because most practitioners only understand the concepts in terms of that mathematical language, and it's quite hard to translate them, since you can't easily put yourself in the shoes of someone who doesn't understand that language.

Also, it's not clear that there's any point in doing so; say you can explain a very technical concept to a layman using terms and concepts that don't require two years of study. Then what? What is that person supposed to do with that knowledge, if they lack the mental tools to apply it? It becomes little more than trivia, no?

Still, there are some attempts: http://math.stackexchange.com/questions/275/best-maths-books...

Mr. Tao does, in fact, not understand prime numbers. That's not to say that he is stupid or hasn't done his reading. He probably understands them better than anyone else in the world, but he still doesn't understand them. Otherwise, he wouldn't make any mistakes.

But the literature is not to blame for that. He simply tries to do something that nobody else has ever achieved before. Of course he's going to make mistakes.

The difference between math and writing programs is that in math, there's no compiler. When you go in the wrong direction, nobody is going to tell you about it. But this doesn't mean that any of the proven theorems that he bases his work on are faulty. He can rely on each and every one of them. They are proven to be true.

His issues stem from the fact that he wants to do things that are unexplored. Think columbus discovering america. Its not that his maps are faulty. There simply is no map for the new continent yet.

The rigor in math has nothing to do with an elitist attitude. The italians tried to do handwaving math for a hundred years. 100 years of italian algebraic geometry had to be erased because they began dropping the elitist attitude. They made progress at an amazing pace until eventually, they discovered inconsistencies in their "findings" and had to start over.

> The difference between math and writing programs is that in math, there's no compiler.

Increasingly, there are tools so that there could be, if you want to do math that way.

http://us.metamath.org/index.html

You mispelled Kato. Tao is an analyst not a number theorist. As for the Italian school tge foundational issues were common to all algebraic geometers. Ultimately concepts like generic point pointed the way towards scheme theory, even if not rigorously defined.

Tao definitely knows about prime numbers. Whether mathematical approach he takes, he is relevant to the field.

https://en.wikipedia.org/wiki/Green–Tao_theorem

https://en.wikipedia.org/wiki/Terence_Tao

> You cannot communicate using dense language and expect non-math people to relate or even care.

You seem to be misunderstanding mathematicians' goal. It is not to communicate with the general public. It's to communicate with other mathematicians.

You could argue that the culture of the field should change and should be focused on public exposition (although I'd disagree with you, as I don't think modern math is really interesting or important for more than a small subset of people). But regardless of the outcome of that separate argument, it's currently the case that in practice that is not the goal.

> if you want more rigor in society you should introduce more people to math rather than having them being put-off by some elitist attitude.

Again, "mathematician" is not the same job as "general public mathematics educator". Most professional mathematicians do not care about what you're talking about except in the same vague way everybody else cares about it.

This is a bit like asking me to write my code in such a way that people who don't know C++ could understand it. That might be nice but it isn't the primary goal and I'm not paid to put extra effort into it.