The biggest project in modern mathematics [video]
youtube.com
youtube.com
https://www.quantamagazine.org/what-is-the-langlands-program...
> I’ve never succeeded in understanding the slightest thing about it.
[0] https://golem.ph.utexas.edu/category/2010/08/what_is_the_lan...
In seriousness, having had some exposure to the Langlands program (through the wonderful Love and Math by Frenkel), I was counting the minutes to hear about it.
I found the video to have a great layman explanation of what it is about.
That attempt famously and spectacularly failed with Gödel's incompleteness theorems.
Since then it seems that mathematicians have lost interest in foundations and are content to search for interesting results, structures, and systems, even if they don't have a solid foundation.
More recently I've heard some proposals to revisit the foundational project but with higher-order logics proving the consistency and completness of lower-order ones, which sounds interesting, but I'm not sure how much progress has been made, and to a non-mathematician/non-logician even that attempt sounds a bit like a house of cards.
Does anyone here know about this and if there are even any mathematicians around these days who are still interested in it?
This is very much not the case. What's closer to truth is that the discussion moved on from a framework laymen can seemingly understand conclusions, to one where conclusions (or their implications on mathematics proper) are a lot harder to explain to laymen. Foundational work is still a thing, but I don't think it affects the nature of mathematics in a way laymen can conceptualize.
Take Godel's incompleteness. People say it's something laymen can understand, and people attempt explaining it to masses every day in youtube, reddit etc. But if you truly get into the formal conclusion (i.e. with Rosser's trick, the conclusion is: "a theory cannot be an extension of Q, complete and consistent all 3 at the same time") you'll see that it's already pretty far away from what laymen thought they understood. And modern foundational work exponentially drifted away from this too.
I'm not a mathematician so everything in this comment should be taken with a grain of salt.
Computer-checked mathematics is growing very fast.
Stuff like category theory ("Not real maths" - Kevin Buzzard) is also extremely popular.
The classification of finite simple groups aka The Enormous Theorem might also interest you. It is around 10,000 pages spread across 100s of journal articles by ~100 authors over a 50 year period.
https://en.wikipedia.org/wiki/Enormous_theorem
You could jump to the history section if you want to skip some technical parts.
There have been other huge programs but they might be harder to describe without a lot of jargon.
A tiny bit from section 9:
> The 20th century can be divided roughly into two halves. I would think the first half has been dominated by what I call the "era of specialization," the era in which Hilbert's approach, of trying to formalize things and define them carefully and then follow through on what you can do in each field, was very influential. As I said, Bourbaki's name is associated with this trend, where people focused attention on what you could get within particular algebraic or other systems at a given time. The second half of the 20th century has been much more what I would call the "era of unification", where borders are crossed, techniques have been moved from one field into the other, and things have become hybridized to an enormous extent. I think this is an oversimplification, but I think it does briefly summarize some of the aspects that you can see in 20th-century mathematics.
https://leanprover-community.github.io/
I think it is the future of mathematics. Yes I know that 99% of mathematicians will disagree. That's not unusual for a fundamental change to how people think. And yes I know it will take a very long time for this change to manifest itself. That is also not unusual for a fundamental change to how people think. But don't underestimate the exponential power of real formal mathematics. What mathematicians are currently calling "formal" proofs aren't. They are just informal proofs with lots of details. Again, 99% of mathematicians will strongly disagree. However eventually we will see math journals dedicated to formally proven correct mathematics. And those proof will start to be regarded above and beyond the current informal proofs. It will take a long time. But IMHO it is inevitable.
We are still far from those goals (it is a big project for a reason) but the work of professional mathematicians could look very different in a hundred years if those efforts succeed.
[1]: And the distinction between contemporary and modern might be relavant.
1st) you have to generate a 'numbers-room'
So, when you multiplicate two 'one-digit' numbers, the 1st calculation with a two digits result is 2 * 5
2 * 6
2 * 7
2 * 8
2 * 9
3 * 3
3 * 4
3 * 5
3 * 6
3 * 7
3 * 8
3 * 9
4 * 4
4 * 5
4 * 6
4 * 7
4 * 9
5 * 5
5 * 6
5 * 7
5 * 8
5 * 9
6 * 6
6 * 7
6 * 8
6 * 9
7 * 7
7 * 8
7 * 9
8 * 8
8 * 9
9 * 9
10 * 1
10 * 2
10 * 3
10 * 4
10 * 5
10 * 6
10 * 7
70 * 8
10 * 9
and 12 * 9 is the first sum with a 3-digits result.
> But there was 10 * 10 a '4-digits' multiplication with onla a 3-digits result.
And if you took physics -acustics, you know there are primary- and secondary waves spreading...
...must be my humor, but... hm?*
(-;
edited: (asterixes, readability ^^)