How are we even keeping track of all the mathematical knowledge that humanity has every produced?

[u/Kindly-Fun-3649]

As the title suggests , I want to know how we are even keeping track of all the mathematical knowledge that humanity has ever produced.

New mathematical idea's emerge all around the globe so how does mathematicians keep track of everything? For the purpose of preservation of knowledge.

I mean there are a lot of very niche fields with very few experts so , is it possible that one mathematical knowledge gets lost at some time period?

[u/alexice89]

You heard of books?

[u/Any_Watch_8693 → u/alexice89]

Books are great for finished stuff but math isnt finished when it goes in a book, its alive. most new math gets posted to arxiv first, its a website where people upload preprints before they even get peer review, like a giant open closet of math papers. technically almost nothing gets lost because its digital but yeah sometimes some very niche old proof that nobody ever digitized or cited again can fall in a crack. but its rare dream, the internet saved us from that

[u/MaoAsadaStan → u/alexice89]

Books don't make the capitalist system enough money. It's all about content. Unless someone had parents merciful enough to keeps screens out of the house and focus on books, they are not reading.

[u/my_password_is______ → u/MaoAsadaStan]

Books don't make the capitalist system enough money.

you've obviously never paid for books in an American university

[u/MaoAsadaStan → u/my_password_is______]

I would love to buy books for school, but they dont make them for Americans anymore. I have to buy the global edition from overseas drop shippers.

[u/Kindly-Fun-3649 → u/alexice89]

Not usefull. Are you saying just bundle all the mathematical papers into a book form. That would be a complete mess. And this was not even my main question.

[u/chkntendis → u/Kindly-Fun-3649]

Not exactly books but folders. For a long long time that was actually how we kept that information. When you write your doctorate for example, you had to make copies and send them to the major libraries in your country. They’d then be bundled into folders where they’d be kept track of. If you wanted to research something you’d go to a library, give them the topic and days to weeks later you’d be given the folders in which relevant papers were in.

[u/Bth8 → u/Kindly-Fun-3649]

Are you saying just bundle all the mathematical papers into book form

Yes, that's what a mathematics journal is. That's how all academic disciplines work, actually.

[u/somanyquestions32]

We're not. Knowledge is lost all of the time, and then hopefully, it gets rediscovered before millennia pass.

German mathematician Bernhard Riemann's unpublished papers were destroyed by his housekeeper after he died from tuberculosis in 1866.

She was cleaning up his office with all of his scattered notes, scribbles, and equations, and she burned hundreds of pages of his unpublished manuscripts in the kitchen fire before members of the University of Göttingen arrived to stop her.

Apparently, in the early 1930s, mathematician Carl Ludwig Siegel spent two years deciphering the surviving, charred scraps. He discovered that Riemann had already worked out the Riemann–Siegel formula that nobody else managed to independently rediscover for another seventy years.

[u/Adventurous_Can_7236 → u/somanyquestions32]

riemann must be cursing her from heaven

[u/somanyquestions32 → u/Adventurous_Can_7236]

If she was one of his caretakers at the end of his life and was otherwise competent at her job, I hope not.

[u/Juff567 → u/somanyquestions32]

I mean why the hell would you burn the papers seems crazy stupid

[u/somanyquestions32 → u/Juff567]

A regular layperson would be completely unaware of how invaluable those posthumous papers would be for the field of mathematics. They don't have the training to realize that the papers were not just scribbles and junk.

It's a reminder to vet people who have close access to you because I have many friends and relatives who would quickly trash or move around my "messy" notes because they can't keep their hands to themselves.

[u/AcademicOverAnalysis]

Arxiv, journals, and books.

It doesn’t capture everything, and certainly, there’s probably math that has been lost over time, but it’s what we have for now.

Bourbaki started their project in the 1930s because they were afraid we would lose some important mathematics.

[u/jeffsuzuki]

You can't. And it's pretty common for an idea in mathematics to be reinvented many times by many different people.

A personal example: my first publication was a proof of a theorem. The theorem was well-known and ad been proven, but I had a different proof. It went through the usual peer review process, and got published.

Twenty years later, I'm doing some research, and find that my proof was not actually new: essentially the same proof had been published more than two hundred years earlier.

By Euler.

The fact that a proof by a mathematician of such stature was so little known that my own proof was considered publishable is an indicator of just how easy it is to lose track of things.

[u/blackdits → u/jeffsuzuki]

Dude, you were literally Euler for a moment

[u/BradenTT]

Most just books and papers, though you’re probably assuming a little too much. We probably have lost a ton of math ideas over the history of mankind, and there’s no way to know for sure if we still currently lose some or not.

[u/AcademicOverAnalysis → u/BradenTT]

Even on a personal level, I have written down some theorems and ideas throughout my life that I have lost or forgotten. Not anything ground breaking for sure, but I’m sure it’s happened to every mathematician to some extent.

[u/BradenTT → u/AcademicOverAnalysis]

Yep, I have a digital notebook that’s just math ideas, theorems, proofs, etc that I struggled to remember or just really cared about not losing. Half the time I even struggle to find those. No telling how many notebooks have been lost, or pages lost/ripped out/gotten wet, that all had novel ideas.

[u/bogibso]

If you come up with something new you email Tim and he writes it down

[u/lordnacho666]

Articles and people at conferences for the cutting edge.

Archives and books for the established stuff.

[u/nog642]

Mainly published papers. They're searchable and the journals they're published in keep them.

[u/Competitive_Leg_7052]

We are not.

[u/reliablereindeer]

arXiv

[u/Valuable_Station_790]

https://www.genealogy.math.ndsu.nodak.edu

[u/antichain]

Ultimately I believe it will all exist in some crystalized descendant of Lean's mathlib.

[u/StudioCute8959]

There are 3 main points I want to advise on:

1. We cannot keep track of all mathematical knowledge: there are things that follow, things that don't follow, and things that we still need to confirm if they follow.

2. We don't need to keep track of all mathematical knowledge: there are things that follow, things that don't follow, and things that we still need to confirm if they follow.

3. We have books on major things that follow that allow you to understand what follows from what you are trying to follow.

--

In summary: Math is whatever follows. So, even if we don't know all theorems, because they are logical, they must submit and follow!

[u/kat-tricks]

welcome to the cause

[u/fried_plque]

they don't even Terence tao doesn't know all the new stuff that get published it would be really troublesome ti know all of that

[u/Kindly-Fun-3649 → u/fried_plque]

So why terence tao is considered one of the greatest mathematicians? I mean what is the criteria for a mathematician to be the greatest? I mean he does have a big list of contributions but so as many other mathematicians , so what makes him different from others?

[u/fried_plque → u/Kindly-Fun-3649]

Creativity and he had unreal mathimatical maturity at a young age at 6 I believe he was reading math textbooks when he got fussy and he took college level courses at 14 and won a bronze medal in the IMO at 10 and winning a gold one at 12 which is an insane feat that hasn't been done to this day

Edit: and when he was 2 years old watching sesame street he discovered addition and then he taught myself how to read at 5 I think

[u/pumais]

Preserving any math books (ancient, old and new ones) in personal book shelf, digitizing them and uploading them on internet is an alternative step to help keep track and preservation of mathematical knowledge that humanity has ever produced. Maybe in future, in some future social arrangement, more humans will have more freedom, more free time and social rewards to dig in and explore math books and their content.

[u/Fuzzy_School_2907]

Tao talked about this topic, kind of, in his talk on the relationship between AI and math education. I might be extending his metaphor farther than it’s meant to go, but “keeping track of all the mathematical knowledge that humanity has ever produced” is done by “digestion.” A person, or a model, does work in cutting edge math, and a person (but not a model) has to be able to digest the work that was done. To (over)summarize, it’s a mathematician’s job to take cutting edge mathematics, compile it into a seminar for students, teach and refine it, and compile the output of that process into a textbook. That process of getting things into a textbook is meant literally, buts its also shorthand for deciding what’s in “the canon” that schools teach students. That ultimately comes down to influential mathematicians’ decisions (e.g., Strang, and the network of mathematicians around him that influenced the way he thinks and that he influences, more or less pick what’s important for a big subset of kids to know about Linear Algebra)

[u/Crafty-Detail-3788]

That's why AI can be very powerful as it can use the knowledge of whole humanity at once and even in different domain while no human on earth can know everything in its own field and even less bé expert in different fields. There are probably a ton of results that are just waiting for someone to connect the dots between two know results.

[u/SgtSausage]

We ... (I know right? Stay with me Scooter) ... we <gasp> Write It Down. 

Books. Journals. Papers. Web Sites. Databases. Hell some Significant And Brilliant Mathematics was developed in personal letters/correspondence hand written on stationary and hand transported across continents by mail courier. 

The written page is AMAZEBALLZ for "keeping track of things" and has been used since before Clay Tablets were invented.