I was joking with a colleague today about replacing Mathematica (a symbolic math program) with an abacus, and it started me wondering: how would one go about making a "symbolic abacus"?
Let's just limit it to finding roots of polynomials, for example. Could you make a mechanical device that lets you slide/fold/twist "x^2 = x+a" and then slide/fold/twist to get "x = (+/- sqrt(4a+1) + 1 )/2" ?
(Edit: To emphasize symbolic, not numeric solutions)
@catselbow You can generate roots for solvable polynomials just by straight edge and compass constructions; the general n-th degree polynomial equation can be solved in terms of modular forms ( see Thomae's formula for instance) so one might try to translate those functions into a physical machine, similar to how square roots can be dealt with by compass constructions.
This is a lovely youtube video exploring code optimizations by cleverly pruning the state space in a Code of Advent problem; it has a lot of good generic advice, and quite a funny ending.
Yesterday, before going to bed, my son explained to me the mathematical rules of life that he saw on YouTube. I understood what he was talking about, I was amazed that he saw the video once and remembered the variety of figures. Today we read a wiki article about it and found a cool online simulator
The Putnam Competition is the premier mathematical competition for undergraduate students in the USA. This collection contains tex and pdf files of Putnam problems and solutions with commentary, as well as links to secondary resources related to Putnam....
By far the most precious resource Reddit gets from you is your insight; Reddit needs posts, especially posts with good insights on specific topics. This is the treasure trove they are sitting on and the value proposition for shareholders: a gigantic collection of long-form discussions on all kinds of niche topics that can be used for targeted and generic AI training.
So by continuing to use reddit, you are providing them with the most precious resource they seek anyway. This is why I am anxious to see a genuine alternative to reddit.
@cazabon Indeed, these buzzwords are just 21 Century versions of the 90s Clipper chip arguments.
That being said, "encryption is math" is a weak argument in the court; of course a copyrighted song in flac form is also just math, but that does not prevent it from being legislated. There are much better arguments for E2EE, both or practical and foundational character; the cryptography stack exchange has an extensive list of questions related to these issues.
Here's a link to one of my favorite math news websites. It's always interesting (to me, at least) to see how sometimes even niche or obscure parts of math end up being applied to solve problems in ways I likely never would have dreamed up myself....
Non-affiliated publications include The Chalkdust and Quanta Magazine. There is also a rather big Mathematics discord server at https://discord.gg/math that includes graduate topics, graduate admissions etc.
I would love further recommendations from people outside the US and Europe.
Like for example, how someone thinks because you work in IT you can fix their TV, or how if you're into music you must be able to play any random instrument....
There are tons of misconceptions about mathematics, but the biggest and most baffling one is: that no new mathematics is being created, that the field is "done".
The opposite is true: there are more open problems than ever, and research is frantic in mathematics with hundreds of thousands of serious new theorems being proven every year by professional mathematicians, and entirely new mathematical vistas being discovered every few years.
In fact, the pace of research is so fast that we are now creating the foundations for databases of mathematical theories and their proofs in order to better classify and preserve them.
This is the main expository publication of the American Mathematical Society; it features articles on various topics at the forefront of mathematical research written for the non-expert, as well as community news, jobs openings, reader correspondence and more....
This is an introductory book to programming in Lean 4, a pure functional language that started as a theorem prover at Microsoft Research by Leonardo de Moura. It is a dependently typed language similar to Idris, with many features inspired by Haskell....
The American Mathematical Monthly is an excellent resource for mathematics enthusiasts, with articles selected for high quality exposition and broad appeal....
I don't care too much about the Fediverse in itself; I was looking for an old.reddit.com-style place to share all sorts of hobbyist and technical content and have meaningful discussions on it. The interface kbin is offering suits me aesthetically better than the alternatives, so I am sticking with this site now. I like the clean but not too sparse feel, the simple threading, and the ease of browsing magazines. I would like to see comment thread collapsibility and easier navigation within a thread's comments (remove or improve pagination, for instance).
There are many limitations, but these can also be opportunities: precisely because this site is in its infancy, it has the potential to incorporate ideas from the community much faster and with more forethought than a mature, established product.
For my part, I would like to lobby slightly for native LaTeX rendering throughout kbin.social, similar to what mathstodon.xyz has. It is a somewhat niche functionality, but it would put math, physics and computer science-related magazines far ahead of corresponding subreddits in infrastructure.
Videos from an online seminar on Number Theory that features experts from all over the world on all subjects related to arithmetic and its applications.
I am a mathematician working in homogeneous dynamics and number theory; I came here from Reddit looking for an alternative and still trying to get the hang of things. I see there is little mathematics activity at kbin.social at this moment, but hopefully this will change.
It seems that the administrator is currently swamped with the influx of users, but I am wondering if in the foreseeable future we can look forward to enabling some sort of LaTeX rendering in the threads, putting us far ahead of reddit in capabilities. Currently, I know only one federated place with LaTeX rendering, which is mathstodon.xyz. I wonder if the methods they are using can be transferred to kbin.
Right now we insert mathematical symbols on kbin.social directly from the list on the magazine column, but this is awkward and limited. Without any meaning to offend, I can see that r/math discussions tend to be less about mathematics and more "around" mathematics, and I have a pet theory that the lack of easy LaTeX input contributes to this phenomenon.
I would love it if this place could host a forum for mathematical discussion at all levels, and would like to hear other people's thoughts on this.
I'm not sure I understand why "Threads" and "Microblogs" are separate entities in kbin. From my understanding, "Threads" are like Reddit's link/image posts and "Microblogs" are like text posts. Why are these only viewable in separate tabs? It seems like a bad thing to completely separate certain content from the same Magazine and make it unable to view everything at once. Am I misunderstanding something?
I am a little confused; so, if I want to make a text thread with threaded replies/comments etc. like in a normal forum, do I select microblog? In particular, how was this thread created, where the first post is text?
@fabian There isn't one, even historically, as far as I know (I am a mathematician, but not a historian of mathematics). The reason, I suppose, is historical happenstance. Most mathematical functions don't get their own symbol (sin, cos, tan, tanh, cosh...) and the log family is no exception; I think it is the square root that is the exception, whose first symbol was invented by Regiomontanus probably for his convenience.
Turbulence through sustained vortex ring collisions (youtu.be)
An amazing video on a fluid dynamics experiment that produces a confined turbulent region in sustained fluid flow.
Going fast is about doing less (www.youtube.com)
This is a lovely youtube video exploring code optimizations by cleverly pruning the state space in a Code of Advent problem; it has a lot of good generic advice, and quite a funny ending.
Still, better than Emacs (sh.itjust.works)
The Putnam Archive (kskedlaya.org)
The Putnam Competition is the premier mathematical competition for undergraduate students in the USA. This collection contains tex and pdf files of Putnam problems and solutions with commentary, as well as links to secondary resources related to Putnam....
Is it okay to lurk reddit without engaging?
Hello there everyone!...
Society for Industrial and Applied Mathematics (SIAM)
Here's a link to one of my favorite math news websites. It's always interesting (to me, at least) to see how sometimes even niche or obscure parts of math end up being applied to solve problems in ways I likely never would have dreamed up myself....
What's an innocent misconception about your hobby/profession that drives you up the wall?
Like for example, how someone thinks because you work in IT you can fix their TV, or how if you're into music you must be able to play any random instrument....
Notices Of The American Mathematical Society (www.ams.org)
This is the main expository publication of the American Mathematical Society; it features articles on various topics at the forefront of mathematical research written for the non-expert, as well as community news, jobs openings, reader correspondence and more....
Functional Programming in Lean (leanprover.github.io)
This is an introductory book to programming in Lean 4, a pure functional language that started as a theorem prover at Microsoft Research by Leonardo de Moura. It is a dependently typed language similar to Idris, with many features inspired by Haskell....
Archives of the American Mathematical Monthly (archive.org)
The American Mathematical Monthly is an excellent resource for mathematics enthusiasts, with articles selected for high quality exposition and broad appeal....
I just got done exercising by choice for the first time since 2016.
I'm entering my late 30s, and my body isn't taking care of me because I have not taken care of it for most of its adult life....
A lot subreddits end their blackout tomorrow. Will you go back to Reddit, or continue with kbin and the Fediverse?
I haven't used Reddit at all since the blackout began. Even if they change course, the Fediverse is growing on me, and I think I'll stay here....
The Number Theory Web Seminar (www.youtube.com)
Videos from an online seminar on Number Theory that features experts from all over the world on all subjects related to arithmetic and its applications.