#mathblr

[paintthedeadflag]

Calculators are flawed and aside from computing large numbers have not much purpose in pure mathematics.

This is not a statement about generative ai (although it would be completely useless in all facets of mathematics).

I will not pretend that I am an expert, I am no mathematician, but I absolutely adore the subject. It is what I want to spend my life doing. I will not pretend that I am the most knowledgeable so I would be delighted to hear some other opinions.

In my experience I have found the standard scientific calculator to be flawed. It has failed to give a distinct answer when the answer logically is different. As in, the difference between the numbers is so small it counts it as the same number. However, this is not 0.999... = 1. This has a finite number of decimals.

Aside from the actual calculation calculators can only aid in checking arithmetic really. The basis of mathematics is proof, which requires the human mind. I believe that in no way can the human mind can ever be replaced in terms of proofs and concepts.

Thank you for coming to my uninformed shittalk.

[ivansirkumcision]

That’s like the old trick of posting the week’s challenge problem on math stack exchange and then answering it incorrectly so it’s answered correctly faster by summoning the “um actually”☝️🤓 crowd who invariably look like the emoji

[here-by-chance]

im obsessed

[justactgaussian]

So I've seen the whole 'Math's Saddest Love Stories' (asymptotes that drift ever closer but never meet etc.), but I think we're missing the potential of Math's Funny Love Stories. The couple whose destiny is an infinite cycle of breaking up and getting back together again:

Oscillating rapidly in and out of each other's life for a while before drifting apart in opposite directions:

Drifting ever closer, until you finally meet and go fuck that:

One who drifts slowly closer to the other, until they acutally meet and decide to make a very sharp turn in the other direction:

Whatever hellscape of contrived coincidences these series of infinite near misses are:

[official-rhode-island]

I think the higher in math you get the more prone you are to forgetting basic things. This one kid in my linear algebra class spent half the time trying to prove to me why 16 minus 9 does NOT equal 7.

[sleepy-bebby]

[as-if-and-only-if]

I'm interested in forming a sort of...math & physics reading group network. well, with some very important modifications to the concept of "reading group".

for example, right now, I'd like to learn algebraic geometry, qft, and/or refresh myself on representation theory with someone—maybe just one or two people—meaning that traditionally, we'd pick a text for one of these topics, discuss the material (asynchronously or synchronously?), exchange exercises, etc.

but currently (being Between Institutions), my best bet is posting on tumblr. and that's a pretty good bet, tbh! there are a lot of us here!

though, wouldn't it be great if there were a way to coordinate groups like this across institutions? you make a post proposing a group, specifying your goals and constraints...

even that would be a boon. but I think the concept of a "reading group" itself could be changed in interesting ways. this is what I'm really interested in.

there are variations among reading groups themselves already. sometimes you have directed reading groups, where someone already knows the material and "leads" it; some people are looking for more or less people involved; and there are probably things to explore for making sure that reading groups stick through it instead of falling apart when some motivation flags. default meeting times help with this, for example.

there are many experiments to be done! I think lessons for group-making can be taken from a maybe-surprising source: theater. there are a lot of things that make groups which put on shows more robust and rewarding than reading groups. a sense of building to something; many factors that create informal group cohesion (e.g. such a structure should make sure it creates more-informal "cafe" time in addition to more-formal "practice" time, just as rehearsal in physical spaces facilitates that casual sort of interaction on its periphery); ways to get into the right headspace during discussions (just as warm-ups do in theater; the engagement with this material is an event); clear goals (e.g. "understand ___"); successive shared accomplishments...to that end I wonder if it makes sense to form math troupes, which do successive reading groups together, drawn from its members.

it might be useful to envision some sort of public-facing artifact created as the culmination of this learning, whether a presentation, or an article, or some novel application or research...the crucial question is: how do we choose a goal that we find meaning in?

one idea, for example, is to have a collection parallel reading groups learning different things, and end by presenting to each other! that way we know what we learn will be meaningful to others, too, from the beginning. in general, I think it's important to feel that our own development of insight and understanding can be meaningful to others and to the group. it's nice to participate; it's nice to be able to offer something that is valued. what form can this take? how can you set up the interactions such that everyone has a part to play, and so this meaningfulness is tangled up in participation in the group?

I've also got a couple of ideas for "activities" that let us engage, re-engage, and play with the concepts we're learning with each other, beyond the text itself. how can we give ourselves the opportunity to toss around the concepts we're learning? I believe that the fun ultimately comes from the understanding itself, and therefore that any group exercise which lets us effectively play with the ideas will be fun.

it's a lot to ask people to come up with structure like that themselves, but using a pre-existing structure is not so difficult! sort of like how it's hard to make a TTRPG itself, so simply saying "go off and roleplay" isn't that helpful, but it's easy to use the structure of an existing one to run a game.

you might say, well, the existing form of a reading group is fine. okay! existing reading group structures can be low-stakes, relaxed, and accessible...but they can also fall apart easily (especially when not tied to an institution, in my experience), and you have to get lucky to find a truly rewarding one. I find reimagining our mechanisms of learning pretty exciting, and I think the space of ways to learn math with each other is underexplored at this level (emphasis on the with each other). there's a lot of potential!

anyway! reply or tag with "!" if this is something you could maybe be interested if done well? or if you're at least curious! I'm just taking a temperature. :)

[pv1isalsoimportant]

mathematical revelation so great i almost became religious

[bakingmoomins]

anyway look at the voderberg tile. it's a nonagon (nine sides).

and the only shape that can surround itself completley with only two iterations of itself

and it also creates a spiral tessellation <3

[algebraic-dumbass]

(me reading a paper for the first time) that's a lotta words. why they gotta be so complicated

[cams-math-rants]

Finite and Infinite Sets

Recently, in my Discrete Mathematics course, we have been discussing the title of this blog post. It took me some time to understand these concepts, but it is finally clicking in my mind and it’s all I can think about at the moment.

First, I’d like to discuss some definitions.

When I mention the notion of a set, this refers to a collection of objects/numbers (we call each number in a set an “element”) in which the order doesn’t matter (unlike with sequences). An example of a set is ℝ, the set of all real numbers. Another example that will become important later is ℕ, the set of natural numbers (positive integers starting at 1).

A bijection refers to when every element in one set maps onto a unique element in the other set. When we map a set onto another, we write X → Y. This is shown in the image below, because it helps to see this visually.

When two sets are equinumerous (written X ≈ Y for two sets X and Y), this simply means there is a bijection between these sets.

By definition, in order for a bijection to be possible, the two sets have to contain the same amount of elements, or have the same cardinality (written |X| = |Y|, which in English means “the cardinality of X equals the cardinality of Y”). This means the two sets have the same size.

Now, we can talk about finite and infinite sets. The notion of a finite set is rather intuitive: there are n elements in a set X where |X| = n. An infinite set also makes sense conceptually, where the elements never reach a boundary. However, there are different kinds of finite and infinite sets that makes things interesting.

We can say a set is denumerable, which means we get a bijection when mapping ℕ to said set. An example of this is the set of integers, ℤ. When we have ℕ → ℤ. We can show this by representing this as a piecewise function and separating the integers into even and odd, and we find that there is a one-to-one, unique correspondence between the two sets (perhaps I will go through this proof in another post but there are examples online).

A denumerable set can be infinite or finite. In the example above, ℤ is infinite and denumerable. When a set is countable, that means a set is either finite or denumerable.

What is interesting is when we have an infinite and uncountable set, such as ℝ. In this case, there is a beautiful way to prove such a thing using Cantor’s Diagonal Argument. I won’t discuss this in full here, but here is the link to the Wikipedia article: https://en.wikipedia.org/wiki/Cantor's_diagonal_argument?wprov=sfti1

Thanks to anyone who has read my post. My name is Cameron and I’m a math major that loves to discuss what I’m learning in my classes. Keep in mind that I am not an expert, so I am open to anyone scrutinizing my explanations if you believe something is represented wrongly.

This is the song I’m currently listening to on repeat:

[lvl10blvkmage]

oh no , the dog is drinking the wave equation

[eulerseverything]

Was anyone gonna tell me we found who Cleo was??? The integration genius on math stack exchange from 10 years ago?

TLDR it was a professor from Uzbekistan named Vladimir Reshetnikov who did it because he wanted people to be more interested in the niche problems people would post on there. Cleo wasn’t even his only account, he was doing multiple people

[mathematics-official]

Thanks, I appreciate the workout! ^_^

A lot of diagrams were chased today.

[tumbler-polls]

Pick an option at random :)