<![CDATA[What is a math concept or theorem that you wish there were a better explanation of?]]>What is a math concept or theorem that you wish there were a better explanation of?

It could be from arithmetic: Why is adding fractions so complicated?

From grade-school algebra: Why does the teacher get so sad and angry if I just √(x²+y²)=x+y

From the calculus: Why do I need to write dx with the integral?

or beyond.

]]>https://board.circlewithadot.net/topic/7fd9eeae-ea7e-49c4-9d49-539295017647/what-is-a-math-concept-or-theorem-that-you-wish-there-were-a-better-explanation-ofRSS for NodeThu, 09 Apr 2026 06:52:35 GMTSat, 28 Mar 2026 10:42:59 GMT60<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 23:19:18 GMT]]>@futurebird Like I said, it's been a minute. 😁 I think that may be it, because it's part of why I found integral calculus so hard in university. I understood an integral of a function being the area under it's graph, so it's the sum of all the Y values along the X axis, and I could follow the professor working out the answer, but I couldn't figure out how to make it happen by myself.

Mind you, I dropped out and tried a few other things until I discovered that I really like factory work, so grade 10 math more than got me by professionally.

]]>https://board.circlewithadot.net/post/https://mstdn.ca/users/Space_Burger_Steve/statuses/116309357932420030https://board.circlewithadot.net/post/https://mstdn.ca/users/Space_Burger_Steve/statuses/116309357932420030Sat, 28 Mar 2026 23:19:18 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 23:04:44 GMT]]>@Space_Burger_Steve

It occurs to me you may have been vexed by the analysis of infinite sums, which is another matter.

]]>https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116309300628893839https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116309300628893839Sat, 28 Mar 2026 23:04:44 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 23:03:36 GMT]]>@Space_Burger_Steve

Do you program with "for" loops ever? If not no biggie, but if you do? That's what those are. They are "for loops" in math notation.

]]>https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116309296192240501https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116309296192240501Sat, 28 Mar 2026 23:03:36 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 23:01:36 GMT]]>@futurebird Sums. As in the functions that begin with a capital Sigma. But it's been so long (class of '97) I don't even remember what part I don't understand.

]]>https://board.circlewithadot.net/post/https://mstdn.ca/users/Space_Burger_Steve/statuses/116309288317616350https://board.circlewithadot.net/post/https://mstdn.ca/users/Space_Burger_Steve/statuses/116309288317616350Sat, 28 Mar 2026 23:01:36 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 22:16:47 GMT]]>@llewelly @Meowthias @futurebird I don’t think this follows. There is no evidence that the true value of PI has (or could be) represented in our universe.
In particular, Quantum Mechanics has a smallest size that can exist, not to mention the various other limitations on measurement that are achievable. So PI will always be approximated in any physical system. Even if you think the universe is evaluating the true value of PI, I would expect QM measurement limits would is only allow you to observe an approximate value of PI. No different from what a finite simulation would be able to compute.

]]>https://board.circlewithadot.net/post/https://hachyderm.io/users/Jmj/statuses/116309112085833387https://board.circlewithadot.net/post/https://hachyderm.io/users/Jmj/statuses/116309112085833387Sat, 28 Mar 2026 22:16:47 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:51:37 GMT]]>@futurebird I also got one hell of an education, so I'm grateful. I'm also critical at the deserved areas

]]>https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116309013124406656https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116309013124406656Sat, 28 Mar 2026 21:51:37 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:39:03 GMT]]>@futurebird I was definitely too clever by half in a unique education environment

]]>https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308963710463092https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308963710463092Sat, 28 Mar 2026 21:39:03 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:37:04 GMT]]>@autolycos

You need calc 1, calc 2 and probably multivariable (sometimes called calc 3) before you mess with this. This is differential equations.

This is when you write equations about rates of change and then solve them for functions or rates.

eg. "There is a function whose rate of change is equal to ten times it's value, who am I?"

It's not awful, but 'intro to calc' isn't enough at all.

]]>https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116308955926648158https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116308955926648158Sat, 28 Mar 2026 21:37:04 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:33:50 GMT]]>@futurebird related, in a just world, I would have had my ADHD diagnosed and treated before my third year of med school. That would have helped immensely with rigorous math classes

]]>https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308943177634539https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308943177634539Sat, 28 Mar 2026 21:33:50 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:26:16 GMT]]>@futurebird

I was introduced to it doing NMR stuff and I had just done intro calculus and being Greek would be an improvement. So obtuse to me
https://en.wikipedia.org/wiki/Hamiltonian_system

]]>https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308913429355929https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308913429355929Sat, 28 Mar 2026 21:26:16 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:18:47 GMT]]>@autolycos

IDK about that hamiltonian, but matrices aren't so bad. Once you just accept them as linear multivariable functions... though I assume you are talking about something deeper than that.

]]>https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116308884028535648https://board.circlewithadot.net/post/https://sauropods.win/users/futurebird/statuses/116308884028535648Sat, 28 Mar 2026 21:18:47 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:18:34 GMT]]>@futurebird I can work in Hilbert space all day though

]]>https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308883168028838https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308883168028838Sat, 28 Mar 2026 21:18:34 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 21:17:17 GMT]]>@futurebird hamiltonian math and matrix math

Good Lord those things make my brain hurt

]]>https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308878105889776https://board.circlewithadot.net/post/https://beige.party/users/autolycos/statuses/116308878105889776Sat, 28 Mar 2026 21:17:17 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 20:56:44 GMT]]>@Meowthias @futurebird

Yes, with the help of shrooms.

]]>https://board.circlewithadot.net/post/https://wandering.shop/users/asakiyume/statuses/116308797357344592https://board.circlewithadot.net/post/https://wandering.shop/users/asakiyume/statuses/116308797357344592Sat, 28 Mar 2026 20:56:44 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 19:25:12 GMT]]>@Meowthias @futurebird Joke's on you. According to Contact there is finally a pattern in there somewhere way in there and it's something that makes even the aliens wonder if there might be something meaningful behind that.

]]>https://board.circlewithadot.net/post/https://urusai.social/users/nazokiyoubinbou/statuses/116308437403487722https://board.circlewithadot.net/post/https://urusai.social/users/nazokiyoubinbou/statuses/116308437403487722Sat, 28 Mar 2026 19:25:12 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 17:49:10 GMT]]>@Meowthias @willyyam @futurebird I hope it made at least some sense. πŸ˜‚

]]>https://board.circlewithadot.net/post/https://anarres.family/users/faithisleaping/statuses/116308059755405104https://board.circlewithadot.net/post/https://anarres.family/users/faithisleaping/statuses/116308059755405104Sat, 28 Mar 2026 17:49:10 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 17:15:36 GMT]]>@faithisleaping @willyyam @futurebird Thank you for taking the time to write this response.

]]>https://board.circlewithadot.net/post/https://mastodon.world/users/Meowthias/statuses/116307927773113594https://board.circlewithadot.net/post/https://mastodon.world/users/Meowthias/statuses/116307927773113594Sat, 28 Mar 2026 17:15:36 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 17:00:21 GMT]]>@futurebird @seachaint @rallias @Meowthias

To elaborate:

That Ο€ is transcendental (and thus both non-repeating and not expressible in closed form algebraically) follows from Euler's identity: e^iΟ€ = -1 and that e is transcendental.

Proving e is transcendental takes a few pages of playing around with series and integrals: https://en.wikipedia.org/wiki/Transcendental_number#A_proof_that_e_is_transcendental .

]]>https://board.circlewithadot.net/post/https://mastodon.online/users/michael_w_busch/statuses/116307867839479067https://board.circlewithadot.net/post/https://mastodon.online/users/michael_w_busch/statuses/116307867839479067Sat, 28 Mar 2026 17:00:21 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 16:57:36 GMT]]>@futurebird I've had very good teachers, so I don't think that I needed more explanation than what I received for most concepts

I do wish they had spent more time about the multidimensionality of complex numbers

]]>https://board.circlewithadot.net/post/https://mastodon.bsd.cafe/users/clf/statuses/116307856996581982https://board.circlewithadot.net/post/https://mastodon.bsd.cafe/users/clf/statuses/116307856996581982Sat, 28 Mar 2026 16:57:36 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 16:20:08 GMT]]>@futurebird pretty much everything. i gave up even trying in 10th grade math class cause it was just more of the same "if you don't understand, it's all your fault and you will get big angry red zeros on all of the tests you fail because you don't understand and have given up bothering with it".

]]>https://board.circlewithadot.net/post/https://beige.party/users/burnitdown/statuses/116307709669210419https://board.circlewithadot.net/post/https://beige.party/users/burnitdown/statuses/116307709669210419Sat, 28 Mar 2026 16:20:08 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 16:04:36 GMT]]>@futurebird @seachaint @rallias @Meowthias I feel like there's a sub-proof here that any repeating decimal is non-repeating in some base.

]]>https://board.circlewithadot.net/post/https://mastodon.online/users/quizzicus/statuses/116307648597447918https://board.circlewithadot.net/post/https://mastodon.online/users/quizzicus/statuses/116307648597447918Sat, 28 Mar 2026 16:04:36 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 15:56:23 GMT]]>@futurebird @SeanPLynch @Meowthias

I think it's not about the circle being "unsquarable". A square has a ratio of sqrt(2), which is as irrational as pi. (Although less trascendental, I guess)

]]>https://board.circlewithadot.net/post/https://mstdn.social/users/javierg/statuses/116307616277557062https://board.circlewithadot.net/post/https://mstdn.social/users/javierg/statuses/116307616277557062Sat, 28 Mar 2026 15:56:23 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 15:39:08 GMT]]>@futurebird @SeanPLynch @Meowthias Ο€ = 1 in base pi…
I'll see myself out πŸ˜„

]]>https://board.circlewithadot.net/post/https://ottawa.place/users/MichaelPorter/statuses/116307548449793951https://board.circlewithadot.net/post/https://ottawa.place/users/MichaelPorter/statuses/116307548449793951Sat, 28 Mar 2026 15:39:08 GMT<![CDATA[Reply to What is a math concept or theorem that you wish there were a better explanation of? on Sat, 28 Mar 2026 15:36:46 GMT]]>@futurebird @Cheeseness @Meowthias I don't know! But Greek mathematicians often didn't write things out. They did some of their proofs geometrically. They had these giant compasses, about a meter long, and they would draw out their proofs in the dirt on the ground. Supposedly Archimedes died with his compass in his hand. When they did write out proofs, they were verbal and logical -- not equations. Euclid's proofs are a good example.

]]>https://board.circlewithadot.net/post/https://cosocial.ca/users/evan/statuses/116307539151164956https://board.circlewithadot.net/post/https://cosocial.ca/users/evan/statuses/116307539151164956Sat, 28 Mar 2026 15:36:46 GMT