Is the current way we teach mathematics broken? How come we don't

>>8273369
Voyevodsky pls.

>>8273369
How the hell are you going to write a program that solves diffeq for you if you can't?

>>8274004

This.

>inb4 import "diffeq"

File: ref.png (6KB, 280x200px) Image search: [Google]

6KB, 280x200px

>>8273369
Is that stuff useful when studying math? Like checking proofs and such?

File: trash.jpg (34KB, 369x246px) Image search: [Google]

34KB, 369x246px

>>8273369
>hurrr durr mathematics is just calculations and solving equations

Back to your CS shithole.

>>8273369
>>8273369
knowing how to do a computation by hand teaches you a lot, basically >>8274004

that said, elementary math-for-engineers computation classes are meant to be simple, so stop being so smug and obey your teachers

File: 13249767_1221556224529498_1692500979_n.jpg (50KB, 640x640px) Image search: [Google]

50KB, 640x640px

Bump for interest. I'm interested in knowing whether you can use programming for doing abstract math. In the theorem proving sense.

>>8275280
Yes. In fact, we have been doing this since the 1970s: http://www.win.tue.nl/automath/.

>>8273385
https://github.com/UniMath/UniMath

>>8273369
> Is the current way we teach mathematics broken?
Yes.

> How come we don't teach mathematics through a formal language such as Lambda Calculus or a programming language based on Lambda Calculus?

Because the education system is outdated and because most teachers probably don't even know about lambda calculus. There would have to be a massive reform to make this happen.

> Why do I need to know how to solve a differential equation by hand when I can write a program to do it for me?

If you can program it, then there is no need to "do it by hand"; moreover, it shows that you have a deeper understanding of the material.

>>8274016
>Back to your CE/SE shithole.
ftfy and fucking this.

Because you are retarded. You are not thinking about learning maths but learning how to become a dumb calculator.
Learning maths is all about trying to compress difficult concepts into accessible language so that humans could think and reason about it. It is the most human activity possible, arguably even more so than literature. Things like Urysohn lemma and Carathéodory's extension theorem are all about intuition and imagination, not calculation. Until programs can understand life and write better fiction than human writers, don't even think they can give you any royal road to mathematics.
> Why do I need to know how to solve a differential equation by hand
Because you are gonna create models and solve equations that no humans or machines have solved before. Where the fuck do think those algorithms come from? Flying pasta monsters? Are you gonna say no one needs to learn about addition because calculators can already do it?
>Every professor I have had can't even use summation notation correctly
When you suspect every professor is a retard, objectively speaking there is a higher probability that you are suffering from the Dunning-Kruger effect.

>>8275886
>You are not thinking about learning maths but learning how to become a dumb calculator.

How do you know this is the case? Maybe the OP is looking for a more formal understanding of the mathematics he/she's learning.

>>8275897

I was open to that possibility until he complained about knowing how to solve diff eqs by hand.
That would mean learning about Green's function, Fourier transforms, Sobolev spaces etc. which are absolutely crucial to understanding maths and physics on a conceptual level. So you definitely have to learn how to solve diff eqs.

>>8274004
>>8274012
I bet you don't believe in logarithms or trigonometry either. :^)

>>8275886
reading comprehension

what is it

>>8275886
>Every professor I have had can't even use summation notation correctly
When you suspect every professor is a retard, objectively speaking there is a higher probability that you are suffering from the Dunning-Kruger effect.

Fuccin this ^

>>8273369
From regular formula to natural formula:
¬a -> (b v c -> d ^ e)
¬¬a v (¬(b v c) v (d ^ e))
a v (¬b ^ ¬c) v (d ^ e)
(a v ¬b)(a v ¬c) v (d ^ e)
(a v ¬b)(a v ¬c) v (d ^ e)
((a v ¬b)(a v ¬c) v d)((a v ¬b)(a v ¬c) v e)
(a v ¬b v d)(a v ¬c v d)(a v ¬b v e)(a v ¬c v e)
(¬a ⋺ (b ⋺ d))(¬a ⋺ (¬d ⋺ ¬b))(b ⋺ (¬a ⋺ d))(b ⋺ (¬d ⋺ a))(¬d ⋺ (b ⋺ a))(¬d ⋺ (¬a ⋺ ¬b))(¬a ⋺ (¬b ⋺ c))(¬a ⋺ (¬c ⋺ b))(¬b ⋺ (¬a ⋺ c))(¬b ⋺ (¬c ⋺ a))(¬c ⋺ (¬b ⋺ a))(¬c ⋺ (¬a ⋺ b))(¬a ⋺ (c ⋺ d))(¬a ⋺ (¬d ⋺ ¬c))(c ⋺ (¬a ⋺ d))(c ⋺ (¬d ⋺ a))(¬d ⋺ (c ⋺ a))(¬d ⋺ (¬a ⋺ ¬c))(¬a ⋺ (b ⋺ e))(¬a ⋺ (¬e ⋺ ¬b))(b ⋺ (¬a ⋺ e))(b ⋺ (¬e ⋺ a))(¬e ⋺ (b ⋺ a))(¬e ⋺ (¬a ⋺ ¬b))

>>8275910
>That would mean learning about Green's function, Fourier transforms, Sobolev spaces etc. which are absolutely crucial to understanding maths and physics on a conceptual level.

So you're saying Newton did not understand math/physics because he never learned about Green's function, Fourier transforms, Sobolev spaces?

>>8273369
because the program will only give approximations
you can't the the integral of a curve without the infinit recctangles

what about COQ programming lang
or ADA

>>8275930
I guess you've never used Wolfram|Alpha.

>>8275932
>or ADA
Ada? You mean Agda?

>>8275932
Good luck teaching Coq to kids

They'll just laugh at you

>>8275929
BTFO :^)

>>8275935
yup, agda, sorry
I forgot

>>8275936
because of the name?

>>8275943
Yeah, to vulgar english speakers, the word Coq evokes the wrong idea. Blame the porn industry for this.

>>8275951
Then go with Matita or Lean. They're basically the same.

>>8275929
That's a dumb comeback. Intelligent people in the past lacked today's knowledge. They understood their age's math/physics better than anyone but they do not know how things are today. Euclid doesn't know about Poincare conjecture either.
If you want to stay in the past and forgo all discoveries since then, go right ahead.

>>8275929
Newton's interest in physics was in optics. And all his work was done under paraxizl approximation. He did not delve into electronic physics in his lifetime whatsoever, and it's this type of physics where these things are obviously applicable. So no, if he doesn't understand these basic mathematical concepts he didn't understand math. Saying he did is an appeal to authority.

File: cock.png (112KB, 1184x502px) Image search: [Google]

112KB, 1184x502px

>>8275951
>Blame the porn industry for this.

>Slang sense of "penis" is attested since 1610s

>>8275964
Nice. I have a funny feeling that sailors are to blame.

>>8275962
But by that argument, then nobody know understands physics now because maybe some other kind of physics will appear in the future that we don't know about.

>>8275958
>That's a dumb comeback. Intelligent people in the past lacked today's knowledge.
An intelligent people today lake tomorrow's knowledge.

>>8273369
>Is the current way we teach mathematics broken?
At the most elementary level yes, and I do believe that learning a little programming at an early age would help kids understand what variables and functions are (seriously, how many kids go through high school without understanding what solving an equation actuallt means or what a function is ?) and, more generally what abstraction is and why it is interesting.

Now I don't know what you were trying to say beyond that

File: lake.jpg (797KB, 1920x1200px) Image search: [Google]

797KB, 1920x1200px

>>8275982
>An intelligent people today lake tomorrow's knowledge.

Well put.

>>8275993
Oops. That should have been "lacked".

>>8275977
What kind of off-the-rail non sequitur are you chasing? Try using logic. Newton understood his age's physics. To understand our age's physics, we need to learn Fourier transforms and all that jazz. There is no constant "physics" because it changes with time and the discoveries we make.

>>8275977
>then nobody know understands physics now
Yeah exactly, what's your point?

>>8275999
Try again - 3rd time is the charm?

>>8276016
And intelligent people today lack tomorrow's knowledge.

There, I did it.

>>8276011
The point I was trying to make is that you don't need to understand Green's functions, etc. to understand physics from a *conceptual level*. However, if you need to calculate shit, then and only then do things like Green's functions, etc. come into play.

>>8276028
Actually you do need them. Understanding Fourier transforms for instance tells you about the duality between decay and regularity, and the underpinnings of the uncertainty principle. There isn't even numeric calculation here; it is about providing insights. You might want to assure yourself you understand stuff, that is your freedom. I'd personally choose to be curious, to study more and see why things are the way they are.

>>8276175
>Newton could have known about quantum physics, he just didn't try hard enough

>Lambda calculus
>useful and relevant
nice bait

>>8276191
>look at me mom I can shitpost too

>>8276193
>look at me I'm outside of /pol/ xD!!

>>8276195
>redditard
>namefag
>constant shitposter
why is nobody surprised...