Is the current way we teach mathematics broken...

>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.

>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.

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.

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

reading comprehension

what is 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.

Fuccin this ^

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))

>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?

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

I guess you've never used Wolfram|Alpha.

>or ADA
Ada? You mean Agda?

Good luck teaching Coq to kids

They'll just laugh at you

BTFO :^)

yup, agda, sorry
I forgot

because of the name?

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

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

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.

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.

>Blame the porn industry for this.

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

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

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.

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

>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

>An intelligent people today lake tomorrow's knowledge.

Well put.

Oops. That should have been "lacked".

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.

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

Try again - 3rd time is the charm?

And intelligent people today lack tomorrow's knowledge.

There, I did it.

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.

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.

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

>Lambda calculus
>useful and relevant
nice bait

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>redditard
>namefag
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why is nobody surprised...