[augustt]

Honestly what are you talking about. You can simulate for 100 years without finding a counterexample, but that doesn't make a proof. The whole point of math is to understand why things are true, not to just be satisfied that it seems true.

[foobar_]

The way I see it ... Most mathematicians nowadays use mathematica or matlab or even python, proving my point. The notation is medieval ... and probably the only reason it survives is because of form factors of paper.

> Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

I see simulating as a part of the experiment. If the proof is wrong it wouldn't last a seconds worth of simulation. I suppose a proof in essence is a pattern or an invariant of the system ... but most proofs have really no meat to them. The notation is merely intimidating like obfuscated code.

[gspr]

> The way I see it ... Most mathematicians nowadays use mathematica or matlab or even python, proving my point.

Yes. But most of us don't use those to prove anything; rather, a lot of us use it to implement computations based on those proofs (and do some exploratory "could this possibly be tru?" kind of work). Useful tools, for sure, but not something that remotely proofs your point. Most mathematicians also eat bread. That does not mean that math is a baked good.

> The notation is medieval ...

It is not. Read Gauß or Euler from the 18th and 19th century, and the notation is nothing like modern mathematical notation. I can't even imagine what medieval mathematics notation looks like!

> https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

That is indeed the opinion of Arnold, a giant of mathematics. An opinion that, I daresay, does not reflect the majority opinion on mathematics.

> I see simulating as a part of the experiment.

Sure. Simulating is a valuable experimental tool to many mathematicians (where available; of course it isn't always).

> If the proof is wrong it wouldn't last a seconds worth of simulation.

At face value this statement betrays how little you know about this matter. There can very well be errors in proofs that cannot be uncovered without thousands of years of simulation, if at all.

Now, even interpreting your statement in the best possible light, namely something along the light of "simulation can often uncover mistakes in proofs", I would say: fine, but what about the converse?

> but most proofs have really no meat to them. The notation is merely intimidating like obfuscated code.

Are you insane? Take something that is patently "useful" and patently "real world", like the fundamental theorem of calculus. Meatless?

[foobar_]

I'm not insane ... you are just the type of person who will defend roman numerals. Maybe you just have OCD.

1. Socrates is mortal

2. Mortals die

3. Socrates dies

Deduction is really like amazing. Holy shit we really proved something spectacular here. I guess you would be really impressed if I used tau and sigma and defined death with vietnamese alphabet.

Almost the entirety of calculus was derived from problems related to physics. Volumes were calculated for doing engineering. Mathematics != Thinking. The last time I checked both logic and critical thinking were branches of philosophy.

All good mathematicians are physicists or engineers. Heck some even learnt maths on their own. All mediocre mathematicians write textbooks and hide behind notations. Come to think of it they remind me of OO programmers in their utter arrogant mediocrity. Most abstract mathematics is like the definition of protocols/interfaces and other platonic garbage. I suppose this debate will never end. Plato vs Aristotle, Deduction vs Induction, Analytic vs Synthetic ....

[an_android]

Don't use phrases as "Maybe you just have OCD". This is offensive and trivializes the problems those with OCD face. OCD is a serious disorder and your use of that phrase illustrates your lack of mental maturity.

Further, that phrase is bigoted. What you are implying is that someone with OCD is "lesser" or "other" as you are using the phrase to discount the person you are talking with. Hence it is bigoted.

In fact, it is obvious that you have no idea what you are talking about. Mathematics is not "just notation" in the same way software engineering is not "just programming language syntax", music is not just "notes on a piece of paper", and literature is not just "grammar rules".

If you cannot see that, I suggest you read more and expand your view of the world. Don't hurl insults at others.

If you want a more concrete example, show that the sum:

1 + (1/2)^2 + (1/3)^2 + (1/4)^2 + ... = pi^2/6

That is, first define what it means to take a sum of an infinite number of terms, prove that your definition is consistent with a sum of a finite number of terms, and then show that the sum is exactly pi^2/6. Showing that they agree to 100 billion decimal places is not enough. You need to show they are exact.

When you are done with that, find an exact closed form for the sum:

1 + (1/2)^3 + (1/3)^3 + (1/4)^3 + ...

[gspr]

> If you want a more concrete example, show that the sum […]

He won't. I keep running into people like this all the time. They are hellbent on the idea that anything they don't understand must be meaningless, useless, or the fault of others. If you get a reply at all, I suspect it will be something like "pi is just a meaningless approximation to a real physical concept" or "infinite series don't actually exist in real life, I'll sum the first 1000000 terms on a computer and that's all that exists".

[foobar_]

Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers.

The internet makes it easy for pedantic losers to have a loud opinion. Hell I have even run in to pedantic losers who have the time to create multiple new and fake accounts and use old sock puppets to create the illusion of an audience because these friendless, loveless losers literally have no one to talk to IRL.

> I keep running into people like this all the time.

Psychological attacks, amazing! I'm guessing you are one of those deeply insecure symbol twiddlers. Let me guess, as kid you were crap at everything, especially sports except symbol twiddling so you latched onto those praises your teacher gave you and as an adult that is the only source of your self-esteem. And you can't handle it when someone on the internet thinks abstract mathematicians are full of shit.

[gspr]

> you are just the type of person who will defend roman numerals.

In the face of what? No system for writing numbers? Sure. Arabic numerals? No way, they're far superior to Roman ones.

> Almost the entirety of calculus was derived from problems related to physics.

No it is not. It is/was largely motivated by problems in physics. One may obtain a lot of intuition about calculus from physical intuition, but one does not obtain calculus from it.

> Volumes were calculated for doing engineering.

Yes. And?

> Mathematics != Thinking.

I don't see anyone in this thread claiming that.

> The last time I checked both logic and critical thinking were branches of philosophy.

I thought we were talking about math?

> All good mathematicians are physicists or engineers.

This is patently not true. Tell me how many Abel prize winners of Fields medalists are physicists or engineers. There are indeed some, but they are a minority – your claim is absurd.

> Heck some even learnt maths on their own.

Absolutely. Can you elaborate on how this is relevant?

> All mediocre mathematicians write textbooks and hide behind notations.

What are you on about? As a mediocre mathematician myself, I must admit I have never written a textbook.

> Most abstract mathematics is like the definition of protocols/interfaces and other platonic garbage.

You have made it abundantly clear that you haven't that slightest grasp of abstract mathematics. Would you at least humor me as to provide a few examples?

[parralelex]

"Mathematics is a part of physics."

It's kind of amazing how quickly that article got so wrong. Math isn't a subset of physics. Physics is the estranged brother of Math, always needing to borrow some money from him or else the power goes out or he can't afford food or some other sob story.