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.
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.
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.
> 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!
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?
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 ....
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:
> 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".
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.
> Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers.
Mathematicians will not say anything like "infinity is real" or "infinity is not real". We are careful creatures, and will ask what you mean by "infinity". In this subthread we've been discussing infinite series. What part of the definition of those do you have a problem with? (Prediction: you'll never answer this, but instead go on ranting with no ability to focus on the topic at hand. I can definitely see why math is hard for you, you have a severe problem with focus).
> The internet makes it easy for pedantic losers to have a loud opinion.
I can see that.
> 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.
That's pretty sad. It's also very sad that this is the conclusion you jump to when someone speaks out against your insane ravings in an entirely logical and coherent way.
> Psychological attacks, amazing!
It's a bit entertaining that you can go from what you wrote above (and what you write below) straight into accusing me of this.
> I'm guessing you are one of those deeply insecure symbol twiddlers.
I am indeed quite insecure. I'm working on managing that. If you by "symbol twiddler" mean mathematician, then yes – and quite proud of it too. You'll do well to get back on track to the topic at hand though, seeing as you're currently coming off a bit like the people one sometimes see yelling incoherent nonsense on subway trains.
> 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.
Not at all. While I was quite mediocre at sports (though far from crap), I did really well in most things. I was not a favorite of the teachers, because I had (and probably still have) a bit of problem with authority. Are you done derailing the discussion now? I'll remind you: we're discussing the usefulness of mathematics, not my childhood or athletic abilities.
> And you can't handle it when someone on the internet thinks abstract mathematicians are full of shit.
I can handle it just fine, primarily because what raving lunatics believe has no influence on the extreme actual power and usefulness of mathematics. The reason I care to have the discussion is to set the record straight for third parties' sake.
> I would not reply if not for the delicious irony the georoge cantor was a schizophrenic lunatic who died poor and homeless.
Do the mental problems and drug addiction of a brilliant musician detract from his or her music? Do you yell "madman" at a painting by van Gogh?
> Unlike you I welcome the death of mathematicians and mathematics as we know it
Even you, with the most pedestrian definition of what is "useful", must surely acknowledge that a lot of mathematics is immensely useful. Yet you wish for its death. You have nothing to replace it with. You sound like Trump and his non-existent healthcare "plans". You're hell-bent on destroying something simply because you cannot grasp it.
> No we are not. The post was about the value of notation and my thread was about the refutation of notation as useless and programming as a better alternative to it.
Yes, and in a sub-thread of the post you've made it clear that you doubt the usefulness of mathematics. So now we are having a sub-discussion about that. Yet you've still to contribute anything of value. On several occasions have I and others invited you to comment on very concrete mathematical constructions. You evade those invitations. I can only surmise that that is because you do not understand the questions you are being asked, or are unable to provide an alternative to the current standard mathematics. That standard mathematics is done in a somewhat formal language built around the very notation that this thread is about.
> Do the mental problems and drug addiction of a brilliant musician detract from his or her music? Do you yell "madman" at a painting by van Gogh?
Yes. Completely ignore the degenerates. There are many sober people who have made art and science. You should not allow mentally ill lunatics to define art, music, religion, maths or politics anymore than you will allow them to be your cab driver or spouse.
Clearly science is about sobriety and not schizophrenia. I guess mathematics was hijacked by schizophrenics, music and art by depressed losers. No wonder you are out of touch with reality, practicality and are defending symbols which you think have magical "powers" beyond mere convention.
You can also see this in physics with the string theory garbage, however unlike "pure" mathematics ... in physics people need to test experimentally.
> Yes, and in a sub-thread of the post you've made it clear that you doubt the usefulness of mathematics.
No, I said proofs were tautological and pointless and notation is useless. Formal mathematics is bullshit.
> On several occasions have I and others invited you to comment on very concrete mathematical constructions.
Your sock puppets ?
1. You were asking about fundamental theorem of calculus
This has a very geometric proof. Why would I have a problem with that ? I am all for geometry, visualization, simulation , testing ....
2. A number puzzle
I don't care for number puzzles. I will try to solve that number puzzle if you can write vietnamese jokes.
> Yes. Completely ignore the degenerates. There are many sober people who have made art and science. You should not allow mentally ill lunatics to define art, music, religion, maths or politics anymore than you will allow them to be your cab driver or spouse.
What a vile attitude.
> Clearly science is about sobriety and not schizophrenia.
Of course. No endeavour is about schizophrenia. That doesn't mean the contributions of sufferers of schizophrenia should be discarded. Evaluate the contributions on their own merits. Which is something that you can do with science and math and art.
> No wonder you are out of touch with reality, practicality and are defending symbols which you think have magical "powers" beyond mere convention.
I and others have repeatedly challenged you to reproduce "useful" math without these tools. You consistently avoid the topic.
> You can also see this in physics with the string theory garbage, however unlike "pure" mathematics ... in physics people need to test experimentally.
That is because physics is about deducing facts about the natural word. Mathematics is about deducing truths within a logical framework, given certain assumptions. If the assumptions are reasonable, the things math deduce can very often be extremely useful in describing said natural world. You have clearly not understood this.
Said differently: given a mathematical model for the physical world, mathematics can predict its behavior. This is, needless to say, extremely powerful. It is the job of physicists to determine whether the underlying model is a good one.
> No, I said proofs were tautological and pointless and notation is useless. Formal mathematics is bullshit.
And I will have to repeat myself then: Is calculus useless? If you say yes, you're clearly deranged, as physics and much of engineering die with it. If you say no, then I challenge you to construct a useful and consistent version of calculus without formal mathematics. Come on now! Enough with the ad hominems, get cracking! Put your money where your big mouth is.
> Your sock puppets ?
No.
> 1. You were asking about fundamental theorem of calculus. This has a very geometric proof. Why would I have a problem with that ?
Care to give that proof? Or point me to it? I bet you that it will either turn out to be correct and I can show you how it uses formal mathematics, or it will turn out to be incorrect or not a proof at all.
> 2. A number puzzle
What the hell are you on about? What's the number puzzle you're talking about? The series mentioned? It's not at all a "number puzzle" – it's a direct consequence of (among other things) Fourier analysis. Ask any "real life" signal processing engineer whether Fourier analysis is "real" or "just a number puzzle".
Flamewar like this will get you banned on HN. Please don't post anything like this again. Ditto for your comments upthread a la "What are you on about?" and "Are you insane?" That style of commenting is not allowed here.
Instead, if someone is particularly wrong on the internet, just step away. If another commenter is breaking the site guidelines, flag the comment and don't feed it by replying. What we want on this site is curious conversation, not arguments to the finish.
Clearly you are too much of a pedant to do anything useful in life, so why don't you build a time machine and interrupt your birthing process ? It should be easy ... you can build it using calculus.
Science is about modelling the real world. Mathematics is about modelling. Programming is "interactive" modelling. Its all about modelling accurately.
Clearly you are also too much of a bigot to understand that models are just models and unreadable and undecipherable models are useless and full of shit, especially those built by schizophrenics or priests.
> If you say no, then I challenge you to construct a useful and consistent version of calculus without formal mathematics.
That was how it was constructed in the first place genius. Both calculus and fourier were built for practical purposes before formalist clowns were even alive probably. So why don't you go read the originals.
Formal calculus is beyond useless, its unreadable.
> 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?
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.
