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The Math

Comfopleb

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“The math” - the sum of all possible and impossible mathematical truths.
How much of the math does humanity know? There are some unsolved problems in mathematics. Could there be undiscovered problems or do we know all of them? Is there an upper limit to how much math there is to learn? How much of the math did Einstein, Euler and Nash know? Who knows/knew the most math? How much of the math is possible to learn through 60 years of devotion? How much is learned through 3 years in university? Optional bonus question: How much of the math do you know?
 

BigApplePi

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“The math” - the sum of all possible and impossible mathematical truths.
What is that?
How much of the math does humanity know?
A lot.
There are some unsolved problems in mathematics.
Indeed. The strange thing about those are that they relate seemingly unrelated concepts.
Could there be undiscovered problems or do we know all of them?
There are undiscovered problems but so far no one has been able to hold onto them in their undiscovered state.
Is there an upper limit to how much math there is to learn?
Yes, but I don't know it. Do you want me to stop you if I think you've gotten there?
How much of the math did Einstein, Euler and Nash know?
Euler knew a lot. The other two probably knew not much more than what they needed to know.
Who knows/knew the most math?
For their time, Archimedes, Newton, Gauss.
How much of the math is possible to learn through 60 years of devotion?
A lot but nowadays one specializes. Probably somewhat less than 60 years worth allowing for vacations and illness.
How much is learned through 3 years in university?
Three years worth if you are a math major; less if not.
Optional bonus question: How much of the math do you know?
I used to know five years worth. Now I've forgotten more than most know.
 

Comfopleb

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My opening description of ”The math” – It’s not a proper description of what I mean. Let me scratch it. I think the clearest way to describe what I mean really is “all the math”. All of it. Does this make sense? Your post seems insightful. It’s fascinating how the unsolved problems relate – I wasn’t aware of it and I’m not even close to understanding specifically how they may relate.
I got another two questions for you. First, I’m wondering how far humanity has come and would love to see it in numbers. I understand that it’s impossible to give as a fraction of “the math” (all of it) as it can’t be known how much there is. So I’ll ask this; how many years worth of mathematics would you suggest humanity knows collectively, how many lifetimes would it take for one human to learn all math all humans before him/her has known?
Another question, a personal one, for Big Apple Pi and any other mathematician in here: how has your specialization affected you, practically and intellectually? I understand if you do not wish to answer this question.
And yes, please shake me out of my illusion if I were to believe I knew all of “the math”.

@BigApplePi
 

BigApplePi

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My opening description of ”The math” – It’s not a proper description of what I mean. Let me scratch it. I think the clearest way to describe what I mean really is “all the math”. All of it. Does this make sense? Your post seems insightful. It’s fascinating how the unsolved problems relate – I wasn’t aware of it and I’m not even close to understanding specifically how they may relate.
I got another two questions for you. First, I’m wondering how far humanity has come and would love to see it in numbers. I understand that it’s impossible to give as a fraction of “the math” (all of it) as it can’t be known how much there is. So I’ll ask this; how many years worth of mathematics would you suggest humanity knows collectively, how many lifetimes would it take for one human to learn all math all humans before him/her has known?
Another question, a personal one, for Big Apple Pi and any other mathematician in here: how has your specialization affected you, practically and intellectually? I understand if you do not wish to answer this question.
And yes, please shake me out of my illusion if I were to believe I knew all of “the math”.
@Comfopleb
Just a general answer. I'm not up on the latest research in math. Mathematics like science in general has many specialties. One specialist may not and will not understand another. A specialist I would expect should know 95 percent of his area. How many special areas are there in mathematics? Some would say six; some dozens. One lifetime per speciality though it would not take a lifetime to master 90 percent of one area. One has to define "mastery." Are we talking basics? Or are we talking all the latest research papers?

One thing a mathematician may do is create his own system by trying out postulates. Seeing what he can build. That would be highly personal and no one else may know about it. If the system has applications, it may last. If the system is worthless, and it can be, it will be forgotten. I created this psychological/philosophical system with a mathematical attitude in mind. Understanding Made Simple. I like it but no one else has said it has much value. So I don't know what will happen.

Mathematics need not be working on unsolved problems. Those could be enticements for acknowledgments, challenges and perhaps fame. Most would be working on simple advancements in their field or on writing books. Reference: http://en.wikipedia.org/wiki/Timeline_of_mathematics

No you cannot learn all of math anymore than all of science or anything. How deep does one wish to go?

You asked, "how has your specialization affected you, practically and intellectually?" (May I ask you if you wish to go into mathematics or are just inquiring?)

I'm disappointed in myself I could not go further in math. No Ph.D. which is needed to specialize professionally. I went into computer programming professionally.

Intellectually it has affected me enormously. I studied pure mathematics, not the practical stuff which is imprecise. I love to make jokes about logic and use it all the time without self-consciousness as you can see if you read many of my posts. I tend to apply the need for definition, foundations (assumptions) and logic to areas in the real world and it helps a lot in seeking truth and avoiding self-deception. Not an easy Q to answer.
 

Comfopleb

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I won’t comment on the contents of your UMS model. Perhaps I will in the future, I doubt my comments would have much value. The fame and spread of it however, I think can be expanded regardless of the quality of the model. Have you posted it outside INTPf? Have you presented it to other professional mathematicians? I doubt that the most prominent mathematicians and head hunters browse these fora. There is a saying I haven’t been able to find the source of: “genius gets you nowhere. Execution is everything.” Well, what do I know? I am not familiar enough with you, the UMS model, or how ideas usually are spread within mathematics.

Going into mathematics is one of several options for me; I haven’t decided what I wish to spend my life on yet. It’ll either be mathematics, physics, or engineering. I’ve got 3-4 months to decide so I’m trying to dig into the different fields to reduce the chance that I’ll regret my choice in the future. Studying mathematics seems to go beyond the professional life. As you describe, it aids “seeking truth and avoiding self-deception”. The contents of that quote, I believe, is of such enormous significance to most INTP, whether they are aware or not. Learning to use mathematics as a tool for understanding the universe and all that’s in it really attracts me.

Your posts have helped me towards understanding the structures and scales of things within mathematics, thank you. It’s also interesting to read about your personal relationship to mathematics. Reading your posts here, and elsewhere on INTPf, I am left with the impression that you have developed a very clear view on things. I appreciate the effort you’ve put into your posts.


@BigApplePi
 

BigApplePi

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@Comfopleb
I won’t comment on the contents of your UMS model. Perhaps I will in the future, I doubt my comments would have much value.
Any comments at all are welcome. What I'm looking for are personal reactions. Like is it worthwhile to you? It is too obvious once known or too complex or too unwieldy to use?

The fame and spread of it however, I think can be expanded regardless of the quality of the model. Have you posted it outside INTPf? Have you presented it to other professional mathematicians? I doubt that the most prominent mathematicians and head hunters browse these fora. There is a saying I haven’t been able to find the source of: “genius gets you nowhere. Execution is everything.” Well, what do I know? I am not familiar enough with you, the UMS model, or how ideas usually are spread within mathematics.
It's not a mathematical model. It's a psychological/philosophical one with some logical thinking behind it. Psychological because "understanding" is human behavior; philosophical because of the concept relationship.

I've shown it to a Columbia University philosophy professor. He liked it said he would reread it when he wanted think things over. He said I should take it to one of the NYC philosophy discussion groups , but I've hesitated. I prefer to write. Yes it will go nowhere unless someone of influence notices it and tries to use it somehow. I would like to publish it somewhere else but don't know where. When I've shown it to friends, they don't have anything to say. I may not have known how to ask.

Going into mathematics is one of several options for me; I haven’t decided what I wish to spend my life on yet. It’ll either be mathematics, physics, or engineering. I’ve got 3-4 months to decide so I’m trying to dig into the different fields to reduce the chance that I’ll regret my choice in the future. Studying mathematics seems to go beyond the professional life. As you describe, it aids “seeking truth and avoiding self-deception”. The contents of that quote, I believe, is of such enormous significance to most INTP, whether they are aware or not. Learning to use mathematics as a tool for understanding the universe and all that’s in it really attracts me.
Going into math probably won't get you very far unless you are a Ph.D. specialist in applied math or go into academia. Engineering or physics is more practical for making a living.

Your posts have helped me towards understanding the structures and scales of things within mathematics, thank you. It’s also interesting to read about your personal relationship to mathematics. Reading your posts here, and elsewhere on INTPf, I am left with the impression that you have a very clear, unbiased and undisturbed view of things. I admire that. I appreciate the effort you’ve put into your posts, I really do.
I like to think my internal thinking strives to be unbiased, but sometimes I put out a one-sided post to stimulate (not provoke). Then it's easy to misinterpret what I've said and things can go wrong. I'm not alone in this error and it's embarrassing, lol.
 

BigApplePi

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Zero989

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Yep. I'm interested in how it affects people? Does it suck?

As far a some knowing critique is concerned, I'm probably the best one to critique it. I know it hasn't reached its potential and don't quite know how to continue ...

I generally have to read something over 4-5 times, possibly more to tell what I seriously think. That's what philosophy is about. Word association differs with whatever mood is present.

Right now I just see this:

1. PERSPECTIVE Know that there are "2 sides to a coin", "6 sides to a cube" etc..

While we see the 6 sides there are also corners to the cube but don't necessarily take in those details consciously.

2. TRANSLATION Know that insight is limited. Even if knowledge is extracted by 2 individuals, there might be similarities in thoughts but differ by the content that's communicated. Take the time to consider what that person is saying and read between the lines, per se. Optimization of meaning by acute use of language.

3. DISTANCE Use the analogy of a camera lens. The bigger the lens, the more scenery and details to be viewed. However, these steps are necessary to get a through understand of that "object". Only through looking from all distances can we thoroughly grasp t
hat object and its parts. Only from understand the tiniest parts to the holistic synergy and its operation can we then truly begin to understand. Take caution and tread carefully.

4. MOTION Automorphism Vs. Polymorphism

5. FUZZINESS Always be skeptical of own thoughts and challenge them

6. HIERARCHY Deconstructing never ends. Know that even isolated systems have their associations and can be affected by their surrounding systems. Acknowledge that there are always emerging systems within the hierarchy. Knowledge is fickle.

6. Number 6 is quite unclear. I'm not really sure what you're even trying to say. For one, it's impossible to deconstruct carefully in real-time events. Where and when is this tool applied?


Most of your tools already have names such as introspection, deconstruction, systems are subject to Godel's incompleteness, learning never ends, the medium is the message and other idiomatic expressions.

Another issue is when writing obscure guides or "tools", it leads to the "everyone understands in their own way, or differently".

For example, to even further discuss this we'd automatically use your "translation" tool, and as you can see some of these "tools" exist automatically in the real world. Also the names of your tools are really abstract, even for me as an INTP who is flexible with titles and semantics.

Anyway, as far as I know most people aren't interesting in being taught "how to think". It conflicts with their belief systems etc... I gave it up years ago. It was seemingly a waste of time. Not to discourage you. (There are few who are actually interested in these fields of thought).


@ OP

Uhh, Math is quite far in the 21st century but there is much more to be learned. It would also help if they stopped bitching out when using or looking at infinity.

Prodigies often know the most math. Autism also increases chance for knowing more. Einstein wasn't a prodigy but was a genius (something different). There are tons of people today who know more than him now.

I know that 0^0 = 1 because of factorials.

Mind = blown.
 

BigApplePi

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@Zero989. I replied to the UMS things here: An UMS Critique

@ OP

Uhh, Math is quite far in the 21st century but there is much more to be learned. It would also help if they stopped bitching out when using or looking at infinity.

Prodigies often know the most math. Autism also increases chance for knowing more. Einstein wasn't a prodigy but was a genius (something different). There are tons of people today who know more than him now.

I know that 0^0 = 1 because of factorials.

Mind = blown.
0 factorial is defined to be 1.
http://www.zero-factorial.com/whatis.html
 

The Introvert

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It would also help if they stopped bitching out when using or looking at infinity.

@Zero989
What do you mean by this?

@OP
We do not understand everything there is to know about math. Ironically, we are trying to prove what we do not understand with something that we do not understand. I think what Zero said may be hinting at this.

Of course, this is just my personal take on it. I wouldn't consider myself particularly good at math.

Also, Einstein was admittedly not a wunderkind at math; he repeatedly expressed his displeasure of the subject and even said that math was not needed to understand the physics he was working on.
 

BigApplePi

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The Introvert;354217Also said:
Right on. There is a big difference between discovering things in math or creating new math systems and using math. As far as I know Einstein was a user. His work was physics; he created no math.
 

The Introvert

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Right on. There is a big difference between discovering things in math or creating new math systems and using math. As far as I know Einstein was a user. His work was physics; he created no math.

If you ask me, (or if you don't I'll tell you anyhow :p) I think too much weight is put into concrete numbers. If you think about it, we are using a subjective system to explain an objective idea - at least that's the way I look at it.

I think that maybe to understand the universe, we first need to realize that we can only do it through the scope of the universe, and not through the scope of mathematics (or other seemingly related ideas). The key is understanding what we can and cannot explain with what we already have.
 
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