Self Learning Math/Physics

[misterknister]

Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real" scientists and I most certaily won't win the nobel prize

I always was interested in Physics. I remember reading books about Astronomy when I was 8. I wanted to study Physics and become an Astrophysicists from the age of 15 on (before that, I was more into Meteorology). I don't want to tell my whole life story, because it would be too long and it would sound like I am fishing for pity. Let's just say I had problems in school, mental illness followed, depression... and I just gave up.

As I mentioned before, I know that I won't do any research at all or that I will communicate with proper scientists. It's just that over the years I have read so many popular science books and watched so many popular science vids on Youtube, that I got super bored with the "dumbed down" explanations and analogies, because they are often the same. And that I (at least I think) am able to get way deeper into things if I just kick myself in the butt is nagging on me for years... more than a decade to be precise.

I watched "The Biggest Ideas" video series of Sean Carroll and that really motivated me to get started. If you haven't seen it: Watch it. It's the perfect sweetspot between popular science and mathematical rigor.

So I made my plan: First I will brush up on basic math and then properly learn Calculus and Linear Algebra. Parallel to this, I will try to work through a book with Algebra based Physics (Giancoli). After that maybe an Astronomy book. I think that alone may take some time. My goal is to get good enough to get through and understand undergrade textbooks like Classical Mechanics by Taylor or Electrodynamics by Griffith. The big dream is - of course - to get deeper into Quantum Physics, Relativity, Astrophysics and Cosmology. Maybe deep enough to read papers. I know that that will take years and years... and bear in mind that I have to do this as a hobby on the side...

Why am I here? Well, I have motivational problems right from the start And for kind of an odd reason: AI. I have no access to universities or research centers, so I don't know if this is a valid or a super dumb question, but learning this from scratch alone by books gives me the feeling to learn something that isn't relevant anymore.
For example: I wanted to get into programming, too. Python to be exact. For math modelling. Then I read an article that 80% of people using Python are not writing code anymore but rather let an AI do it. What's the point in sitting my butt in front of a book or learning software when in a few years nobody will code anymore.

Furthermore it really constraints self studying even more. I am able to get textbooks. Even very advanced ones. But if math and physics is only done by AI supercomputers in the future, why should I learn all this? I won't have access to this... ever.

So what do you make of this?

 

[berkeman]

Welcome to PF.

Do you have access to community colleges where you live? That is a better option for learning the first 2 years of university physics/math, IMO. It helps a lot to have a university-like setting to learn, with lectures and in-person instructors and other students to form study groups with.

As for AI, at least for the forseeable future there will still be professional humans at least using the AI tools, and at most doing way more than the AI tools alone can do. As you learn more about coding you will likely come to understand where you can use AI to help out, and where you need to do the work yourself.

 

[fresh_42]

So what do you make of this?

I think there is a big difference between math and physics. Sure, calculus, linear algebra, and possibly differential geometry are necessary. But I do not mean the stuff, I speak of the language. Physics is the art of dealing with coordinates in all their variants and transformations between them. So you should get used to it early. Coordinates in mathematics play a minor role, and I know a few mathematicians who really dislike them. This would be my advice if physics remains on your list: learn things like the Einstein notation, Christoffel symbols, and whatever occurs in the world of coordinates.

Here is a collection of articles at PF about self-studying:

F

Studying Post in thread 'Self teaching Gcse and A-Level maths'

Dec 6, 2017

Here's a collection of insight articles available on PF about this subject [self-study]

https://www.physicsforums.com/insights/how-to-study-mathematics/
https://www.physicsforums.com/insights/overcame-learning-challenges-faced-studying-stem/
https://www.physicsforums.com/insights/resources-high-school-math-home/
https://www.physicsforums.com/insights/problems-self-studying/
https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/
https://www.physicsforums.com/insights/self-study-calculus/...

• fresh_42

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They are finally opinions, so don't take them as carved in stone. You should post your questions here whenever you are stuck. That can save time and decrease frustration. Since you have no controlling instance, you should use PF. Also, you can find thousands of lecture notes on university servers. E.g., the search key "Analysis I + pdf" or "calculus I + pdf" yields the first semester of calculus. For differential geometry, I would add "Einführung" or "introduction". This is nowadays a good alternative to expensive textbooks, and if you don't like the style of one professor, simply choose another one. You will probably find English lecture notes even on German university servers. When you are looking for exercises, search for "calculus I + exam + solution + pdf" or "Analysis I Klausur + Lösungen + pdf". The pdf-part in all search keys is important. It makes sure that you find a university server and not someone's homepage.

F

Thread 'How to use the "w" in www'

May 3, 2024

These are some - in my mind - useful insights I gathered over the years on PF. We have members from around the world, studying at universities around the world, in dozens of languages. The language of science nowadays is English, or as a guest professor at my alma mater once said in a terrible accent: "The language of science is broken English." That wasn't always the case. It had been Latin, German, or French to name others. However, whatever your native language is, we live in times where this becomes less and less important. University servers around the world provide lecture notes in...

• fresh_42
• Internet Lecture notes
• Replies: 0
• Forum: General Discussion

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• 

is another list of tips about how to use the internet.

 

[fresh_42]

Do you have access to community colleges where you live? That is a better option for learning the first 2 years of university physics/math, IMO.

We don't have this structure in Germany. There is school and there is university, well, various forms of it, depending on whether you search for a more practical path, like engineering, or a more theoretical path. What we do have is something called "remote study", where you can enroll in a university and study at home. Everything is exchanged by mail, but it counts as university. Gaining access to a university requires a certain school exam and usually personal presence.

 

[gmax137]

But if math and physics is only done by AI supercomputers in the future, why should I learn all this? I won't have access to this... ever.

I see no reason to believe this scenario

 

[jtbell]

First I will brush up on basic math and then properly learn Calculus and Linear Algebra. Parallel to this, I will try to work through a book with Algebra based Physics (Giancoli).

In the US, it's common for colleges/universities to teach calculus-based introductory physics courses in parallel with the introductory calculus courses. Intro physics courses at that level (using e.g. Halliday/Resnick/Walker) usually don't actually use calculus in deep detail, that requires all the techniques taught in a calculus course. You need to know the concepts of derivatives and integrals, and be able to calculate them for simple functions like polynomials, sines, cosines, etc.

 

[CrysPhys]

But if math and physics is only done by AI supercomputers in the future, why should I learn all this?

But why should you care? You led off by stating that you don't intend to pursue math and physics as a career, but to satisfy your own intellectual curiosity:

As I mentioned before, I know that I won't do any research at all or that I will communicate with proper scientists. It's just that over the years I have read so many popular science books and watched so many popular science vids on Youtube, that I got super bored with the "dumbed down" explanations and analogies, because they are often the same. And that I (at least I think) am able to get way deeper into things if I just kick myself in the butt is nagging on me for years... more than a decade to be precise.

So you can still fulfill your goal by learning via traditional methods:

I am able to get textbooks. Even very advanced ones.

It'll take you many, many years of self-study (if ever) before you exhaust traditional resources.

 

[fresh_42]

In the US, it's common for colleges/universities to teach calculus-based introductory physics courses in parallel with the introductory calculus courses. Intro physics courses at that level (using e.g. Halliday/Resnick/Walker) usually don't actually use calculus in deep detail, that requires all the techniques taught in a calculus course. You need to know the concepts of derivatives and integrals, and be able to calculate them for simple functions like polynomials, sines, cosines, etc.

This is part of the school system in Germany that enables you to enroll at a university. We have several different kinds of schools, one leads to the necessary graduation. It lasts longer than the others, 4+9 years. The other main school form ends in 4+6 years. This is also the main obstacle why American high school graduations don't automatically qualify for starting a study at a German university. The gap of content that, e.g., the books on OpenStax seek to close doesn't exist in the first place. However, there are other gaps that many students struggle with in their first year: self-responsibility to learn the material because the automatic control in classrooms breaks away, and the different perspectives. While math at school is mainly algorithm-based, i.e., learning tools to solve problems, math at university is concept-based. The same in physics. While physics at school is usually along the lines of what can be tested by experiments, physics at university concentrates on the calculations.

 

[WWGD]

Many professors in the US will allow you to sit in on their classes without registering. Some may even grade your homework, exams I suggest you speak with them after class to give them plausible deniability, since sitting in without registering is a gray area in some schools.

 

[TensorCalculus]

Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real" scientists and I most certaily won't win the nobel prize

I always was interested in Physics. I remember reading books about Astronomy when I was 8. I wanted to study Physics and become an Astrophysicists from the age of 15 on (before that, I was more into Meteorology). I don't want to tell my whole life story, because it would be too long and it would sound like I am fishing for pity. Let's just say I had problems in school, mental illness followed, depression... and I just gave up.

As I mentioned before, I know that I won't do any research at all or that I will communicate with proper scientists. It's just that over the years I have read so many popular science books and watched so many popular science vids on Youtube, that I got super bored with the "dumbed down" explanations and analogies, because they are often the same. And that I (at least I think) am able to get way deeper into things if I just kick myself in the butt is nagging on me for years... more than a decade to be precise.

I watched "The Biggest Ideas" video series of Sean Carroll and that really motivated me to get started. If you haven't seen it: Watch it. It's the perfect sweetspot between popular science and mathematical rigor.

So I made my plan: First I will brush up on basic math and then properly learn Calculus and Linear Algebra. Parallel to this, I will try to work through a book with Algebra based Physics (Giancoli). After that maybe an Astronomy book. I think that alone may take some time. My goal is to get good enough to get through and understand undergrade textbooks like Classical Mechanics by Taylor or Electrodynamics by Griffith. The big dream is - of course - to get deeper into Quantum Physics, Relativity, Astrophysics and Cosmology. Maybe deep enough to read papers. I know that that will take years and years... and bear in mind that I have to do this as a hobby on the side...

Why am I here? Well, I have motivational problems right from the start And for kind of an odd reason: AI. I have no access to universities or research centers, so I don't know if this is a valid or a super dumb question, but learning this from scratch alone by books gives me the feeling to learn something that isn't relevant anymore.
For example: I wanted to get into programming, too. Python to be exact. For math modelling. Then I read an article that 80% of people using Python are not writing code anymore but rather let an AI do it. What's the point in sitting my butt in front of a book or learning software when in a few years nobody will code anymore.

Furthermore it really constraints self studying even more. I am able to get textbooks. Even very advanced ones. But if math and physics is only done by AI supercomputers in the future, why should I learn all this? I won't have access to this... ever.

So what do you make of this?

Okay so I'm going to give my usual disclaimer when I give academic advice which is that I'm a kid and definitely not qualified: but maybe you will find something valuable in this anyway.

Here's my take:

You aren't planning on doing maths/physics as a career anyway.
You're doing it to learn and satisfy your curiosity.
So why on Earth should you care whether AI can do it or not? If you are unsatisfied with the shallow explanations given in popular science books and you want to learn more, then learn more. So what if AI can do physics (which, for now, it can't, not very well anyway)? You're not going to use that skill for much apart from satisfying curiosity anyway. Whether AI can do physics or not shouldn't change your situation at all.

I would say the same for python programming. Yes it can be done with AI. But if it sounds interesting to you, then go ahead. Just because something is not a skill that can land you a job doesn't mean it is a waste of time.

P.S: For the Astronomy book I recommend Ryden, or for a more brief introduction Salvati. These two have been my favourite from personal experience (though, maybe my bias to Salvati is unfair as I found it a useful guide from the perspective of someone preparing for the Astro olympiad. Maybe stick to Ryden for general learning)

 

[misterknister]

Do you have access to community colleges where you live?

The German community colleges (Volkshochulen) are quite different. They are basically split in three parts: 1. general school education degrees, 2. learning languages 3. skills like pottery or singing. There are no dedicated math or physics courses there.

Here is a collection of articles at PF about self-studying:

Thanks for all the info!

So why on Earth should you care whether AI can do it or not?

But why should you care? You led off by stating that you don't intend to pursue math and physics as a career, but to satisfy your own intellectual curiosity:

Yes, why should I care? I know that it sounds stupid. But let me give you an analogy: When you divide some big numbers, do you do it with a calculator or do you write down long division? Even if you have fun with doing it by hand, doesn't it feel a bit unnecessary or dumb or that you are wasting time?

With AI I feel like: Yes I could derive the Schrödinger Equation for an Hydrogen atom (this is a fictional example, I am VERY FAR from problems like this), but the AI can do that in 1 second.

 

[hutchphd]

With AI I feel like: Yes I could derive the Schrödinger Equation for an Hydrogen atom (this is a fictional example, I am VERY FAR from problems like this), but the AI can do that in 1 second.

If this really bothers you, may I suggest that you take up a more idiosyncratic pursuit. Perhaps painting or sculpture. Each work product has value because of its uniqueness: it will be redolent with individuality not easilly matched by artificial art (unless perhaps you somehow emulate Bob Ross......)
Also I think a more productive paradigm is to try to understand deeply and authoritatively some particular physical phenomenon or set of phenomena. You will learn a lot of physics in the process because one question always begets a host of subsequent questions if you have an inquisitive nature. Behold the ensuing chain reaction of knowledge!

 

[CrysPhys]

Yes, why should I care? I know that it sounds stupid. But let me give you an analogy: When you divide some big numbers, do you do it with a calculator or do you write down long division? Even if you have fun with doing it by hand, doesn't it feel a bit unnecessary or dumb or that you are wasting time?

With AI I feel like: Yes I could derive the Schrödinger Equation for an Hydrogen atom (this is a fictional example, I am VERY FAR from problems like this), but the AI can do that in 1 second.

You are contradicting yourself. Do you wish to pursue a subject matter purely for intellectual curiosity, self-satisfaction, and pleasure ... or not? If I wish to write poetry, compose music, take photographs, or whatever for fun, the creative processes are ends in themselves. Even though I can pull up AI programs to write a poem, compose a song, or generate a photo ... if I am only interested in producing the final results in the shortest period of time with the least effort. So if you believe that AI can generate the physics and math results you seek and don't wish to understand the underlying physics and math, and don't wish to pursue intellectual challenges, then don't study physics and math. Problem solved.

 

[fresh_42]

AIs are dumb as bread. They can collect facts, and if you are lucky, even correct ones. They do not understand a word of what they produce. Physics and math are sciences of concepts. They constantly ask "why". And although the answers to these questions may depend on the level you accept as an answer, an AI does not know why at all. Writing down an equation without knowing what it tells is meaningless. I possess two paperbacks titled "Atlas zur Mathematik" (Atlas for Mathematics), full of equations and summaries. I never used them at all. Yes, the tiny print is awful, and Wikipedia and nLab are faster, but when it comes to details, I use my textbooks or search for lecture notes. The problem with AIs is that you cannot trust them. And if you have to check their answers anyway, there is no point in using them in the first place.

 

[sbrothy]

I know I’ve said this before, but to learn and understand math properly you’ll need to do it. I mean practice it like you would ice skating or playing the trompet. Reading about it simply isn’t enough.

 

[Muu9]

The German community colleges (Volkshochulen) are quite different. They are basically split in three parts: 1. general school education degrees, 2. learning languages 3. skills like pottery or singing. There are no dedicated math or physics courses there.

Thanks for all the info!


Yes, why should I care? I know that it sounds stupid. But let me give you an analogy: When you divide some big numbers, do you do it with a calculator or do you write down long division? Even if you have fun with doing it by hand, doesn't it feel a bit unnecessary or dumb or that you are wasting time?

With AI I feel like: Yes I could derive the Schrödinger Equation for an Hydrogen atom (this is a fictional example, I am VERY FAR from problems like this), but the AI can do that in 1 second.

Whatever joy you would get from understanding (not necessarily even doing) real/advanced physics, can't be obtained for you on your behalf by AI. To give an analogy, if you want to understand the division algorithm and why it works, you wouldn't feel like you're wasting your time just because a calculator can do it fast. If you want to understand what the Schrodinger equation is saying, then how fast a computer can solve it shouldn't matter. Sudoku and chess are trivial for computers to obliterate the best humans, yet are still popular. A computer can perfectly scan an art piece - does that mean art appreciation classes are worthless?

Regarding code, even if AI writes code you still need to know what each line is doing to debug things when they go wrong.

Once you learn calculus, you can look at Leonard Susskind's lectures and books. They were made for an audience like you.

 

[CrysPhys]

I know I’ve said this before, but to learn and understand math properly you’ll need to do it. I mean practice it like you would ice skating or playing the trompet. Reading about it simply isn’t enough.

True. But the OP needs to sort out in their own head whether they want to learn and understand math properly, or whether they are content with entering input to a computer and receiving the output the computer spits out.

 

[sbrothy]

Yeah sorry. Was a little too quick there. The OP explicitly said he wanted to "work through" math books. It just kinda drowned for me in between the OP mentioning having seen all these popular videos and whatnot.

Sadly, I too often see other people having this misconception.

 

[CrysPhys]

Yeah sorry. Was a little too quick there. The OP specifically said he wanted to "work through" math books. It just kinda drowned for me in between the OP mentioning having seen all these popular videos and whatnot.

Sadly, I too often see other people having this misconception.

The OP is even more confused about what they're after. They stated that they want to pursue math and physics to satisfy their own intellectual curiosity, that they do not plan to make a career in those fields. But then they say, "Why should I bother learning all this stuff if a computer can spit out answers in a second?"

 

[sbrothy]

The OP is even more confused about what they're after. They stated that they want to pursue math and physics to satisfy their own intellectual curiosity, that they do not plan to make a career in those fields. But then they say, "Why should I bother learning all this stuff if a computer can spit out answers in a second?"

Yeah welp, sadly a symptom of our times. Already, supposedly grown-ups can’t even do division using only pen and paper.

 

[CrysPhys]

Yeah welp, sadly a symptom of our times. Already, supposedly grown-ups can’t even do division using only pen and paper.

And then there are some who would say, "Errr ... pen and paper? What are those?"

 

[TensorCalculus]

When you divide some big numbers, do you do it with a calculator or do you write down long division? Even if you have fun with doing it by hand, doesn't it feel a bit unnecessary or dumb or that you are wasting time?

Well...
In the case of long division, not many do it because not many find it interesting to divide big numbers. It's the context that the long division is in that is usually the interesting bit (like seriously, enjoying long division has to be some other level of nerd). In my case, yes I would feel useless. Probably because the thing that will give me joy, the thing that I actually care about, is the result of some physics problem or something I'm trying to work out (and they're probably basic enough that ChatGPT-5 could do them on a good day, but that's not stopping me from "wasting all my time" on physics is it?) and I don't enjoy the process of long division. But in this case, you want to do physics and maths for the purpose of enjoying the process. In that case you would not feel useless, and maybe a better analogy would be someone who wants to learn to draw because they find it intriguing and fun even though AI can do it (similar to what @CrysPhys said).
There are "human calculators" out there who do actually enjoy dividing things themselves, or doing long divisions either on paper or in their head. Maybe a calculator can do what they're doing but it's not like they want that as something they can put on a job CV anyway, they're doing it for fun.

Plus as said by @fresh_42 LLMs are stupid. They're a model that quite literally just predicts what the most likely token to come next is given a context, based on the data that they've been trained on. They're a long shot from replacing physicists in my eyes.
(ADD: I know that AI can now "plan" and "think through" its steps and even "check" it's answer to get a slightly more high quality answer. But that doesn't change what it fundamentally is)

And agreed with @Muu9 about the Leonard Susskind books. They're fast paced and only give a high level overview of things however the theoretical minimum "series" is a great set of books to read over quickly and make up your mind as to whether you find maths/physics enjoyable to pursue it in more depth.

 

[PeroK]

With AI I feel like: Yes I could derive the Schrödinger Equation for an Hydrogen atom (this is a fictional example, I am VERY FAR from problems like this), but the AI can do that in 1 second.

Perhaps you need to start with a course in existentialist philosophy. Life is absurd and pointless and we have to find something to do with this brief interlude between two eternities of non-existence.

 

[TensorCalculus]

With AI I feel like: Yes I could derive the Schrödinger Equation for an Hydrogen atom (this is a fictional example, I am VERY FAR from problems like this), but the AI can do that in 1 second.

AI can do that because it's such a standard derivation that it's all over the internet and all it needs to do is spit out the derivation, it's basically no different than google for things like that. It's not "deriving" anything. If you show it basic arithmetic but basic arithmetic that is a bunch of random really high numbers with a bunch of decimal points that it has never seen before, it will struggle a lot more.

 

[sbrothy]

Well...
In the case of long division, not many do it because not many find it interesting to divide big numbers. It's the context that the long division is in that is usually the interesting bit (like seriously, enjoying long division has to be some other level of nerd). In my case, yes I would feel useless. Probably because the thing that will give me joy, the thing that I actually care about, is the result of some physics problem or something I'm trying to work out (and they're probably basic enough that ChatGPT-5 could do them on a good day, but that's not stopping me from "wasting all my time" on physics is it?) and I don't enjoy the process of long division. But in this case, you want to do physics and maths for the purpose of enjoying the process. In that case you would not feel useless, and maybe a better analogy would be someone who wants to learn to draw because they find it intriguing and fun even though AI can do it (similar to what @CrysPhys said).
There are "human calculators" out there who do actually enjoy dividing things themselves, or doing long divisions either on paper or in their head. Maybe a calculator can do what they're doing but it's not like they want that as something they can put on a job CV anyway, they're doing it for fun.

Plus as said by @fresh_42 LLMs are stupid. They're a model that quite literally just predicts what the most likely token to come next is given a context, based on the data that they've been trained on. They're a long shot from replacing physicists in my eyes.
(ADD: I know that AI can now "plan" and "think through" its steps and even "check" it's answer to get a slightly more high quality answer. But that doesn't change what it fundamentally is)

And agreed with @Muu9 about the Leonard Susskind books. They're fast paced and only give a high level overview of things however the theoretical minimum "series" is a great set of books to read over quickly and make up your mind as to whether you find maths/physics enjoyable to pursue it in more depth.

In Denmark they recently changed the way STEM is taught in elementary school. Well math specifically I guess, with the result that the parents now don’t understand their children’s homework and can’t help them. Embarraasing. I mean how hard can an 8 year old’s homework be?

 

[TensorCalculus]

In Denmark they recently changed the way STEM is taught in elementary school. Well math specifically I guess, with the result that the parents now don’t understand their children’s homework and can’t help them. Embarraasing. I mean how hard can an 8 year old’s homework be?

Welp, same in Britain. Though embarrassingly despite still learning basic maths in school I am so insanely reliant on my calculator it is crazy. I never mark my little sister's maths work without a calculator in my hand, despite most of the maths being basic arithmetic...

 

[fresh_42]

In Denmark they recently changed the way STEM is taught in elementary school. Well math specifically I guess, with the result that the parents now don’t understand their children’s homework and can’t help them. Embarraasing. I mean how hard can an 8 year old’s homework be?

Welp, same in Britain. Though embarrassingly despite still learning basic maths in school I am so insanely reliant on my calculator it is crazy. I never mark my little sister's maths work without a calculator in my hand, despite most of the maths being basic arithmetic...

How times have changed!

There was a time here when set theory became popular in schools. Well, set theory is a bit exaggerated. It actually was drawing some Venn diagrams. But the concept of unions, intersections, and complements was new in arithmetic-dominated math classes. I once tutored a granny about this stuff because she wanted to be able to help her grandchildren with their homework.

You should take this old lady as an example, not a calculator.

 

[sbrothy]

Perhaps you need to start with a course in existentialist philosophy. Life is absurd and pointless and we have to find something to do with this brief interlude between two eternities of non-existence.

Come to physicsforums for help with mathematics and get a desiccated lecture on Kierkegaard vs. Max Stirner’s “The Ego and it’s Own” with a side dish of nihilistic ontologism.

Quoting @fresh_42 :

[…] There was a time here when set theory became popular in schools. Well, set theory is a bit exaggerated. It actually was drawing some Venn diagrams. But the concept of unions, intersections, and complements was new in arithmetic-dominated math classes. […]

I remember learning about unions and sets as some of the earliest math lessons I had. At the time it was ineffable and boring; later though I’m glad we had those lessons as they made many other concepts accessible. Without that ballast I highly doubt that a book like Hofstadter’s GEB would have made any sense to me.

 

[symbolipoint]

Well....hat ChatGPT-5 could do them on a good day, but that's not stopping me from "wasting all my time" on physics is it?) and I don't enjoy the process of long division. But in this case, you want to do physics and maths for the purpose of enjoying the process. In that case you would not feel useless, and maybe a better analogy would be someone who wants to learn to draw because they find it intriguing and fun even though AI can do it (similar to what @CrysPhys said).
There are "human calculators" out there who do actually enjoy dividing things themselves, or doing long divisions either on paper or in their head. Maybe a calculator can do what they're doing but it's not like they want that as something they can put on a job CV anyway, they're doing it for fun.

Plus as said by @fresh_42 LLMs are stupid. They're a model that quite literally just predicts what the most likely token to come next is given a context, based on the data that they've been trained on. They're a long shot from replacing physicists in my eyes.
(ADD: I know that AI can now "plan" and "think through" its steps and even "check" it's answer to get a slightly more high quality answer. But that doesn't change what it fundamentally is)

A....e it in more depth.

Excuse for cutting away some of the above quote...

Something is bothersome about what is said in post #22, from @TensorCalculus.

Within main computer programming languages each of them has several dialects (and I am just guessing that the word "dialect" is chosen well). A program during development and at a finish still needs to be TESTED extensively or not, in order to look for and remedy problems in coding. How The infierno will Artificial Intelligence take care of all that?

 

[CrysPhys]

There was a time here when set theory became popular in schools. Well, set theory is a bit exaggerated. It actually was drawing some Venn diagrams. But the concept of unions, intersections, and complements was new in arithmetic-dominated math classes.

Brings back bad memories from many decades ago. Set theory was the pivotal theme for the "new math" in the US, foisted on innocent students by the SMSG (https://en.wikipedia.org/wiki/School_Mathematics_Study_Group). I escaped the new math in elementary school for arithmetic, but it overtook me for junior high algebra. We wasted nearly a school year on it until the math teachers revolted. We then had to undergo intensive remedial work to undo the damage.

 

[WWGD]

Come to physicsforums for help with mathematics and get a desiccated lecture on Kierkegaard vs. Max Stirner’s “The Ego and it’s Own” with a side dish of nihilistic ontologism.

Quoting @fresh_42 :


I remember learning about unions and sets as some of the earliest math lessons I had. At the time it was ineffable and boring; later though I’m glad we had those lessons as they made many other concepts accessible. Without that ballast I highly doubt that a book like Hofstadter’s GEB would have made any sense to me.

Took me a few months to even be able to pronounce his last name without my tongue convulsing.

 

[WWGD]

Welp, same in Britain. Though embarrassingly despite still learning basic maths in school I am so insanely reliant on my calculator it is crazy. I never mark my little sister's maths work without a calculator in my hand, despite most of the maths being basic arithmetic...

For set theory? Either times have changed or you're doing something wrong.

 

[fresh_42]

Took me a few months to even be able to pronounce his last name without my tongue convulsing.

Which one? Gödel, Bach, or Kierkegaard?

I only met two people in my life who grew up with American English and were able to pronounce German correctly. The difference to Danish isn't so big then. I think that the main reason is actually how the tongue is used or placed. This is something you cannot easily switch between languages, and the reason why you cannot say Schrödinger and I break my tongue pronouncing clothes.

 

[WWGD]

Which one? Gödel, Bach, or Kierkegaard?

I only met two people in my life who grew up with American English and were able to pronounce German correctly. The difference to Danish isn't so big then. I think that the main reason is actually how the tongue is used or placed. This is something you cannot easily switch between languages, and the reason why you cannot say Schrödinger and I break my tongue pronouncing clothes.

Hofstadter.

 

[fresh_42]

Hofstadter.

I mean Hofstadter is an American, so where is the problem? Ok, he has a German name, which was at some point in time probably written Hofstädter. But the "ä" is the least problematic for English-speaking people. You use it anyway, only pronounced longer than it should as in "can". And most Germans would pronounce it Hofstedter so that the "ä" is basically not heard at all. The only real difference that I see is that the "o" should be long, not short, since the "f" isn't doubled.

 

[sbrothy]

Excuse for cutting away some of the above quote...

Something is bothersome about what is said in post #22, from @TensorCalculus.

Within main computer programming languages each of them has several dialects (and I am just guessing that the word "dialect" is chosen well). A program during development and at a finish still needs to be TESTED extensively or not, in order to look for and remedy problems in coding. How The infierno will Artificial Intelligence take care of all that?

Tell it to write unit tests along the way?

Sorry, just a silly chivalrous attempt at coming to the rescue of @TensorCalculus ‘s idea. Don’t know if it’s possible. Lots of similar links and citations though. (Also, I never personally liked them.)

 

[TensorCalculus]

Excuse for cutting away some of the above quote...

Something is bothersome about what is said in post #22, from @TensorCalculus.

Within main computer programming languages each of them has several dialects (and I am just guessing that the word "dialect" is chosen well). A program during development and at a finish still needs to be TESTED extensively or not, in order to look for and remedy problems in coding. How The infierno will Artificial Intelligence take care of all that?

Yes there will definitely be a need for programming in the future, such as what you've highlighted above.

I decided to take the absolute worst-case, most extreme scenario and try and show that even then, the OP should not care about the fact that AI can do what they're doing because their aim is to do it to satisfy their curiosity.

For set theory? Either times have changed or you're doing something wrong.

Nonono, not for set theory. Basic arithmetic. My sister is preparing for the 11+, she's doing her last year of elementary maths. I use a calculator to check her long division, her column addition, subtraction, multiplication... things like that. I could probably check it properly but... I would probably be slower than her. I relied on my calculator ever since COVID (so, when I was 8,9,10) when I started trying to teach myself physics...

Beyond a couple of lessons on Venn Diagrams here and there we don't do much set theory anymore. I don't think many secondary-aged children would even know what you were talking about if you mentioned set theory (It's introduced formally in A-level maths I believe).

 

[sbrothy]

Which one? Gödel, Bach, or Kierkegaard?

I only met two people in my life who grew up with American English and were able to pronounce German correctly. The difference to Danish isn't so big then. I think that the main reason is actually how the tongue is used or placed. This is something you cannot easily switch between languages, and the reason why you cannot say Schrödinger and I break my tongue pronouncing clothes.

I actually just assumed it was Hofstadter, even though Kierkegaard is probably more tongue-twisting. In fact, the double As are replacements for the Danish Å. It’s pronounced somwhat like the vocals in “duh” or “or”.

Danes pronounce Kierkegaard like “Keerguegor”. Both G’s, and the “ue” like the G and “ue” in “guest”. The D is silent.

 

[martinbn]

Beyond a couple of lessons on Venn Diagrams here and there we don't do much set theory anymore. I don't think many secondary-aged children would even know what you were talking about if you mentioned set theory (It's introduced formally in A-level maths I believe).

It is done in year 10 and 11.

 

[fresh_42]

I actually just assumed it was Hofstadter, even though Kierkegaard is probably more tongue-twisting. In fact, the double As are replacements for the Danish Å. It’s pronounced somwhat like the vocals in “duh” or “or”.

Danes pronounce Kierkegaard like “Keerguegor”. Both G’s, and the “ue” like the G and “ue” in “guest”. The D is silent.

I love Ångström for that reason. Two for the price of one.

 

[sbrothy]

I love Ångström for that reason. Three for the price of one.

Three? Were’s the third? But that’s Swedish. Swedes don’t have the Æ. They use ä.

(Couldn’t find umlaut on my phone.)

 

[TensorCalculus]

It is done in year 10 and 11.

Huh? I asked a year 11 that I know if she knows what set theory is and she had no idea (and she got 9 on her maths GCSE... so...)
Oh well. I haven't done y10 and y11 yet (even though our school usually teaches us things a year early) so I guess I can't say much.

 

[fresh_42]

Three? Were’s the third? But that’s Swedish. Swedes don’t have the Æ. They use ä.

(Couldn’t find umlaut on my phone.)

I first thought "ng" would be a problem, too, but I corrected it as it might be a bit far-fetched. I copied the name from the German Wikipedia page; that's faster than looking for the ASCII code of the letters. Nevertheless, we have the open "a" and the "ö"; ˈɔŋːstɾœm. Neither of which occurs in English.

 

[martinbn]

Huh? I asked a year 11 that I know if she knows what set theory is and she had no idea (and she got 9 on her maths GCSE... so...)
Oh well. I haven't done y10 and y11 yet (even though our school usually teaches us things a year early) so I guess I can't say much.

I might be wrong. I saw a textbook once that had a bit more than Venn diagrams. It may have been A levels or uni. It looked completely pointless, so I assumed it had to be uk's gcse curriculum.

 

[fresh_42]

It is done in year 10 and 11.

It was in elementary school (or shortly after) here, which is why it was so controversial.

 

[TensorCalculus]

I might be wrong. I saw a textbook once that had a bit more than Venn diagrams. It may have been A levels or uni.

Oh well, we'll see.
I've set a reminder for year 11 me to come back and say whether I learnt set theory or not
This is what the AQA curriculum says for GCSE Maths

It looked completely pointless, so I assumed it had to be uk's gcse curriculum.

 

[TensorCalculus]

It was in elementary school here, which is why it was so controversial.

We do Venn diagrams in Elementary here, but nothing more than that I guess.

 

[fresh_42]

We do Venn diagrams in Elementary here, but nothing more than that I guess.

Yes, that's why I said "set theory" was an exaggeration. However, they called it as such, and it was kind of revolutionary back then since people were used to considering math in early classes as a drill for arithmetic only. I guess, calling it "set theory" and thereby sounding like something new wasn't the best idea. However, I will not dive into the realms of didactics of mathematics in order to avoid ranting.

I basically share the opinion of my former mentor.
(Me, seeing a parcel addressed to a didactician in his office while he was dean): "You send ... a parcel?"
(My mentor): "This was submitted here by mistake. At most, I'll send him something that ticks."

 

[TensorCalculus]

Yes, that's why I said "set theory" was an exaggeration. However, they called it as such, and it was kind of revolutionary back then since people were used to considering math in early classes as a drill for arithmetic only. I guess, calling it "set theory" and thereby sounding like something new wasn't the best idea. However, I will not dive into the realms of didactics of mathematics in order to avoid ranting.

Ah yeah you did mention...
Do they still teach it in elementary now? Considering the fact that it wasn't considered the best idea?

 

[fresh_42]

Ah yeah you did mention...
Do they still teach it in elementary now? Considering the fact that it wasn't considered the best idea?

I don't know, I haven't checked. The problem was not the content; the mistake was labelling it by a name. I assume you will learn this on several occasions in your hopefully long life: People oppose everything new by default! Have a look at the AI discussions here! Or even better, look at "I am a chipper, I am no melter!"

You can easily introduce these basic concepts by, for instance, considering divisors and looking at $\operatorname{gcd}$ and $\operatorname{lcm}.$ The key is to sneak in new concepts rather than calling out a revolution!