What Should Be My Correct View on Math and Physics?

[trees and plants]

Hello there. I think i have wrong views on math and physics. Specifically, i understand that physics and math contain results on more fields that most people think, but perhaps from popular science books and opinions of other people a wrong view of what math and physics are about still remains on me.

I try to move away from it but i need help from someone.I read things from a book now that is about algebra, geometry, topics on convex sets, plane geometric figures, hermitian harmonic functions, quadratic forms, embeddings, connections,curvatures and geodesics on riemannian manifolds. Some people focus only on a very little interest on math or physics mostly up to high school math and physics from popular science books.

What i want to ask is: what should be the correct view i should have on math and physics? If i study about other fields in math or physics like representation theory, Lie groups,category theory , proof theory which contain results on math but other people may find uninteresting will it be worth it? I think it will, but i am not sure for some reasons. Also, if i study math only for math not for their applications to fields outside of math, or physics only for physics and not for applications outside of physics like engineering, technology, industrial uses, is it ok?

Also, some people talk about theorems in math and proofs in physics but if someone reads the textbooks then also examples, applications are provided, which are needed. They could be considered theorems but they are called examples or applications. Other question: personally i think as long as questions are made in math and physics , they will not reach an end and people will not stop doing research on them, but some popular opinions say other things i think. What is correct?

In my high school and junior high school as i remember importance was not given so much on proofs in math and physics but on the statement of the theorem not the proof so much. But proofs are very important in math and physics and focus on them is worth it as i think.Should focus on teaching be more on proofs than it is until today?

Some things in math and physics are very popular like higher dimensional riemannian geometry, differential equations, general relativity, quantum mechanics they are ok, but some people i think know or understand a few basic things on them and do not study them more. Others consider other fields of math or physics or topics not so much worthy. I am a confused from these things. Can you help me solve this confusion?

And about the importance or interest of a question and finding its correct answer in math or physics, what are the criteria for the result to be accepted?Thank you.

 

[Choppy]

It sounds to me like your questions boil down to something like: "Is it okay to pursue the more abstract sub-fields of mathematics and physics for their own sake and because I find them interesting, or should I focus on learning sub-fields that have more immediate application?"

The answer to that is that it all depends on you.

It's fine to pursue the more abstract areas in your field of interest. If this is what drives you, what you're really interested in, where you would prefer to spend your time, and where you feel you'll be able to make the biggest advances, then you should move in that direction.

But do so pragmatically.

At the end of the day, we all need to eat. And one of the realities of the world is that the people who control the money tend to be more interested in direct applications of physics and mathematics. So when you choose your field of study and the skills that you develop, it's important to ask yourself questions along the lines of how those skills and that knowledge set is going to put food on your table.

 

[trees and plants]

It sounds to me like your questions boil down to something like: "Is it okay to pursue the more abstract sub-fields of mathematics and physics for their own sake and because I find them interesting, or should I focus on learning sub-fields that have more immediate application?"

The answer to that is that it all depends on you.

It's fine to pursue the more abstract areas in your field of interest. If this is what drives you, what you're really interested in, where you would prefer to spend your time, and where you feel you'll be able to make the biggest advances, then you should move in that direction.

But do so pragmatically.

At the end of the day, we all need to eat. And one of the realities of the world is that the people who control the money tend to be more interested in direct applications of physics and mathematics. So when you choose your field of study and the skills that you develop, it's important to ask yourself questions along the lines of how those skills and that knowledge set is going to put food on your table.

Except of an occupation i also am interested in math and physics having them as hobbies. Becoming a professor at a university i think is quite difficult thing in science. I do not know the criteria for it but a phd dissertation is at least needed. I have heard that a phd dissertation is difficult and takes for most people at least two to three years and perhaps five or six years to complete. I do not know how difficult it is .

I want to know: if in the future whether after a few weeks or after more time or less i decide to answer abstract questions on abstract topics that have no application for industrial uses but are only for the field i am working on, will they be accepted?What are the criteria to get them published and if the results are correct but i do not publish them are they worth the effort?

Since 1850 or 1950 and until today how do most physicists or mathematicians do their work on physics and math questions?They choose topics, make or find the questions,then learn about these topics and questions and try to answer them?How much time does it take to answer one of these questions?

What happens if i spend like 40 or 50 years only on completely abstract topics and my results are not accepted?That would be tragic.Is it not a little risky? How other physicists or mathematicians insisted on these goals without feeling sad?

 

[Mark44]

I read things from a book now that is about algebra, geometry, topics on convex sets, plane geometric figures, hermitian harmonic functions, quadratic forms, embeddings, connections,curvatures and geodesics on riemannian manifolds.

That's a very broad spectrum of topics. Mathematics is usually taught sequentially, with arithmetic being taught in the lower grades, then algebra, geometry, and trigonometry plus perhaps calculus "lite" in high school. Most of the topics you mentioned above are taught only in university courses.

how do most physicists or mathematicians do their work on physics and math questions?They choose topics, make or find the questions,then learn about these topics and questions and try to answer them?

They normally don't choose the topic themselves, but instead are given a topic for study by their thesis advisor.

How much time does it take to answer one of these questions?

It can take years.

What happens if i spend like 40 or 50 years only on completely abstract topics and my results are not accepted?That would be tragic.Is it not a little risky?

It has happened that some mathematicians in the past did work that at the time seemed purely abstract, and of no practical use to anyone. I'm thinking of George Boole (after whom Boolean Algebra gets its name) and G. H. Hardy, who did a lot of work in number theory. I imagine that many people thought that Boole's work was very elegant, but of no practical use. All that changed when digital computers began to be built, with circuitry that incorporated Boolean algebra in its logic.

Some of Hardy's work was so esoteric that he wrote a paper titled "A Mathematician's Apology," in which he explained his interest in so-called "pure mathematics" (mathematics with no practical applications). In the paper he wrote, "No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years." He was mistaken in this sentiment, as number theory very soon came to be applied in cryptography and a a number of other areas.

These two mathematicians are no doubt exceptions, though, I'd venture to say that many more mathematicians have worked for years to come up with theses that sit in university libraries, covered with dust.

 

[trees and plants]

It can take years.
It has happened that some mathematicians in the past did work that at the time seemed purely abstract, and of no practical use to anyone. I'm thinking of George Boole (after whom Boolean Algebra gets its name) and G. H. Hardy, who did a lot of work in number theory. I imagine that many people thought that Boole's work was very elegant, but of no practical use. All that changed when digital computers began to be built, with circuitry that incorporated Boolean algebra in its logic.

These two mathematicians are no doubt exceptions, though, I'd venture to say that many more mathematicians have worked for years to come up with theses that sit in university libraries, covered with dust.

Questions i have are:how much is the time it takes for most mathematicians or physicists to answer an unanswered question at most times? So, their theories, works, theorems are correct but other people were not interested in them?

Apart from the industrial uses in math and physics what made scientists to get interested in some abstract topics until today?

 

[Mark44]

Questions i have are:how much is the time it takes for most mathematicians or physicists to answer an unanswered question at most times?

That's way too general a question to answer. Some unanswered questions are still unanswered.

So, their theories, works, theorems are correct but other people were not interested in them?

Like I said, I imagine that university libraries have many mathematical treatises that are of very little interest to anyone other than their authors.

Apart from the industrial uses in math and physics what made scientists to get interested in some abstract topics until today?

Who can say?

 

[Choppy]

It sounds like you're trying to figure out the process of academic publishing perhaps.

First off, it's extremely rare for someone to contribute meaningfully to these fields without first going through formal academic training, i.e. graduate school and earning a PhD.

Some of the things you learn in graduate school include how to identify a research problem, how to set up a systematic study of that problem, how to explore potential solutions, and how to present those solutions to your academic peers.

This isn't something that happens over night. These are skills that are developed over time and with mentorship and critical feedback.

One of the keys to identifying a worthwhile problem is reading academic journals. When you have a field identified that you want to work in, you start by reading about what other people are working on. You learn the techniques they are employing to solve those problems and in time this should give you an idea of which approaches are likely to be successful and which are not. Of course it's research, and so you can never know for sure until you dive into a project how it will turn out, but you can at least tip the odds in your favour.

I want to know: if in the future whether after a few weeks or after more time or less i decide to answer abstract questions on abstract topics that have no application for industrial uses but are only for the field i am working on, will they be accepted?What are the criteria to get them published and if the results are correct but i do not publish them are they worth the effort?

Usually the requirements for publication include: a contribution to the field that is novel and meaningful, a rigorous and sound scientific approach to the problem, logical conclusions stemming from the results, and written/presented in a way that is easily understandable by those in the field. Your article also needs to be appropriate for the readership of the journal. As I said above, identifying such factors is something your learn in graduate school.

Since 1850 or 1950 and until today how do most physicists or mathematicians do their work on physics and math questions?They choose topics, make or find the questions,then learn about these topics and questions and try to answer them?How much time does it take to answer one of these questions?

How long is a piece of string?

A lot depends on the specific field, but it's probably safe to assume that most meaningful journal articles are produced by collaborative groups, and are the result of months, if not years of work. Sure there are exceptions and it varies from field to field, but in my experience it's rare for someone to have a brilliant idea, write up a solution over a matter of days and get it published.

What happens if i spend like 40 or 50 years only on completely abstract topics and my results are not accepted?That would be tragic.Is it not a little risky? How other physicists or mathematicians insisted on these goals without feeling sad?

Hence the advice to be pragmatic about what you chose to work on. That other piece of advice is not to work alone. If you collaborate with a group of people that includes others who have successfully published in the past, the probability of wasting your time goes down considerably.

Apart from the industrial uses in math and physics what made scientists to get interested in some abstract topics until today?

This is hard to answer without specific example, but generally speaking I think a lot of people recognize that just because a problem or a field has no immediate use today, doesn't mean in won't in the future, once technology advances. Or that someone won't be able to take your solution for abstract problem X and apply it practical problem Y.

 

[symbolipoint]

What i want to ask is: what should be the correct view i should have on math and physics? If i study about other fields in math or physics like representation theory, Lie groups,category theory , proof theory which contain results on math but other people may find uninteresting will it be worth it? I think it will, but i am not sure for some reasons. Also, if i study math only for math not for their applications to fields outside of math, or physics only for physics and not for applications outside of physics like engineering, technology, industrial uses, is it ok?

Mathematics - Numbers, categorizations, measureable drawable structures, especially those which can be fitted with numbers; operations with or on these things.
Physics - The study and attention to matter, energy, and the transformations among them.

Some parts of Mathematics are purely hypothetical but must be fully consistent; and some parts of Mathematics are practical. For study, both sides are important. You need to decide which of those parts is most appealing to YOU.

 

[symbolipoint]

Since 1850 or 1950 and until today how do most physicists or mathematicians do their work on physics and math questions?They choose topics, make or find the questions,then learn about these topics and questions and try to answer them?How much time does it take to answer one of these questions?

PLEASE, PLEASE, spend more time studying and learning, even if it is in a traditional academic setting; but hopefully in a setting which may also give you some opportunities either for short-term practical exercises, or internships.

 

[trees and plants]

After finishing hopefully, if God wants, my degree in math, i think i want to study more applied fields in physics or engineering perhaps. Studying pure mathematics without any applications gives me the sense of uncertainty of application and the sense of not doing something close to the physical universe.

It is very difficult for me to study pure mathematics without applications especially for a long time like systematically for weeks, months or years. How do those who work on pure mathematics without applications do it?For example doing differential geometry on manifolds of dimentions n≥4?Or algebraic geometry with abstract varieties?

 

[trees and plants]

PLEASE, PLEASE, spend more time studying and learning, even if it is in a traditional academic setting; but hopefully in a setting which may also give you some opportunities either for short-term practical exercises, or internships.

I agree on the parts of the setting and the opportunities. Perhaps i should complete my undergraduate studies and get my degree at least. The difficult part is that after i have failed many times not passing my courses and having delayed my graduation i find it difficult to have interest and courage to concentrate on my courses at my math department.

Practically it is difficult, on January the exams are programmed to begin, i should better focus on the material given for studying at my department. Perhaps, the way i was taught at school got me a little anxious and i still am anxious on studying math or generally studying. What should i do to surpass this?

Perhaps just try read and if i do not remember that good just read again and again until i eventually remember it and not care about if others evaluate me on this?