Theoretical physics or pure mathematics?

In summary, the person is torn between their interests in mathematics and physics and is seeking advice on how to decide which path to pursue. They mention being more comfortable with theoretical physics and applied mathematics, particularly topology and differential geometry, but also have a love for number theory. They are unsure if they should continue studying theoretical physics or switch to pure mathematics, as they feel they may not have enough background in advanced analysis. They have a strong understanding of string theory and high-energy physics, but struggle with analysis. They are seeking guidance on which path to take.
  • #1
LevLandau
14
2
have a nice day. I was torn between mathematics and physics. I do not know which one I wanted. How can I decide? for me; theoretical physics, applied mathematics - topology (dif.topology, alg.topology, geom.topology), differential geometry easy than pure, proof based mathemics. I'm better spatial ability. but at the same time I love the numbers theory. How can I decide? Thank you. I am very little backgorund advanced analysis. what should I do? Up to this time I study always in applied mathematics and theoretical physics. Please help. Thank you
 
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  • #2
for example, I understand all string theory research papers; I understand all articles in high-energy physics. I'm fine with it. but I'am not too good at analysis. Can I be pure mathematician? or continue study theoretical physics ?
 

1. What is the difference between theoretical physics and pure mathematics?

Theoretical physics is a branch of physics that uses mathematical models and concepts to explain and predict the behavior of physical systems. Pure mathematics, on the other hand, is a branch of mathematics that focuses on the abstract study of mathematical objects and their relationships. While both fields use advanced mathematical concepts, theoretical physics is more focused on applying these concepts to real-world phenomena, while pure mathematics is more concerned with exploring these concepts for their own sake.

2. What kind of research is typically done in theoretical physics and pure mathematics?

In theoretical physics, research is typically focused on developing and testing new theories and models to explain and predict the behavior of physical systems. This can include studying the fundamental laws of nature, such as those in quantum mechanics and general relativity, as well as exploring new areas of physics, such as string theory and cosmology. In pure mathematics, research is often focused on developing new mathematical theories and proving theorems, without necessarily having a specific real-world application in mind. This can include topics such as number theory, algebra, and geometry.

3. How do theoretical physics and pure mathematics intersect with each other?

Theoretical physics and pure mathematics have a strong overlap in terms of the use of advanced mathematical concepts. Theoretical physicists often rely on pure mathematical theories and techniques in their research, while pure mathematicians may draw inspiration from physical phenomena in their exploration of abstract mathematical concepts. In recent years, the two fields have also become increasingly intertwined with the development of mathematical physics, which applies mathematical methods to problems in physics.

4. What kind of skills are needed to pursue a career in theoretical physics or pure mathematics?

A strong foundation in mathematics is essential for both theoretical physics and pure mathematics. This includes a solid understanding of calculus, linear algebra, and other advanced mathematical concepts. In addition, critical thinking, problem-solving, and analytical skills are important for success in both fields. The ability to think abstractly and creatively is also highly valued in theoretical physics and pure mathematics.

5. What are some potential career paths for someone with a degree in theoretical physics or pure mathematics?

Some common career paths for individuals with a degree in theoretical physics or pure mathematics include research positions in academia, government laboratories, or private industry. These individuals may also pursue careers in teaching, data analysis, or computer science. Additionally, many theoretical physicists and pure mathematicians go on to work in fields such as finance, engineering, and technology, where their strong analytical and problem-solving skills are highly valued.

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