There are situations of applications of mathematics in physics which

• seem to work well enough for physicists (for example they agree with the experimental data)
• but are considered unacceptable or at least non-rigorous to mathematicians

Please help me gather some examples. Which of these techniques were eventually made rigorous?

Thank you.

I apologize if for some this question may seem inappropriate for MO. I consider these examples a great source of research problems for mathematicians who are interested in mathematical physics.

There are situations of applications of mathematics in physics which

• seem to work well enough for physicists (for example they agree with the experimental data)
• but are considered unacceptable or at least non-rigorous to mathematicians

Please help me gather some examples. Which of these techniques were eventually made rigorous?

Thank you.

I apologize if for some this question may seem inappropriate for MO. I consider these examples a great source of research problems for mathematicians.

There are situations of applications of mathematics in physics which

• seem to work well enough for physicists (for example they agree with the experimental data)
• but are considered unacceptable or at least non-rigorous to mathematicians

Please help me gather some examples. Which of these techniques were eventually made rigorous?

Thank you.