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Most students encounter a life-changing decision during their undergraduate years. That is either to choose a high paying yet a career they might not be passionate about or a career they like but is unlikely to be high paying.

It is not unusual to find career advice popping in various internet circles that fixate on the importance of passion. The general rhetoric is "If you have a "sufficient" passion for X, you are guaranteed a "good" career in X and hence a good life."
Now, on some levels, the advice makes sense. Students are usually willing to sacrifice guaranteed-to-pay-well professions in hopes to excel in their own professions fueled by passion.
Now my question is, What is the sufficiency precisely in this context?

To be more precise, say I think I feel passionate for mathematics. Maybe because I am good at it. Maybe because I contemplate on it in my free time. Now when it comes to the actual profession, the "apparent" passion fades away and I am left regretting pursuing the field (something that is not unusual to see with Ph.D. students).
Or say, I feel I like physics and mathematics but I also get easily swayed away by high paying professions like data science.

How can I come to "know" whether I truly have a passion for mathematics or whether I was merely deluded into thinking that because I was made to feel that I am good at mathematics by the relevant education system?

I'm going to just guess that if you are asking the question, then you don't have it. Yet. Or at least, not a lot of it. Yet. But there is time to develop it and, at your age, my suggestion is that you don't worry too much about it. Yet. And you look around at the possibilities.

A wasted life is one in which you can't really do what you really want to do. Too many people have that forced on them by circumstances, but if you can manage it, spend some time to see what develops.

And also expect that at different times in your life you will have passion for different things, some quite distinct from the others. If you can manage to follow those passions then you can have a rich and rewarding life. And you don't get a do-over.

You will know it when you experience it. But first, experience a lot of things.

If you were really passionate about something, you'd know because you'd want to do it in exclusion of all else. You think about that thing even if you're bathing, eating, etc.

Having said that I can understand what you're asking because if we define passion this way, precious few people would be passionate about anything that they can actually make a living from. That includes academics - e.g. this question

I just want to get married, and have weekends and evenings off, and chill out and play board games, and have nice conversations with friends, and have time to exercise and eat good food, and partake in hobbies, and read books and play computer games and watch movies and write a novel or two.

And from there it's just a short way to "I just want to get married and have my entire week off ..."

So now what? I suggest:

1. Can you imagine yourself doing it as a career? You don't have to like it more than board games, conversations with friends, etc, but you should like it enough that you can do it for upwards of 40+ hours a week. On the other hand if it starts getting painful to go to work every day, it's not a good idea to do it.


2. Are you good at it? If you are, then you can get results even if you aren't passionate (by above definition) about it.

It may not be a popular position, but you can certainly base your career around things that you aren't passionate about (by above definition). For example, my mother became a doctor because that's traditionally what all good students at her high school did. She didn't particularly like it any more than other careers, but she studied it, did well at it, became a trained doctor, became a specialist, and eventually managed her own department. She would often complain about her work at the dinner table, and talk about e.g. how she would rather teach language at a local high school, but by all metrics she still had a successful career.

I suppose the point of this answer is to reject the notion that having a passion for area X is any sort of prerequisite for working in area X and having a successful career. I should make clear that I'm an assistant professor of mathematics at Oberlin College, a small liberal arts college in northeastern Ohio. My job affords me a balance between teaching and research that I love and wouldn't give up for the world. Whether this counts as success is obviously a matter of opinion.

Throughout college (and grad school) I met math majors that knew they wanted to study math for the rest of their lives from the age of 12 or 13. Myself, I became a math major because my engineering pre-major advisor thought that taking two math classes in the spring of my freshman year was a bit much and thus I registered for five math classes to spite her. I had many interests as an undergraduate (mostly in history, foreign languages and literature), and feel that I probably could have gone on to a successful career in any number of them that I would have ultimately found rewarding.

Now there's no way to get around the fact that to succeed in grad school you're going to have to work very hard. In fact you'll probably work so hard that you'll convince yourself that it's a blessing you're even being paid because you'd gladly do this work for free.

I guess my point is that if you really enjoy a field and have a talent for it then you shouldn't discount going on to grad school for it. Even if your passion for the subject doesn't coincide with the romantic notions of some of your classmates. At the end of the day hard work is likely the stronger predicter of success in any event.

People who say you still need to find it and stuff are screwing up your brain. There is no the "lazy" type of passion that will drive you to do something same and specific every day. It's human nature. "Specialization is for insects". That's why you need some external motivator. Like, I want to be a great mathematician and then specialize even more in which field and stick with it.

Passion is a combination of external and internal motivation.