It’s important to note that students from many different majors go to work in finance (by finance I mean investment banking, sales and trading, wealth management etc.). Because finance companies offer a lot of on-job training, they don’t just look for students who studied economics. In fact, the economics major doesn’t provide many skills that are relevant to finance (although certain classes offered by the department do).
To be successful in an entry level finance job, one needs to be able to work long hours, have moderate quantitative skills, and diligently pay attention to detail. With this in mind, financial institutions look for indicators like GPA, the difficulty of the major, and how quantitative the major is. A successful hire might be a history major with a 3.9 and a demonstrated interested in finance, or, a math major with a 3.7. Because they’re both rigorous and quantitative, majors like physics and math are desirable–but they’re definitely not essential.