In my experience (undergraduate mathematical statistics, currently "quant financial engineer") this is exactly right. If you want to continue "doing" math in th

In my experience (undergraduate mathematical statistics, currently "quant financial engineer") this is exactly right. If you want to continue "doing" math in the sense you did in school, or in the sense we assume a "mathematician" does, it really is almost exclusively a consideration accompanying having a doctorate in the field. Mainly because as stated above, undergraduate mathematics really just scratches the surface of core competencies. That being said, while not many fields offer pure math tracks for undergrads it certainly doesn't make it irrelevant. In most "quant" fields mathematical literacy and the thought patterns accompanying having studied mathematics are far more valuable than actual proficiency. Outside of research few individuals are "paving new roads" mathematically, they are most often applying the results of cutting edge research or long standing industry standards in mathematics within the context of their job. This requires a high level of mathematical fluency and comfort with abstract formalisms, not theory expertise akin to that of a phd.