Does math lose the connection with the physical world after a point?

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I am an engineering student, completed the course and worked for a while as a research associate, I always loved mathematics, but I couldn't pursue it as a full-time career. Now I wish to do a master's and Ph.D. in mathematics, but I have been warned that it's not rosy as you think, because you may lose the connection with physical problems and you will deal with numbers only.