Colleges have decided that even if you are not a math or science major the study of college algebra will provide you with a more rounded education. Just like why math majors have to take literature, music appreciation, art appreciation, sociology etc.
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Physics is the study of matter and energy and their interactions. These can be understood and described using mathematics and that is the reason that mathematics is referred to as the language of physics.
There is no good reason: it is simply a convention.
Archimedes' achievements in mathematics are some of the greatest ever made in the field, and include being the first person to mathematically calculate pi. He is considered to be the Father of Mathematics for this reason.
There really was no question of survival in connection with algebra. It was a very useful tool invented by Muslim mathematicians Other cultures found good reason to study it and expand it.
The most common reason is because when the student go home he/she doesn't continue there studies there.