It's amazing what someone who propounds ignorance is ignorant of.

I must remember not to work with/for/over this person.

An algebraic solution might have a unique answer, but Math is more than pure Algebra. For instance, Machine Learning problems rarely have a single solution and I would argue that Machine Learning is tightly related to Math.

Very few "real world" math problems reduce to easily computable closed form expression. You're almost always dealing with numeric approximations. So even when your problem has a unique correct answer finding it is either impossible or computationally impractical. A large part of applied math is finding newer, faster and cleverer ways of approximating these solutions. Making the best choice between all the different ways to get the right answer can often be the difference between run times measured in hours vs centuries.

It's actually the case that even in straight up "theorem/proof" math, it's instructive, useful, and informative to have multiple ways to prove a given theorem. This is how you link multiple subfields of mathematics together and create cross-pollination of understanding between areas as advances in one feed into the other via the multiple correspondences (and, yes, that's a very handwavy and not terminology-correct way to put it).

One solution, zero solutions, infinitely many solutions, ... this is grade school math.