I would put it a little differently.
First, I would suggest that the emergence of Higgs bosons itself depends on mathematics (chaos theory). They do not exist independently, but emerge from the Higgs Field.
Peter Higgs developed the theoretical mathematical model of values and functions required for a Higgs boson to become manifest in physical reality. When those maths were fed into the Cern collider and the
mathematically required amount of energy was applied, presto a Higgs boson materialized for an instant and promptly decayed again.
IMO, pure Mathematics are descriptive of the essence of universal relative values and functions.
The universal potential and ability to do work.
Human mathematics are the
symbolic representations of the universal relative values and functions, enfolded and unfolded physical patterns.
A cosmologist once said "If you ask the universe a question and you ask it nicely (using the proper mathematics), it will give you the correct answer, every time".
If this is true, then that proves the hypothesis of a Mathematical Universe.
When we ask the same question but use the wrong maths, the universe will not respond as expected, which is the falsification as required for theory, no?
Mathematics allows us to "communicate" with the Universe......