Of course not. Algebra in particular, and math in general are tools.
Mathematical tools have proven themselves to be outstandingingly
useful in physics. Amazingly useful.
OTOH it should go without saying that any tool can be abused.
When I write A+B and somebody interprets that as A "then" B, that
is a blatant abuse of the mathematics. That is attempting to take
out of the equation something that was never in there. Math is
not unique in this respect; non-mathematical English sentences
can be abused in the same way. Actually math has the advantage of
being relatively hard to abuse ... but still, it can be abused.
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Math is expressive. It can express wrong ideas as well as right
ideas. For example, I am free to write
E = m c^3 [A]
You don't have to agree with equation [A]. If you disagree, it would
be silly to blame mathematics in general. It would be much more
practical to use the mathematical tools to your advantage by expressing
a better equation such as
E = m c^2 [B]
I say again, math is expressive. And English is expressive, too. In
the current discussion, there are at least four ideas that have come
up:
1) F equals ma
2) F causes ma and not vice versa.
3) F is defined in terms of ma and not vice versa.
4) F is calculated in terms of ma and not vice versa.
There is really no trouble expressing these ideas. We can also express
the notion that some of them (e.g. 4) are sometimes true and sometimes
definitely not true.
There is abundant evidence that F equals ma to high precision over a
wide range of practical conditions. Leaping to the conclusion that
F causes ma (and not vice versa) would be a huge leap beyond the
available evidence.
As a separate statement running parallel to the previous paragraph,
we can say that writing the equation F=ma is a wonderful tool for
summarizing the available evidence. Interpreting F=ma as a statement
that F causes ma is a gross abuse of the tool.