I think this question would be clarified as "Is free will an even logical possibility with respect to some set of laws of nature we could in principle design, or is it impossible in every possible world". What you're getting at is a very deep, very interesting question, but the "mathematician" somewhat obscures it the core idea here.
That out the way, it's a clever, but unsuccessful, attempt to side step some of the conceptual issues at play in the free will debate. We still need to agree on a definition of "free will" to see whether we can design a possible world with features that allows for it. And so you'll be dragged, inevitably, kicking and screaming perhaps, into the compatibilism debate. Does it REALLY follow that, if an arbitrary action of mine, X, is determined, but part of that determiniation is things we consider part of our "will", that I haven't willed it? And so on. Standford encyclopedia will be helpful there.
But your strategy is a fruitful one if we do the following. Suppose we list every definition of freewill within the free will debate, and then try to be "mathematicians", as you put it, and try to design a possible world that satisfies it. I imagine that's been done by someone, but it's a useful thing to do for yourself: see which definitions of free will are logically possible. But the two crucial questions still remain. In order of depth (ascending), they are:
Is our world one which satisfies the criteria of being a world W, where W is the set of worlds that allows some definition D of free will to exist?
Even if this definition, D, of free will is possible on our world (that is, our world is a member of the set W with respect to D), is this definition the "right one"? What is even the criteria for the "right" definition?
As you can see, your line of reasoning is absolutely worthwhile, but can only get us so far.
I hope this is helpful.