No, my claim that brains contain a mind is that I can think.
This makes no sense. That you can think is evidence for the claim that brains contain a mind; is that what you're trying to say?
Do you deny the existence of the mind? Without a mind we cannot think.
Depends on how you define "mind."
Provide an example of chemicals and electricity doing math without programming.
There are two issues in your request that need to be separated. One is, what is the nature of the substrate that is performing the calculation? Can it be mere chemicals, or does it need to be a mind? Minds can do calculations, but so can chemicals, as in calculators and computers. Note that the need for humans to program the calculators doesn't alter the answer to the question, what is the nature of the substrate that is performing the calculation? Programming is irrelevant to that question.
If we dont have free will and the ability to go "outside' the box of simple causes and effects, then we would not have that potential.
Why reasons can you offer to show that the above is true?
You claimed that numbers have to be instantiated in a mind, my point is that they dont in order to exist. I am not sure why you brought it up and how it relates to free will. I guess my point was that like numbers minds are nonphysical but they still exist and therefore not bound by causes and affects. And since we are not bound by causes and effects then we have free will.
I don't see how your conclusion in your last sentence follows from the sentence beforehand.
Ideas for are not limited, so that means our minds are not limited, thereby providing free will.
How does a mind not being limited somehow create free will? A computer can generate a random number from the entire set of infinite numbers, which makes it not limited, yet you wouldn't call the computer free.
They may have some minor pieces of puzzle
On what objective criteria does you evaluate animal's pieces of culture to be minor?
but they do not have all the elements that make up a true culture
Agreed, but without the implications of the No True Culture fallacy.
and those elements require a free will.
How so? What is in the definition of culture that requires free will?
Genes are physical entities, therefore are controlled by cause and effect, minds are not, so our minds can override our genetics.
This does not engage with the specifics of the point to which it is responding, and merely re-asserts your claim (minds are not controlled by cause and effect).