I'm sorry, but I just disagree that that's how mathematics is defined and that it doesn't depend on our biology and perception, because we are making those definitions.
A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez. The origin and meaning of mathematics is strongly influenced by cognitive sciene, and thus biology. I've been downvoted, but this is not a totally novel or off the rails idea. It is basically accepted in robotics that embodied cognition is how you get a robot to understand and perceive its environment. Where do you think that idea came from?
A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being
I haven't read that book, but I did just read the wikipedia page for it, for what it's worth. Based on that I feel it's more that they're arguing that the path we've taken and the metaphors we've used while exploring our way to our current understanding of mathematics is based on our biology. Our biology has greatly affected the order we've discovered things and how we understand those thing and how we actually 'do' math day to day, and all that I agree with. It's also very likely that aliens will have taken a very different path and have very different metaphors and proofs for understanding and doing their version of what we call mathematics. Because of this it might very well be very difficult for us to initially understand each others mathematics.
Indeed looking through human history our philosophical understanding of mathematics fundamentally 'is' has changed many times. Yet mathematical truth's we've found along the way have always remained constant (barring errors in calculation or reasoning) even as our understanding of mathematics has changed.
I believe that once we gotten passed all that both us and the aliens will find that, at the core, we both agree on what is "mathematically" true.
I will however also concede that some of the arguments in this thread has made me slightly less sure than I was before, so that is something I guess.
A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez. The origin and meaning of mathematics is strongly influenced by cognitive sciene, and thus biology. I've been downvoted, but this is not a totally novel or off the rails idea. It is basically accepted in robotics that embodied cognition is how you get a robot to understand and perceive its environment. Where do you think that idea came from?