I just read an interview with Mario Livio who wrote a book entitled "Is God a Mathematician?" His thinking is so stupid, with such basic misunderstandings, that I wanted to respond to them. Interview in:
In the interview Livio claims that math is simply a human invention because:
"Let me start with this silly idea - the isolated jellyfish. Imagine
that all the intelligence resided not in humans, but in some isolated
jellyfish at the bottom of the Pacific Ocean. This jellyfish - all it
would feel would be the pressure of the water, the temperature of the
water, the motion of the water. Would this jellyfish have invented the
natural numbers - 1, 2, 3, 4, 5, and so on?"
His general claim seems to be that math is a human invention because: "Humans at some level chose the mathematical tools based on them being suitable for the particular problem." And when asked "How is math different from other human inventions, like art?" Livio answers: "Mathematics is somewhat special in that it has an incredible longevity."
There is an obvious misunderstanding in his argument - there is a difference between making up something and discovering only what you care about. Whether Jellyfish would come up with a different chunk of mathematics is the same, by his logic, as whether a Russian and an American would. Or simply different people have different interest and are drawn to different questions and so will solve different questions. Obviously. An algebraist would have a different math, so to say, than an analyst. This question has no bearing whatsoever on whether math is true and whether it is objective. We find out the chunks we need but his argument accepts it all as a discovery.
Moreover his argument seems especially stupid coming from a scientist. To ask whether the scientific rules are true or not is a very different question from whether if we were living underwater we would uncover other theories before uncovering Gravity. The order and interest of the theories have nothing to bear on the basic question.
In any case his arguments in some form could have been interesting 150 years ago, but he's a bit late. When it was discovered, more than a 100 years ago, that there are other kinds of geometries and not simply Euclidean that was revolutionary. Math just appropriated the different kinds into it, and now all of them coexist inside math. It is not whether math is true or not anymore. Even finding different axiomatic bases for mathematics where it only works inside them, even that was appropriated into math.
Could one ask whether math is true? Yes. One can ask whether 2+2=4 or whether it is a manner of agreement, and perhaps 2+2=5. The more one really sees how things operate in the mathematical world the more one feels comfortable asking this. Of course the arguments for and against would have nothing to do with Livio's arguments.
Sidenote: the article starts by adding a quote from a "Nobel Laureate," in a manner which reminded me of Layla's recent post on quoting