Edit - better phrasing/summary:
Maybe this phrasing helps "the same object expressed in different ways". That's one meaning behind 'equals'. 10 = 1+...4 --> 10 really is 1+...4. So if mathematically we can treat the same object in multiple ways via equals, and holism and Maudlin are saying: one way you cannot treat an object is just summing its separate parts to equal the whole, is there a conflict in something like the 10 = 1+...4 example, where LHS and RHS really are the same? Is the mathematical structure of equals and plus preserving holism?
I'm not trying to be provocative. I just wanted some perspective (good and bad) on this thought I had.
In mathematics, 1+2+3+4 = 10 means both sides of the equals sign are the exact same in any mathematical context. Or said differently, equal operations done to both sides will preserve the their equal relation. If left and right have some kind of difference, it is not picked out in the math. For any operation, each side will have the same mathematical behavior. In the realm of mathematics, = means each side can be swapped for all mathematical purposes. And I think even further, each side really is the other. 10 really is 1+2+3+4 and really is 2*5, etc. Just like an equation can be thought of as a function, it also has a geometric interpretation too. Neither is more correct than the other.
But for holism, we often see it summarized as "the whole is greater than the sum of the parts", a paraphrasing of Aristotle I believe. And a quote by Tim Maudlin "The world is not just a set of separately existing localized objects, externally related only by space and time. Something deeper, and more mysterious, knits together the fabric of the world. We have only just come to the moment in the development of physics that can begin to contemplate what that might be." from Interpreting Bodies.
Don't I have a plain as day conflict when I say 1+2+3+4 = 10 in the perspective of holism? Maybe mathematically they are no different, but in the physical world holism says there is some kind of difference between the parts and the whole. It seems like no physical objects can be split into any constituent objects in regards to holism, yet splitting is a mathematical operation (- and +). Objects that live in the physical world, as Maudlin says in his quote can't be so easily split. Whatever the universe is, it cannot be gotten to by thinking about individual components of it.
And could Euclid when he said "the whole is greater than the part" (Euclidean property 5 I believe), been getting at this idea? Was he avoiding saying "the whole is greater than the sum of the parts" deliberately, putting it in a milder form? Because mathematics does not make the distinction holism (of the physical world) does.
Those restrictions do not seem to enter into math. I can take any whole object, say a circle, and mathematically say it really is certain numbers added together.
Are =, +, etc possibly disconnected from the physical world?
*If this is all too vague please let me know. I don't have a great deal of mathematical philosophical knowledge but I hope I made a point.