Is studying mathematics chronologically a good idea or not and why?

There is little intrinsic value to studying mathematics chronologically, unless you are interested in the history of mathematics, as opposed to purely mathematics itself. You reasoned that learning the history of physics is interesting and can help 'flavor' the learning. Of course, the history of physics is not the same as that of mathematics -- I would consider the history of physics a little more interesting.

It is reasonable to study mathematics by moving gradually from the basics to the more advanced topics. It makes sense that this naturally carries you throughout the ages, as the basic ideas are older (at least in part) -- but there have been important revisions even to basic mathematics in recent history (for example, Zermelo-Fraenkel Set Theory). If you wish to simply build a good understanding of mathematics, then I suggest you disregard the history and simply focus on learning the math itself.

I don't think so, here are the reasons why I think it's not:

First reason: mathematical methods for pedagogy have advanced through time. A lot of effort has been put to develop mathematical content which is useful for learning.

Second reason: efforts during the last centuries have developed new tools which are useful for analysing mathematical knowledge, simple examples include algebraic notation, the definition of a function, mathematical notion, and other things like category theory or abstract algebra which to my eyes are tools which are by themselves useful for learning new things. These tools give you a broader vision and "boost" you learning experience.

Third reason: Just because something was discovered a long time ago does not mean that it isn't going to be really complicated. For example: some Greek theorems in geometry are really complicated, while some basic results in graph theory are a lot easier to grasp (at least to my eyes).

EDIT: Of course, I think learning the history of mathematics is not only very important, but also very fun. I'm just saying learning mathematics in chronologically order is going to be very hard.(you're going to understand Ferrari’s formulas before knowing a graph has an even number of vertices with odd degree)

For studying math for the first time ? No ! For deepening one's understanding of math not usually taught in school ? Yes ! E.g., I've tried once, for instance, to find a parametric form for the sum of two cubes, only to find out later, (using Google, no less!), that Euler has already done it $300$ years ago! And the list of pointlessly wasted time and effort could go on and on and on, but I think suffice it is to say that quite a lot of it could've been spared, were I only to have known about and/or have had access to such vast and hidden treasures of mathematical riches ! Not to mention the fact that Archimedes more or less discovered calculus some $2,000$ years before Newton ! :-)