No study of mathematics can be considered complete without attention to its history.
Mathematics without history is soulless
Junaid Mubeen

Nice article on mathematics and history. Thank you. I am not sure that I agree with your title and your last sentence. For me, the soul of mathematics is its purity, elegance, and certainty. The history of mathematics is interesting, but it is not mathematics. There is a debate in mathematics education about contextualizing mathematics to help student learning, by embedding it in real life situations, and I suppose that the history is another form of contextualization. However, actually to do the mathematics and learn it, students need to separate the mathematics from its context. The context is not mathematics, and separating the mathematics from its context is an additional task that weaker students may find particularly difficult. Nevertheless, the history is interesting, and it may inspire the stronger students.