Of all the constructions of the reals, the construction of the surreals seems the most elegant to me.

It seems to immediately capture the total ordering and precision of Dedekind cuts at a fundamental level since the definition of a number is based entirely on how things are ordered. It avoids, or at least simplifies, the convergence question of Cauchy sequences. And it naturally transcends finiteness without sacrificing awareness of it.

The one "rumor" I've consistently heard is that it is hard to naturally define integrals and derivatives in the surreals, although I have yet to see a solid technical justification of that.

Are there known results that suggest we should avoid further study of this construction, or that show limitations of it?

Of all the constructions of the reals, the construction via the surreals seems the most elegant to me.

It seems to immediately capture the total ordering and precision of Dedekind cuts at a fundamental level since the definition of a number is based entirely on how things are ordered. It avoids, or at least simplifies, the convergence question of Cauchy sequences. And it naturally transcends finiteness without sacrificing awareness of it.

The one "rumor" I've consistently heard is that it is hard to naturally define integrals and derivatives in the surreals, although I have yet to see a solid technical justification of that.

Are there known results that suggest we should avoid further study of this construction, or that show limitations of it?