This is a too routine and smug to be really enjoyable fluff, but some themes are amusing, especially for a 1906(?) novel.
The difficulty is that the parts are too disparate, and the highflown lectures by the protagonists stop the action and display the patched seams between the parts, attempting to combine the science of the day with plot-advancing nonsense. There are elderly and combative mathematicians, one of whom gains the ability to travel in 'the fourth dimension', but the author gets too confused about what an axiom is to let the character rumpus in any disbelief-allowing way. The 'fourth dimension' is sometimes timelike; the Mummy of the title is a prior life of the rich, degreed Miss Nitocris; the Mummy committed murder-suicide to avoid an evil arranged marriage, and in 1906 all the characters are trotting through their parts again. Miss Nitocris ascribes romance simultaneously to 'affinities' between souls who always have been engaged, and to Natural Selection that improves the race. I can't even think how that would work. Monads in the gonads, I guess.
The evil guy is reincarnated as a Russian tyrant, and there's an American heiress who has a bachelor's degree and can drive, which is clearly quite dashing for the time; but it all bogs down in these annoying sludges of badly-digested classist/racist pop scientism.
Project Gutenberg etext #19231
So wrote clew in Fiction (20th c.).