The true history of mayonnaise is the following. Already in the Viandier, by Guillaume Tirel ("Taillevent", at the beginning of the , 15th century, cooks were preparing sauces called "rémoulade", based on mustard, with a hot or cold liquid.
Later, cooks added egg yolk, because we know how such food ingredient is improving the flavour.
Then, in the 18th century, and we don't have details, someone forgot the mustard, and got an emulsion similar to the cold rémoulade based on mustard and oil, but with a much more delicate flavour, because the mustard is somehow acrid. The sauce mayonnaise was created, and it was a wonderful discovery!
Alas, at the very beginning of the 20th century, the book entitled Guide culinaire (which was written by Philéas Gilbert, Emile Fetu and Auguste Escoffier, but the last one was alone on next editions) proposed to used mustard in the mayonnaise, whereas Gilbert correctly said that there should be no mustard in one of his own book published in 1934. This was a real mistake, and this is why I hate this wrong book, showing the utmost ignorance (mayonnaise is not the sole mistake). Worst, M. Grégoire and M. Saulnier, students of Escoffier, popularized the mistake... so that, today, many cooks confuse rémoulade and mayonnaise.
But it's not difficult! In order to make a mayonnaise, you need one egg yolk, one teaspoon of good wine vinegar, salt, pepper, and oil that you add drop by drop while whisking.
But no mustard, otherwise you get a rémoulade, not a mayonnaise !