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Professor Elvin Gadd, more known as Professor E. Gadd, E. Gadd (for short), or "Professor Egg" by Mario is, in the Mario series a small and old experienced researcher with knowledge in various domains, especially the paranormal, who can help Luigi and Mario with his knowledge.
In real Mario games, he appears in the series Luigi's Mansion and in the two first games of the Mario & Luigi series (Superstar Saga and Partners in Time).
In SMG4's canon, he appeared in a few bloopers. He is very smart with machinery, as his inventions have been the cause of a plot every once in a while, however, he can also be very idiotic, just like the rest of the cast. It's revealed he often needs Luigi to do experiments or small tasks for him, although Luigi himself has almost never talked about doing this.
E. Gadd is short, wears huge glasses and a lab coat, a bucktooth, and only one curl of gray hair.
Like Toadsworth, he is elderly, which is part of the reason why he trains Luigi to be his apprentice.