Ted Cruz is the Schrödinger's cat of politicians. He is both eligible and not eligible to be president.
There's no argument – Ted Cruz is not eligible to be president because he was born in Canada. That's according to Mary Brigid McManamon, a constitutional law professor at Widener University’s Delaware Law School. She makes her argument in the Opinions section of The Washington Post.
The Constitution provides that “No person except a natural born Citizen . . . shall be eligible to the Office of President.” The concept of “natural born” comes from common law, and it is that law the Supreme Court has said we must turn to for the concept’s definition. On this subject, common law is clear and unambiguous. The 18th-century English jurist William Blackstone, the preeminent authority on it, declared natural-born citizens are “such as are born within the dominions of the crown of England,” while aliens are “such as are born out of it.” The key to this division is the assumption of allegiance to one’s country of birth. The Americans who drafted the Constitution adopted this principle for the United States. James Madison, known as the “father of the Constitution,” stated, “It is an established maxim that birth is a criterion of allegiance. . . . [And] place is the most certain criterion; it is what applies in the United States.”
On the flip side, Jonathan H. Adler, who teaches at the Case Western University School of Law, argues that Cruz is indeed a natural-born citizen, and therefore eligible to be president:
Ted Cruz was born in Canada. His mother was a U.S. citizen. His father, a Cuban, was not. Under U.S. law, the fact that Cruz was born to a U.S. citizen mother makes him a citizen from birth. In other words, he is a “natural born citizen” (as opposed to a naturalized citizen) and is constitutionally eligible.
To settle the matter, we don't need legal scholars. We need a beaker of poison, a radioactive source, and a sealed box.