I was a math major undergraduate (alas, not at an Ivy League school), and I found the math background to be useful for the LSAT, for law school, and for the practice of law.
Not because I do linear algebra on the job, but because math, more than anything else I know, teaches dispassionate and methodical analysis. And, as far as I am concerned, "thinking like a lawyer" just means that you treat everything like a math problem: ignore the real world implications, and show your work. This is doubly true in law school, where the work counts far more than the answer.
In actual practice nobody wants to see your work anymore, but if you don't go through the full process your answer will be worthless. A mathematician is not distracted by appearances - a "6" with sparkles on top is still just a "6." In that same fashion, a good attorney sees the facts and the law for what they are, not what he would like them to be, or what somebody else says they are.
Moreover, while it is unlikely* that you will be doing complex analysis on the job, most lawyering involves money, and money means accounting and numbers. So while your math-phobic colleagues freak out at the elaborate debt service coverage ratio calculations, you can view it as simple algebra. Math is everywhere, and that includes the practice of law.
*but it does happen. My office whiteboard is currently filled with complex analysis equations for a client project, and I am not an IP lawyer. Math does have real-world applications, and those real-world applications need lawyers too. Over the years I have had opportunities to directly apply various math and quasi-math disciplines, including calculus, sequences, trigonometry, geometry, vector analysis, complex analysis, and, of course, algebra, to various client projects. Required? No. Nice bonus? Absolutely.