Can someone identify this math font?

People who already know LaTeX are usually fond of it. People who don't know it typically have a hard time getting started, and they have an even harder time if they want to do any document formatting that's a bit out of the ordinary. In my opinion, there's absolutely nothing wrong with the Equation Editor in MS Word, but I expect most people on this site are LaTeX veterans, and they will disagree with me. I have used both packages fairly extensively, and I'm confident that either of them would do a nice job of your thesis.

The specific font (family) shown in your image is called Computer Modern. It's the font traditionally used with TeX and LaTeX systems. The standard font used by the MS Word equation editor is called Cambria Math. If you want to get the Computer Modern look in MS Word, you have to use a font called Latin Modern. If you want the Cambria Math look in LaTeX, you have to use the "fontspec" package or something equivalent. Here is what your formula looks like with the Cambria font in MS Word:

If you are considering a career as an academic, and you'll be publishing a lot of papers containing mathematics, then learning LaTeX is definitely worthwhile. Outside that community, MS Word is the standard, so learning to use that competently would be more valuable, in my view.

You might find that your university has some sort of thesis template that they will force you to use. So, you may not have a choice in this matter.

I expect this post will generate some heat. People get pretty passionate about (La)TeX, for some reason.

I would highly recommend using something other than Word 2007 for your thesis. You seem to know how to use $\LaTeX$, as you used it to create your post, so why not write your thesis in it? There are a number of guides on the internet for creating documents in $\LaTeX$, one frequently recommended one is this, from the Art of Problem Solving. Although if you are using Word 2007, there is a formula editor.

From the MS Office documentation:

Equations are edited directly from within Word. To do this, click the Insert tab then click the Equation button.

Anyways, the font is Cambria Math. It comes prebundled with Microsoft Office 2003 and above.