For complicated mathematic calculations, are extra threads or high-speed disk access more important?

Next semester, I intend to start doing research in combinatorics. I have used and fallen in love with Mac computers and Wolfram Mathematica 8, and I intend to get these for use with this project and in college. I will be a Physics and Mathematics double major. Because I have a limited budget, I was wondering which would take priority for my applications: Having a four core processor instead of a two core processor, or having a SSD instead of a hard drive?

For the applications you will be doing, 4 cores would be preferred over an SSD.

Mathematica specifically supports mutli-core processors, and scales extremely well. See here:

http://www.wolfram.com/technology/guide/MulticoreSupport/

You would not expect that much difference from an SSD drive in math and physics applications, which are not processing gigabytes of data from disk.

In scoping your new computer requirements, I recommend you get your professors' recommendations on coping with combinatorial explosion. You will doubtless have to work some problems which have this side effect. If your intermediate storage requirements exceed your available main memory, your system will start disk memory swapping (thrashing), and even simple problems will take "forever" to finish.

When I've had to work such problems with Mathematica in past years, my motto was, "If you thrash, you're dead."

I'm offering this as a separate answer because none has mentioned the elephant on the couch yet:

CPU is impractical to change later on most Macs (anything other than a Mac Pro) but fast external storage can be added later if you have really huge datasets, which would be impractical to store on the internal drives anyway.

For anything that doesn't require high GB to TB of data, the CPUs will be more beneficial, and if you need high GB/TB of data, the SSD won't cut it either, and you'll need an external box.

My recommendation: 8GB of RAM and the fastest CPUs you can afford. If you need very fast disks later to process TB of data, buy an external box with a Thunderbolt interface. (The largest SSDs won't hold that much anyway)