virtualbox.org

Hello I need to run many VirtualBox, however I don't know which is the most important hardware that I should focus on, let's say that I'll use non-gpu (no games, no graphic software, no 3D) but only applications that perform mathematical operations on these virtualbox. I want to purchase a PC, but don't know on which hardware I should invest my money, do you have any ideas ?

Always go for the biggest bang for you buck processor you can afford and the biggest amount of RAM. Intel based seem to work better with VirtualBox. Make sure that you get a processor that supports EPT as this makes a difference as well.

Calcualte how much ram you want to assign to all vms + ram you need for host os = ram you need.
Also consider +32 MB ram for each vm you run for virtual graphics adapter + about 60 MB, but that depends what os you plan to run on a vm.
For cpu you need to find out if application you want to run supports multiple cores/processors. MB and CPU must support VT-x/AMD-V.
I would concentrate on ram and cpu. Also find out if that software create large data files so you could assign right vhd capacity and vhat type of disk you should run it on (SATA, SAS, SSD) depending of how much data i/o is needed for that software.