IMac – How to operate 2 XServes and 2 iMacs from 1 keyboard and 1 mouse (both bluetooth)

The trouble is with the devices, the Apple mouse and the keyboard in your case. They don't pair with more than one BlueTooth host at a time. You need a BlueTooth host that's "central" to both Macs if you want to use them.

You can find KVM switches that have BlueTooth host receivers in them. For example, the Zonet KVM3322W (dead link) worked over USB and provided BlueTooth receiver capabilities. I cannot attest to how well that would work. Presumably you'd pair the keyboard and mouse with the BlueTooth receiver in the KVM instead of in either Mac and then using the keyboard shortcuts, switch between control of the Macs who are connected to the KVM via USB. How the Macs would respond to the BlueTooth receiver in the KVM coming and going as you switched between them is unclear to me. Could be they handle it just fine.

The other option is to seek out BlueTooth accessories that allow themselves to be paired with more than one host. And then switch between those hosts from hardware keys on them. For example, this keyboard+trackpad combo from IOGear supports switching between 6 BlueTooth hosts. So you'd pair it with both Macs and the use the keyboard switches to decide which one you were talking to at any point in time. That, to me, seems like the more reliable approach. Of course: now you're stuck using IOGear's keyboard instead of the Apple peripherals.

The main thing to tackle is booting up the xServes. Luckily, Intel xServes (which yours should be if they're running 10.6) have Lights-out-Management (LOM) that should support this sort of thing (all Macs support Wake-on-LAN, but that only works on a local network).

Apple Remote Desktop (ARD) has support for this. It looks like you'll need to forward a few ports (looks like 623 for the LOM, and then a bunch for ARD - do a search), unless you have some sort of VPN access to your home network.

The basic method will be, use ARD to power up your xServes, then remotely connect via ARD or a VNC client, build your Mathematica app and run it. Then shut down the xServes.

If you have a Mac with you, all this can be done via ARD, but if you want to do it with an iPad, you'll need your desktop Mac running whenever you want to remotely access it. The process there would be to enable Screen Sharing (in the Sharing panel of System Prefs), forward the appropriate ports, then use an app like Screens to connect to your desktop Mac, run ARD and Mathematica remotely on it, and do the above.

If you don't have your desktop Mac running all the time, you could in theory use Wake-on-LAN to turn it on, then access it with Screens, but that requires some other device to be always on, remotely accessible and capable of sending the WoL packet to the Mac (some routers are capable of this, typically with 3rd party firmware).