At the time, the Hewlett-Packard CEO wanted to be sure I knew he hadn’t temporarily lost his mind. He had just announced a $13.9 billion deal to buy EDS, a tech outsourcing company, and he was well aware that EDS’s 140,000 employees would sink HP’s profits unless he slashed costs. “I already know the math,” he told me more than once.

Now we do, too: Hurd will cut 24,600 jobs over three years, half of them in the U.S., for an annual savings of $1.8 billion. Or at least, that’s what he told a gathering of Wall Street analysts on Monday. I expect that when all’s said and done, he’ll have cut a bit more than that.

What we don’t know is how the EDS/HP combination will stack up against entrenched competitors like IBM , CSC , and dozens of Indian firms that compete for contracts to handle back-office technology functions. During his presentation, Hurd didn’t get into details like how HP will expand its customer base, offer high-end consulting and mollify EDS partners who worry about getting pushed aside now that HP is running the show.

Instead, he and his lieutenants mostly stuck to big-picture cost cuts and opportunities to sell more HP gear through the services organization. They promised that HP Services would hit operating margins of 9-10% in fiscal 2009, and 11-13% in 2010. “Longer-term, we believe the services segment has the potential to deliver 13-15% operating margins,” said Chief Financial Officer Cathie Lesjak. “We’re not confused. We know we need to create and deliver shareholder value.”

IBM, meanwhile, isn’t taking any guff from HP. During Monday’s analyst meeting, in a not-so-subtle dig, Big Blue announced a new initiative to move people off of standard server equipment like HP’s, and onto its own System Z mainframes. IBM’s fighting back in other ways, too; when HP closed the EDS acquisition, IBM vice president Michael Svinte sent a rally-the-troops memo to the sales staff. “HP bought yesterday’s model, with a huge labor force in higher-cost jurisdictions,” he wrote. “To catch up with IBM’s current skills and capabilities will take HP/EDS years, if ever. This is our time to capture share!”

And really, Svinte has a point. Even combined with EDS, HP’s services business is puny next to IBM’s – last year IBM recorded $54.1 billion in services revenue and margins near 30 percent, while EDS and HP together managed $39 billion in revenue and far thinner margins.

But on Monday, Hurd & Co. made it clear that they’re not focused on going to go toe-to-toe with IBM just yet. Instead, they’re working on getting their own house in order. Their goals include issuing half of the 24,600 pink slips in the next 12 months, and keeping HP’s other business units chugging along.

If HP can cut workers and stay focused enough to avoid losing business to IBM, it could eventually emerge as a major force in the services business – and Hurd has a record of cutting and growing the company at the same time. During his first year at HP he and his team cut 15,000 workers while overhauling the company’s operations.

When an analyst asked about his expertise at slashing jobs, Hurd was careful to nod to the human cost of cutbacks. “This is a really tough day for us. There’s a human aligned to every one of these actions,” he said. But don’t think that will slow the flow of pink slips. “We’ve had to deal with taking thousands of people out before,” Hurd reminded him a moment later, “and taking them out globally.”

In other words, Hurd still knows the math. And once he trims HP down, he plans to pose a growing problem for IBM.