From the title I thought this was going to be about a team member who died, glad that's not the case.

He's a bit arrogant but

In any relationship, whatever irritates you at the outset has the potential to become a real source of resentment later, so be clear about where your boundaries are.

A lot depends on how much work this potential partner is proposing to put in before bringing in the big bucks and potentially cashing out. But putting all those meta considerations aside, if you want 30%, he wants 40%, and you really feel he has something you don't which would be hard to find elsewhere, 33 1/3% seems like the natural inflection point.

I would look at it like this, as 2 entities. There was an entity that developed this IP, this algorithm. You own 100% of that entity and the IP. If you go in with this guy, there is a new entity. You two need to do slicing pie with the new entity- arrogant smart people have a way of not putting in the work, so you need a mechanism that will accumulate equity by effort. Probably your hours are equally weighted in that accumulation. And then you need to value the contribution of the algorithm/IP to the new entity. There are ways of valuing that contribution. It could be valued as equity, or it could be a license (so there is an income agreement). If equity, maybe it is 50% of the new entity, maybe it is 25%, maybe it is 75%. It really depends on a rational valuation of that algorithm in the context of the competitive space. My honest opinion, I use parking apps, your particular innovation (no disrespect, it is an achievement, for sure) is not a game changer to me, so I would put it at 25%, but I don't know really how to structure the value of the space. But you should have an analytical opinion (not based on your hours you put in, based on how the algorithm changes the dynamics) about the importance of the algorithm to the proposition the new business has, relative to the work the two of you would do together, which should use an accumulation mechanism for allocation.

In spite of whatever number you choose, remember: 4 years vesting with 1 year cliff

If you want someone on your team, give them what they’re worth. Don’t base it on what you think you’re worth, but rather on what you think they are worth to you

If you think he’s overvaluing himself, showing him the door is the best way to communicate that

IF to hire an equally smart engineer/exec would cost you more that the actual market value 10% of your company would equal, I would probably give him 40%.

If you’re doing this to get into YC then make his stake dependent on actually getting into YC

EDIT: I meant I wanted to give him 30% but he wanted 40%

I'd be surprised if this app has legs but what do I know.

30% is too rich IMO. There's no correct answer so I doubt you'll be able to get one. Given that the co-founder is someone you just met, not a long time acquaintance or friend that you know you can work well with and you know their skills, I would simply look for another co-founder. There is a YC matching program if you want to do that.