How hard is it to succeed in research after an adviser's death midway through PhD?
In academia, as everywhere, life happens.
Fortunately, a lot of people understand this.

It will definitely be harder to succeed when your advisor has passed away than if your advisor had lived.  I suspect, however, that it will be much easier than if you had a falling out with your advisor, which has been addressed in a number of different questions on this site.

It sounds like your institution is doing the best it can to offer you options for getting new advising, and that those options are not so bad.  It is also the case that you are reaching the point in your program where you would in any case need to start reaching out to build strong relationships outside of your home institution.  Where your advisor might once have helped bootstrap your connections, you have instead your institution's offer to help you meet with other mathematicians.  This is a big juncture in your life and career, and everything changes.  Despite the fact that the original quote is false, a crisis really is both danger and opportunity.

Also, make sure to take care of yourself.  You just had somebody close to you die, and that might affect you in a lot of ways, including interfering with your ability to work.  If you aren't already doing so, I would suggest proactively starting to see a counselor to help you navigate any psychological challenges that may come up: even if you don't feel you are having troubles now, they may start and it is better to catch them early, rather than having troubles that you might attribute to your new advising and then realizing six months down the road that it was actually your reaction to the death.