[rosser]

Slight clarification:

The key thing is that you want the delta (between exercise price and FMV) to be as small as possible — at the time of exercise.

If you exercise any time but (effectively) immediately upon being granted your ISOs, you're liable for the taxes on the delta between your strike price and the FMV at time of exercise. If you exercise immediately, that should be zero. But it's that delta — between strike price and FMV at time of exercise — that can factor into AMT in a particularly surprising, and often very unpleasant way.

Forward-exercising and making an 83(b) election also starts the clock ticking on capital gains tax. Effectively, if you're starting at a brand new unicorn, and exercise your entire grant on Day 1, you'll only owe Long-Term Capital Gains tax (15%, instead of regular income rates — or, worse, AMT) on the entirety of your (initial) option grant, the day you hit your vesting cliff.

IANA Tax Attorney, or Accountant. Caveat lector.