> the execution was vastly more difficult than the idea

But the execution was fully routine, that is, low risk.

> couldn't have been done by a startup

Right. But maybe in the future, and because of my main point: It's fully possible for the planning to be rock solid and lead to a successful product with low risk. That's the main point -- it really is possible, indeed, in applied science and engineering, nearly standard.

That the examples were not commercial products need not detract much from the main point -- again, we can plan just on paper and have a low risk, high payoff project.

But now we have enhanced opportunities: The math I assumed can be cheap, for someone with an appropriate math background, dirt cheap, fast, fun, easy, and low risk. Then for the product, I assumed that that is just software. So the guy who does the math also does the software -- we're still in the low budget area. Next, the product needs computer hardware, but now enough computer hardware to execute 100,000 lines of code can be less than $2000.

If the product is just a Web site supported by ads, then for just a focused start, where I agree with Altman, might do quite well: E.g., maybe the start up sends Web pages of 400,000 bits per page. Each page has on average 5 ads. From the Mary Meeker data at KPCB, maybe get paid $2 per 1000 ads displayed (CPM = $2). Maybe have an Internet connection with 25 million bits per second upload bandwidth. Maybe half fill that 24 x 7. Then the monthly revenue would be

2 * 5 * 25 * 106 * 3600 * 24 * 30 / ( 2 * 400,000 * 1000 ) = 810,000

dollars. That's enough to fuel organic growth.

So, on average, how many Web pages sent per second?

25 * 106 / ( 2 * 400,000 ) = 31.25

Depending on the project, that
might take several computers at $2000 each, but
if early on send just 1 page a second, and for some projects early on one computer could do that, and get monthly revenue of

1 * 2 * 5 * 3600 * 24 * 30 / ( 1000 ) = 25,920

dollars
so that in one month have free cash flow enough to buy computers enough to send 31.25 Web pages a second.

The 31.25 Web pages a second is a lot of Web pages per month, is

31.25 * 3600 * 24 * 30 = 81,000,000

So how to justify this? Well, as we assumed, the first good or a much better solution for the problem is a "must have". The problem has been selected so that we can attack it essentially just with math. We do the math, as theorems and proofs, and check the proofs carefully -- fairly routine and low chances of errors for a well trained pure/applied mathematician. We convert the math to software and check the software -- again, fairly routine with low risk of errors. Now we have the product, and it is a "must have". Then we go to Altman's lecture and use what he said about viral growth. And we use the assumption that the problem is such that many people want the solution (I hope I made that assumption clear also). What's left to do? Get the checks from the ad networks. Yes, very much do need to meet the assumptions, find the solution, write the software, etc., and if can't then return to (1) and try again.

Once I had a project that looked pretty good on the alternative approach, but the software was going to be too much work because I'd need to write a lot of code for a lot of data collection and with too little information about what the APIs and interfaces were or would be. So, I dropped the project. That is, back to step (1).

You are correct that nearly all the successful, famous projects I listed were, yes, routine, but expensive to execute. And for a start up, we need projects that are cheap to execute. Do such projects exist? I believe so.