There isn’t a single inventor and reusable rockets emerged through decades of research.
But: SpaceX was the first to make orbital-class reuse routine and economically viable.
The backing table is on page 8. Falcon 9 is (was, in 2018! It’s only cheaper now.) at $2700/kg to LEO. No one else is below $4k, except… Falcon Heavy.
And I say that as someone that despises Elon and the way he casts his companies as due to his personal technical genius.
Not true. What about STS?
Soyuz-2 capacity to LEO: 8,600KG
Falcon 9 capacity to LEO: 22,800KG when expended, 17,500KG when not.
Soyuz-2 Cost to Launch: $35 Million
New Falcon 9 Cost to Launch: $70 Million
Used Falcon 9 Cost to Launch: $50 Million (cost to SpaceX: ~$25 Million)
Soyuz-2 cost per KG: $4000 (data from 2018)
New Falcon 9 cost per KG: $964 when expended, $1250 when not.
Use Falcon 9 coster per KG to Customer: $893 when expended, $690 when not
So realistically, Falcon 9 is roughly 20-30% the price per KG when new, and dropping to a minimum of 17.25% of the price when used.
Plus you get a larger diameter payload fairing and the ability to launch a payload up to 4X the size.
I'm pretty sure that even used as an expendable rocket, 1/4 the price per KG (if you need the capacity) is a pretty significant improvement. Now I understand why satellite ride-shares are so popular!
Soyuz-2: 12 launches
Falcon 9: 165!