New proof dramatically compresses space needed for computation

Here's the gist:

For nearly 50 years theorists believed that if solving a problem takes t steps, it should also need roughly t bits of memory: 100 steps - 100bits. To be exact t/log(t).

Ryan Williams found that any problem solvable in time t needs only about sqrt(t) bits of memory: a 100-step computation could be compressed and solved with something on the order of 10 bits.

Huh? What did any of those theorists think about the phrase "time/space tradeoff"?

They were likely the ones that invented the phrase.

I'm not convinced of that if they thought that s=O(t/log(t)) where s=space (bytes or similar) and t=time (clocks, steps, etc.) I dunno about theoretical limits but in practice, there's at least 1-2 orders of magnitude to be exchanged between space and processing time.