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.

> log(t)

log to what basis? 2 or e or 10 or...

Why do programmers have to be so sloppy?

This is very common. Log without further specification can be assumed to be the natural log (log e).