Here's Conway's Game of Life by Arthur Whitney (creator of K):

  life:{3=a-x*4=a:2{+(0+':x)+1_x,0}/x}

I'm guessing a numpy implementation would be between one and two orders of magnitude more verbose, even if you're just comparing the number of operations.

It doesn't quite seem fair to compare numpy to one of the most famous K code golf's ever created, but here is my attempt, 140 characters compared to Arthur's 30, so 5 times longer. Not worry about padding the edges would cut it to 100. I don't think the gap is as wide as you think it is.

  def life(M):
    MP = np.pad(M,[(1,1),(1,1)])
    N = sum(np.roll(MP,(i,j),(0,1))
             for i in [1,0,-1]
             for j in [1,0,-1])
    return (3==N-MP*(4==N))[1:-1,1:-1]

Speedtest (presumably memory bound):

  100 x 100 matrix, numpy  0.2ms, K  0.2ms
  200 x 200 matrix, numpy  0.5ms, K  0.8ms
  500 x 500 matrix, numpy  5.2ms, K  8.0ms
  1000x1000 matrix, numpy 20.0ms, K 36.0ms
  5000x5000 matrix, numpy  0.5s , K  1.2s

Interestingly the K code is designed to return a boolean matrix, but operates much more slowly for me on a boolean matrix compared to an integer matrix, with the result that:

  q)\t klife M

Takes 1.2 seconds whilst

  q)\t klife klife M

Takes 24 seconds. So whilst the idea seems to be that klife is used with scan/over to run a number of iterations, it's actually a bad idea to run it more than once.