Jonathan_Graehl comments on Humans are not automatically strategic - Less Wrong
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Yes. - When I said 'large', I was talking about size in neurons, not physical size. Physical size, within bounds, is mostly irrelevant. (although it does effect latency of course).
No - they really do have more neurons, ~257 billion in the elephant's case. 1 (2014)
According to google, an elephant brain is about 5kg vs a human's 1.4kg. So we have 51 billion neurons per kg for the elephant vs 75 to 60 per kg for the human. This is by the way, a smaller difference than I would have expected.
The elephant's brain has a larger cerebellum than us but smaller cortex: about 5 billion neurons vs our 15 billion ish. Interestingly the elephant cortex is also sparser while its cerebellum is denser, perhaps suggesting that we should look at more parameters, such as synapse density as well (because of course there are many tradeoffs in neural micro-circuits).
Anyway the human cortex's 3x neuron count is a theory for our greater intelligence. But this by itself is insufficient:
Now - is having a larger cortex better for general intelligence than a larger cerebellum? - most likely. It appears to be a better hardware platform for unsupervised learning.
But again the key to intelligence is software - we are smart because of our ability to accumulate mental programs , exchange them, and pass them on to later generations. Our brain is unique mainly in that it was the first general platform for language, not because our brains are larger or have some special secret circuit sauce. (which wouldn't make sense anyway - humans are recent and breed slowly; the key low level circuit developments were already made many millions of years back in faster breeding ancestor lineages)
For humans I was probably just using wikipedia or this page based on older research.