Alpha interpretation in Solow growth model Consider the Solow model (without technology):
$Y = F(K, L) = K^\alpha L^{(1-\alpha)}$
What's the economic interpretation of $\alpha$? Prove and argue the result.

I see it as a share that goes into capital and $1-\alpha$ is the share that goes into labour, but how do I prove this mathematically?
I don't quite understand what you mean by "share that goes into capital", but the common interpretation is that $\alpha$ is the share of income/output spent on capital.

You can show that the following way:
Since the factors will be compensated according to their marginal products, under the assumption of competitive markets, we have (for capital): 

$$
\frac{\partial Y}{\partial K}= \alpha K^{\alpha-1}L^{1-\alpha}=\frac{r}{p},
$$
where $\frac{r}{p}$ is the real rent.

So the amount of income spent on capital is equal to price times quantity, which in this case is,
$$
\frac{\partial Y}{\partial K}\frac{K}{Y}= \alpha K^{\alpha-1}L^{1-\alpha}\frac{K}{K^{\alpha}L^{1-\alpha}} \\
\frac{\partial Y}{\partial K}\frac{K}{Y}= \alpha
$$

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