Q:

How can an an ant lift 50 times its own weight and pull 30 times its weight?

According to many sites like this one, an ant can apparently  lift 50 times its own weight and pull 30 times its weight. Is it true?
Can it be proved using physics? Though most sites agree that an ant can lift many times its own weight, not all agree with exactly how many times its weight. The explanations provided if any are usually vague and do not use specific numbers. Can a specific numerical value be calculated?
Secondly, how is it possible for the ant to pull 30 times its weight? I find it unbelievable. Can anyone explain this? 

A:

This is an example of "scaling laws". Have a look at http://hep.ucsb.edu/courses/ph6b_99/0111299sci-scaling.html - for once Wikipedia doesn't have a good article on the subject.
The strength of a muscle is roughly proportional to the area of a cross section through the muscle, so strength is roughly proportional to size squared. That's why I'm a lot stronger than an ant. However the weight of e.g. a boulder is dependant on the volume, so it's proportional to size cubed. So as you increase size, the weight of the boulder increases faster than my strength does. Or to put this another way, as you decrease size your strength decreases more slowly than the weight does. That's why small creatures can lift boulders that are large in proportion to their size.
Whether an ant can really lift 50 times it's weight I don't know, but it can certainly lift many more times it's own weight than I can. The same sort of argument applies to all small creatures. For example it's why a flea can jump much higher relative to it's body size than I can, but I can still jump higher than an elephant!
Do have a look at the link because it goes into a lot more detail than I can here.

A:

Strength
Strength goes like area.
Intuitively, the cross sectional area of a muscle counts the number of muscle fibers (actually, myofibrils).
Thus, $S\propto A \propto L^2$.
But mass goes like volume, $M\propto V\propto L^3$.
Therefore strength is proportional to the $2/3$ power of mass,
$$S\propto M^{2/3}.$$
This equation expresses the fact that an increase in mass does not give a proportionate increase in strength.
For example, adding $25\%$ to your mass will increase your strength by about $16\%$, assuming your body composition and neuromuscular skills don't change appreciably.
Relative strength
In addition, we find that relative strength, strength per unit mass, goes like $M^{-1/3}$,
$$\frac{S}{M} \propto M^{-1/3}.$$
Thus, after adding $25\%$ to your mass and getting $16\%$ stronger, you are actually $7\%$ weaker in terms of relative strength.
These facts are known, at least intuitively, to all athletes.
In strength sports, formulas such as these are used to compare athletes across weight classes.
For example the Wilks coefficient is used to ``normalize'' weight lifted.
(In fact the Wilks coefficient is roughly $(50/M)^{2/3}$, where $M$ is the lifter's mass in kilograms.)
The ant
From the above we can also see that relative strength is inversely proportional to $L$,
$$\frac{S}{M} \propto L^{-1}.$$
Thus, a man a hundredth the size of a normal man would be one hundred times more strong in terms of relative strength.
In other words, if a man can lift his bodyweight, the same man a hundredth the height could lift one hundred times his bodyweight.
(What if a normal man were to grow one hundred times in height?
He would be one hundredth as strong in terms of bodyweight, and would be crushed under his own weight.)
It is thus not surprising that an ant can lift many times its bodyweight.
Precisely how much is more a question of biology than physics, since we are comparing not only organisms of different size, but totally different morphology.
Certainly an ant can pull, in relative terms, much more than a human.
In fact, ants have hooks on their feet.
Think of our tiny man who can lift one hundred times his bodyweight dragging himself across a rough surface with climbing gear.
It would not be surprising if he could pull on the order of one hundred times his bodyweight.
Figures
You will find below a plot of strength vs mass and relative strength vs mass, in natural units.

