Leiningen's motto is "The human brain needs only to become fully aware of its power to conquer even the elements" (p.81). By believing this motto, Leiningen feels he can overcome anything. On one level, this is true, as rational thought coupled with decisive action can lead to victory. Leiningen is able to control his thoughts, and therefore, he is also able to control his panic in this situation. However, he is also overconfident.

Therefore, his weakness is pride which relates back to his motto. By believing in the above motto and convincing himself he can overcome "the elements" even as the ants approach, he elevates himself to a godlike status that no human can achieve.This raises a very important question: is man the master of his fate? Ironically, in considering his motto, it is not his brain but his courage and physical strength that defeats the ants.

Leiningen's motto in "Leiningen Versus the Ants" is spelled out as he contemplates the natural disasters he has successfully repelled on his plantation:

...Leiningen had met and defeated drought, Hood, plague and all other "acts of God" which had come against him-unlike his fellow-settlers in the district, who had made little or no resistance. This unbroken success he attributed solely to the observance of his lifelong motto: The human brain needs only to become fully aware of its powers to conquer even the elements.
(Stephenson, "Leiningen Versus the Ants," classicshorts.com)

This is a slightly more elaborate version of the classic axiom mind over matter, but without any paranormal intent. Leiningen believes his human intellect and individual abilities to be more powerful than nature's instinctive but unthinking events; Leiningen can act on reason and thought, instead of emotion or instinct, and therefore believes himself able to overcome anything nature can throw at him. Although the onrushing ants are collectively more powerful than Leiningen, he is able to use his reason to unleash an even more powerful natural force on them, and be victorious through thought and rational action.

In "Leiningen Versus the Ants" by Carl Stephenson, is Leiningen's motto true and how do you explain if it is?

In "Leiningen Versus the Ants" by Carl Stephenson, the protagonist, Leiningen, is the owner of a very successful plantation in the jungles of Brazil. He has had success in many areas of his life simply because he refused to fail. 

One day he is warned that a plague of ants, a powerful "act of God," is on its way and he should leave immediately. Leiningen, however, has not yet experienced the ants and is unmoved. He refuses to heed the warnings and leave his home because, he says,

"I use my intelligence.... With me, the brain isn't a second blindgut; I know what it's there for. When I began this model farm and plantation three years ago, I took into account all that could conceivably happen to it. And now I'm ready for anything and everything--including your ants."

He obviously believes two things: everyone is overreacting to a bunch of ants and his plantation will be impervious to the creatures because he has outsmarted them. Leiningen's motto is "the human brain needs only to become fully aware of its powers to conquer even the elements," and he is willing to risk his life as well as the lives of his workers on that motto being true. 

In fairness to Leiningen, he has battled and defeated many other kinds of natural plagues and elements. His belief in his own ability to defeat this plague of ants is so strong that even his native workers--deathly afraid of the ants they have seen before--decide to stay with him rather than evacuate.

The ants were indeed mighty, but not so mighty as the boss. Let them come!

His motto is tested by the ants. They are as formidable a foe as he has ever encountered, and he has to battle them with all of his wits and cunning as well as all of his strength. All of his well planned and ingenious protections for the plantation are tested, and most of them are only mildly successful against the onslaught of devouring ants. 

His "twelve-foot water ditch" serves as a moat and had once seemed like an unconquerable protection; now that Leiningen can see the "thousands of millions of voracious jaws bearing down upon him," however, he feels as if only an "insignificant, narrow ditch lay between him and his men and being gnawed to the bones" in mere seconds.

The ants are a thinking, creative, and determined army which pits itself against Leiningen's cunning intelligence. Every time he makes a move to thwart them, the ants find a way to advance, even though they incur losses. While the potential for physical battle is imminent, what Leiningen and the marauders are actually waging is a battle of wits.

Leiningen's motto is sorely tested as the horde of ants advances, but Leiningen never doubts the outcome.

As the war between his brain and the "act of God'' reached its climax, the very shadow of annihilation began to pale to Leiningen, who now felt like a champion in a new Olympic game, a gigantic and thrilling contest, from which he was determined to emerge victor.

The ants eventually outsmart Leiningen and manage to cross the water. The second line of defense is a moat which he fills with gasoline to thwart their progress, but the ant army maneuvers, plots, and schemes to overcome it until even Leiningen loses his confidence for a time. 

Eventually Leiningen is forced to face the ants physically in order to accomplish one last maneuver to deter the ants. While it nearly costs him his life, Leiningen does defeat this foe by using his brain. His motto does appear to be true, at least for him.