You guys are really pushing my English skills here. Alright, let's see what I can do...
Genius is intelligence, as in the ability to perform above average cognitive processes, whereas madness is the tendency to deviate from the norm not with intelligence, but through sheer disregard for reason and common welfare. One who is a genius can be mad, just like how someone who is mad can also be a genius. They are two independent character traits that involve the commonality of deviation from the average. What is being deviated from, however, is the critical difference. A genius is someone who is very skilled at a particular field: someone who is intelligent and can find ways to use his/her intelligence in a constructive and useful manner. One who is mad, however, is someone who suffers from mental instability. The degree of madness can often vary just as the way the aforementioned madness can reveal itself differently. Someone who can play Beethoven's 3rd on the piano while blindfolded is a musical genius. A scientific genius can perform difficult physics problems in his/her head. One could say the my having jumped off of a cliff into wavy waters below was madness. One could also argue that Hitler was mad because of his genocide.
Essentially, geniuses and mad people are both within the population of the exceptional. The difference is that a genius is simply one that has intelligence and the ability to use it, whereas one who is mad is simply someone who deviates from sensibility.
How did I do? 🙂 Not bad for my second year using English, huh?