Both temperature scales are (thankfully) rational. Some physicists have been dabbling in complex temperatures, but thankfully most of us don't need to know anything about them.
Celsius used two very reproducible tresholds (freezing and boiling points of water), associated them to two very easy to remember values (0 and 100), and defined his scale according to them.
The way Farenheit got to his scale seems really less practical to me, from Wikipedia :
"Fahrenheit proposed his temperature scale in 1724, basing it on three reference points of temperature.[9] In his initial scale (which is not the final Fahrenheit scale), the zero point is determined by placing the thermometer in brine: he used a mixture of ice, water, and ammonium chloride, a salt, at a 1÷1÷1 ratio. This is a frigorific mixture which stabilizes its temperature automatically: that stable temperature was defined as 0 °F (−17.78 °C). The second point, at 32 degrees, was a mixture of ice and water without the ammonium chloride at a 1÷1 ratio. The third point, 96 degrees, was approximately the human body temperature, then called "blood-heat".[12]"
Sorry, mathematician joke.