Pythagoras (569BC- 475BC) - discovered the numerical ratios which determine the intervals of the musical scale. Theses are the seven tones of the C Ionian or C Major scale. He was a fine musician, playing the lyre, and he used music as a means to help those who were ill.

From the 7 notes of the Ionian scale came the seven modes, all inversions of C Ionian.

Here are the seven modes in C, in the open position.

A mode is when the characteristic scale tone is stressed.
A scale is when all tones are equal.

Once you master the open position for any given scale the hard work is navigating the many possibilities along the fingerboard. Here is a lesson on Navigating the Major Scale using the Six Secrets of Ukulele Fingering of that can be applied to any scale or mode.