We are all taught to accept that units of measure have to be defined. The International Bureau of Weights and Measures (BIPM) is the keeper of the kilogram and meter, and the Consultative Committee on Units (CCU) provides recommendations on how various units are to be defined. In their 2005 report, the CCU stated,

2005 CCU Recommendations

The July/August 2011 edition of IEEE Potentials contains a paper with the title, A Methodology to Define Physical Constants Using Mathematical Constants.

The concept described in the paper identifies a fundamentally different way to apply mathematics to physical law. Those with IEEE membership or associated with an institution that has a membership can read/download the paper from: A Methodology to Define Physical Constants
The paper is on the second page of the Contents.

For those that do not have an IEEE membership, the postprint can be read/downloaded from: Methodology

The IEEE publication has a classic image of Euclid on the first page of the article, which IEEE slightly altered; the technical material is identical.

The concept uses the relationships of a fundamental physical law and basic geometry to define two basic units of measure.

For several years I carried on discussions with various individuals about the concept of mathematically defined units. One very technically accomplished individual stated the following about SI units:

The values defined in the Methodology will not resolve the remaining dimension problems with G, hbar and epsilon0, but they provide a non-arbitrary starting point.

I have attempted to communicate with BIPM, but they never respond.

Basically, the concept presented in the paper affirms that the mathematics that we use has a direct link to physical law. If the correct values are selected for the physical law-mathematical relationship, it allows the base units of measure to be identified.