The ongoing search for absolute math has always been done thru various personal bailiwicks (modus operandi). For Newton and Leibniz these were real simple: primes, ultimate ratios, and infinitely small non-zero numbers. The earliest to employ real bailiwicks was Diophantus http://en.wikipedia.org/wiki/Diophantus. He rejected equations with negative or imaginary roots. Archimedes also searched for exact real solutions. For irrationals he bounded them by rational inequalities.

However, in the 20th century Einstein and quantum mechanicists (Planck, Dirac, and others) used imaginary or complex bailiwicks. These were developed a century earlier by Hamilton, et al. Then, Maxwell developed electromagnetism using quaternions (special type of hypercomplex numbers). Later developments separated quaternions to scalar algebras and vector algebras, notably Gibbs and Heaviside. Together with theory of groups, hypercomplex bailiwicks like tensors, spinors, and twistors formed various pseudo-absolute math of modern theoretical physics.

Unfortunately at present theoretical physicists are beginning to concede that two well developed and well tested complex bailiwicks: general relativity and quantum mechanics could not possibly be combined to describe the real bailiwick of Newtonian physics of gravity, which requires a concept for quantum of mass of real bailiwick.