The guiding principle of the IAS Medal Lecture and of the research it covered was that searching mathematical analysis, depending on good measurements, must underpin sound biochemical conclusions. This was illustrated through various experiences with the amino acid dehydrogenases. Topics covered in the present article include: (i) the place of kinetic measurement in assessing the metabolic role of GDH (glutamate dehydrogenase); (ii) the discovery of complex regulatory behaviour in mammalian GDH, involving negative co-operativity in coenzyme binding; (iii) an X-ray structure solution for a bacterial GDH providing insight into catalysis; (iv) almost total positive co-operativity in glutamate binding to clostridial GDH; (v) unexpected outcomes with mutations at the catalytic aspartate site in GDH; (vi) reactive cysteine as a counting tool in the construction of hybrid oligomers to probe the basis of allosteric interaction; (vii) tryptophan-to-phenylalanine mutations in analysis of allosteric conformational change; (viii) site-directed mutagenesis to alter substrate specificity in GDH and PheDH (phenylalanine dehydrogenase); and (ix) varying strengths of binding of the 'wrong' enantiomer in engineered mutant enzymes and implications for resolution of racemates.