The calculation equations for the minimum teeth number and the minimum modification coefficient of standard involute gears without undercutting are inaccurately described and researched in many studies. These errors are knowledge blind spots in mechanical engineering that have been introduced into the design and manufacturing of standard involute gears. Furthermore, these errors are continually imparted to tens of thousands of students in colleges every yearly. Racks have been incorrectly regarded as the rack-shaped cutters in the derivation of the calculation equations. The theoretical research, numerical simulation and experiments of the undercutting phenomenon of standard involute gears manufactured using rack-shaped cutters are presented. Firstly, theoretical analysis and calculation of the minimum teeth number and the minimum modification coefficient of standard involute gears without undercutting are performed. Subsequently, the correct minimum teeth number and the minimum modification coefficient without undercutting are deduced. The computer simulations of the theoretical calculations are then examined considering the necessary cases. Experiments of standard involute spur gears with z = 10, 12, 17 and 22 are conducted, thereby validating the research. This study addresses the long-standing errors regarding the traditional undercutting phenomenon and provides an effective theoretical guide for gear design and manufacturing.