Relation between Luhn Algorithm and Level sets

Abstract

The Luhn algorithm, a widely used checksum formula, ensures the validity of identification numbers such as credit cards and IMEI numbers by detecting accidental errors. Operating through a simple yet effective process of digit manipulation and summation, it enhances data integrity in financial and technological systems. Though it does not prevent fraud, its efficiency in identifying common mistakes makes it a crucial tool in electronic payment processing. Additionally, the algorithm's mathematical foundation relates to level sets in differential geometry, offering a deeper perspective on credit card number validation. Its continued relevance and public accessibility underscore its enduring impact across industries that require accurate and reliable numeric verification.