The Intel decision provoked a sharp difference of opinion between Brian Krzanich, Intel’s current chief executive, and Craig R. Barrett, a former Intel chairman and chief executive.

Mr. Krzanich has told colleagues privately that the science fairs were the fairs of the past and had become tilted to life sciences and biotechnology, not primary fields for Intel, according to two people who are not authorized to speak publicly for the company.

Mr. Barrett disagreed. In an email, he said, “you might instead conclude that Intel is a company of the past, just like Westinghouse when they dropped” sponsorship of the national science fair in 1998.

Mr. Barrett, who is on the board of the Society for Science, also said that all of science has become data-driven and computational, so Intel has a stake in nurturing youthful innovators in all scientific disciplines, including the life sciences.

Intel, under Mr. Krzanich, who became chief executive in 2013, has become a major supporter of Maker Faire events, where inventors of all ages showcase their homemade engineering projects. The first Maker Faire was in Silicon Valley in 2006. Last year, more than one million people attended Maker Faire events worldwide.

In 2013, Intel introduced Galileo, an inexpensive computer chip board, which supports open-source hardware and software for the maker and education markets. Its marketing tagline: “The Maker Movement Powered by Intel.” Mr. Krzanich has often been interviewed at Maker Faire events, and he and other Intel managers describe them as incubators for the next generation of engineers and innovators.