Madachy moved to
Dayton, Ohio, and worked for
Mound Laboratories. In 1960 he wrote to recreational mathematician
Martin Gardner, asking whether Gardner knew of any publications devoted solely to recreational mathematics, as he was considering starting such a project. Gardner responded in the negative, including a box containing his correspondence and suggesting Madachy could use the addresses to promote the magazine. In 1967,
Greenwood Press asked him to start the journal again under the title
Journal of Recreational Mathematics, which was published by
Baywood Publishing starting in 1973. He authored several books on recreational mathematics, including
Mathematics on Vacation (1966), ''Madachy's Mathematical Recreations
and Mathematical Diversions.'' He served as the literary agent for
Dmitri Borgmann's
Language on Vacation. Longtime colleagues and co-authors include
Martin Gardner,
Harry L. Nelson, and
Isaac Asimov, and
Solomon Golomb (with
pentominos). He worked with
polyominoes,
prime numbers, and
amicable numbers. He worked developing mathematical concepts such as
cryptarithmetic, used in cyber security applications. He made contributions to Fibonacci series and
narcissistic numbers and devised puzzles using
Fibonacci numbers. His recreational mathematics work included areas in chess,
magic squares and calculator art. Madachy retired from editing
Journal of Recreational Mathematics in 2000. ==In popular culture==