I defined operads in 1971, and they are ubiquitous. I defined $E}_{\infty$ ring spaces and $E}_{\infty$ ring spectra soon afterwords. The latter are the starting point of derived algebraic geometry. That was a half century ago. All of the old mathematics seems to be correct. However, answering a question Agnes Beaudry asked me in 2023 has led me to the conclusion that this idiot got the definition of $E}_{\infty$ ring spaces conceptually wrong.

I will explain what I now think is the right way to think about ring theory operadically. The new theory is very elementary and should also have been understood a half century ago. It leads to an operadic definition of bipermutative categories that generalizes equivariantly and leads in turn to a concrete construction of commutative ring $G$-spectra in equivariant algebraic $K$-theory. The talk will focus on the elementary combinatorial foundations. The new theory also leads to many open questions and new directions that I may mention.

I defined operads in 1971, and they are ubiquitous. I defined $E}_{\infty$ ring spaces and $E}_{\infty$ ring spectra soon afterwords. The latter are the starting point of derived algebraic geometry. That was a half century ago. All of the old mathematics seems to be correct. However, answering a question Agnes Beaudry asked me in 2023 has led me to the conclusion that this idiot got the definition of $E}_{\infty$ ring spaces conceptually wrong.

I will explain what I now think is the right way to think about ring theory operadically. The new theory is very elementary and should also have been understood a half century ago. It leads to an operadic definition of bipermutative categories that generalizes equivariantly and leads in turn to a concrete construction of commutative ring $G$-spectra in equivariant algebraic $K$-theory. The talk will focus on the elementary combinatorial foundations. The new theory also leads to many open questions and new directions that I may mention.