His interests include asymptotically fast arithmetic.
He has developed some of the fastest available code for manipulating polynomials over GF(2),[3] and for calculating hypergeometric constants to billions of decimal places.[4] He is associated with the CARAMEL project to develop efficient arithmetic, in a general context and in particular in the context of algebraic curves of small genus; arithmetic on polynomials of very large degree turns out to be useful in algorithms for point-counting on such curves. He is also interested in computational number theory. In particular, he has contributed to some of the record computations in integer factorisation[5] and discrete logarithm.[6]
Zimmermann co-authored the book Computational Mathematics, published in 2018 on SageMath[7] used by Mathematical students worldwide.
In 2010, he co-authored a book on algorithms for computer arithmetic with Richard Brent.[8]
He has been an active developer of the GMP-ECM implementation of the elliptic curve method for integer factorisation and of MPFR, an arbitrary precision floating point library with correct rounding. He is also a coauthor of the CADO-NFS software tool, which was used to factor RSA-240 in record time.[9]
In a 2014 blog post,[10] Zimmermann said that he would refuse invitations to review papers submitted to gold (author-pays) open access and hybrid open access journals, because he disagrees with the publication mechanism.
