Quantum field theory (QFT) is a universal language for theoretical physics, describing the Standard Model of particle physics, early universe inflation, and condensed matter phenomena such as phase transitions, superconductors, and quantum Hall fluids. A triumph of 20th century physics was to understand weakly coupled QFTs. However, weakly interacting systems represent a tiny island in theory space and cannot capture many of the most interesting physical phenomena.

The critical challenge for the 21st century is to map and
understand the whole space of QFTs, including strongly
coupled models. This is the main goal of the **Simons
Collaboration on the Nonperturbative Bootstrap**.
Meeting this challenge requires new physical insight, new
mathematics, and new computational tools. Our starting
point is the astonishing discovery that the space of QFTs
can be determined by using only general principles:
symmetries and quantum mechanics. By analyzing the full
implications of these general principles, one can make
sharp predictions for physical observables without
resorting to approximations. This strategy is called
the *bootstrap*.

The bootstrap idea has its roots in the S-matrix approach
to the strong nuclear force, popular in the 1960's but
largely abandoned after the advent of Quantum
Chromodynamics. The idea that general principles uniquely
fix the dynamics of QFT reappeared in the 1970's and
1980's with the formulation of the *conformal
bootstrap*, an infinite set of consistency relations
for conformal field theories (CFTs). At the time, these
bootstrap equations were applied with great success to
rational CFTs, a special class of two-dimensional models
with enhanced symmetry. However, little progress was made
in d>2 dimensions, and for the next two decades the
bootstrap remained quiescent.

Recently, members of our collaboration discovered new bootstrap techniques that apply in general dimensions. In the past few years we have applied these techniques to a wide variety of seemingly unrelated problems: to perform the world's most precise analysis of the 3d Ising model, to constrain strongly coupled theories of physics beyond the Standard Model, to aid in classifying superconformal field theories, to derive locality and black hole thermality in models of quantum gravity, and to prove irreversibility of renormalization group flows. We believe this is the beginning of a much larger enterprise, crossing traditional boundaries between string theory, condensed matter physics, and phenomenology, and making strong connections to modern mathematics and computer science.

Simons Collaborations, made possible by support from the Simons Foundation, bring together groups of outstanding scientists to address mathematical or theoretical topics of fundamental scientific importance in which a significant new development has created a novel area for exploration or provided a new direction for progress in an established field.