Along with collaborator Pia Malaney, Weinstein showed that neoclassical economics was in fact an Example of a naturally occurring gauge theory. This discovery paralleled a similar discovery linking mathematics to physics by Chen Ning Yang, and collaborators at Stony Brook in the 1970s. The approach has been separately discussed from viewpoints in both the economics and physics literature, but has yet to gain a wider awareness with the few academicians possessing backgrounds in both physics and economics. Recently, a program for 'Geometric Marginalism' by Weinstein and Malaney has been funded by the Institute for New Economic Thinking (INET).

In 1985, he graduated from the University of Pennsylvania as a University Scholar, receiving his bachelor's and master's degrees in mathematics in three years. He then earned a Ph.D. in Mathematical Physics from the Mathematics Department at Harvard University in 1992. He has since held a Lady Davis Fellowship in the Racah Institute of Physics at Hebrew University, a National Science Foundation fellowship in the mathematics department of Massachusetts Institute of Technology, and he was an Alfred P. Sloan Foundation grantee in the Harvard Economics Department and National Bureau for Economic Research where he founded the Project on the Economics of Advanced Training with Economist Richard Freeman.

In May, 2013, Weinstein delivered a lecture, Geometric Unity. It was promoted by Marcus du Sautoy as being a possible answer to some of the problems in modern physics. Few physicists attended the original lecture, and no paper or preprint was published. The claims were met with skepticism by several commentators. A repeat lecture was organised the following week with more physicists in attendance. His theory includes an "observerse," a 14-dimensional space, and predictions for undiscovered particles which could account for dark matter. Joseph Conlon of the University of Oxford pointed out that some of these particles should already have been seen.

In 2017, he contributed a number of videos to Big Think that covered the impact of Technology on capitalism, risks associated with AI, problems with pure rationality, and the cult of achievement.[1] He was also interviewed by Vox on the same subjects.