can anyone point me towards the math behind biquad antennas?
There is a lot of math in antenna design: partial differential equations (PDE), linear algebra, numerical methods, to name a few. Because your question is primarily about quad antennas and not about boundary conditions or material equations, I start my answer not with Maxwell's equations, but with a review of amateur-built high-directivity wire antennas. Whether there is or is not similarity of this review's Biquad Antenna section designs with your project, the description specifies the context of the biquad antenna design and shows design drawings and directivity gain graphs.
We read in the text that the polar plots of normalized gain are obtained with the help of the 4NEC2 software. This application is developed on the basis of the Numerical Electromagnetics Code, a popular antenna modeling system for wire and surface antennas. In the Wiki article we read that the NEC code is based on the method of moments (MoM) solution of the electric field integral equation (EFIE) for thin wires and the magnetic field integral equation (MFIE) for closed, conducting surfaces. The text also mentions, but does not specifies, numerical methods, which we will see later in the section Currents on Linear Antennas from the book of Sophocles J. Orfanidis.
You can peek ahead to this ref to see a lot of linear algebra there. For now,  we return to the EM theory.
The biquad antenna is essentially a few (8?) thin wire edges. We partition those into N thin wire segments (N→∞) and use the electric field integral equation in numerical computations. There is many textbooks and courses on the solution of Maxwell's equations. For a EE student working on the antenna project, the book Electromagnetic Waves and Antennas by Sophocles J. Orfanidis may be recommended.
The Wiki article also mentions a domain specific language (DSL) of NEC input files. Significance of the NEC file format for practical antenna design is similar to SPICE for circuit and VLSI designs. Strictly speaking, the DSL thing is not math, but computer science, but still deserves to be mentioned in the context of antenna design concepts and tooling.
The NEC modeling program is a de facto standard of CAD for antenna design software. The presentation Computer Antenna Modeling Simplified – KE5KJD first introduces a reader to the antenna modeling and numerical calculations with Pocklington/Hallen equations and then reviews a group of NEC-originated utilities and applications.
You may also become interested in the historical reference on the origins of using integral equations for thin wire antenna design: you'll see it in On the Integral Equations of Thin Wire Antennas
Use the emphasized keywords of my answer, the phrases Green's function, Electromagnetic scattering by a straight thin wire, and other terminology of the refs from my answer, and your search will return a great many references on antenna design math.