nhorozov.xyz/aboutme/mathematics

mathematics

• During the pandemic I worked on a paper about the distribution of Gaussian primes and more generally primes in quadratic number fields, working alongside my father and his student. I wrote several Python programs to find the number of primes in angular slices of the complex plane and compare their densities. We found that our results very closely match and support the conjectures we sought to prove, like the idea that two slices with the same angle and radius will have similar amounts of primes as the radius goes to infinity.
• This year I’m taking Multivariable Calculus and teaching myself some more statistics
• This summer (11->12th) I audited Calc 3 and Lin Alg + Probability at Columbia
• Last summer I audited Linear Algebra
• Last year I took AP Calculus BC and was teaching myself some statistics so I could better crystallize my intuition about LLMs
• I often learn math in the context of computer science so many of my programs are math heavy Heres a list of some of the more math heavy ones:
  • Mandelbrot set plotter in p5js - I elaborate more about this here
  • Strange attractor ploters in p5js, plots the trajectory of a particle in a space and has some really cool properties. If you slightly alter the initial conditions of the program the particle will trace out a very different path. Also (ideally) the path of the particle is not self-intersecting. (However it is imposible for a descrete computer running forever to not have the particle self-intersect its previous path, because there are a finite number of positions it can be in). Further elaboration here
    
  • Word2vec implementation, uses machine learning to quantify the meanings of words they take on in a corpus of text. Elaborated further here