Gregory Gundersen is a researcher in New York.
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Before I started taking writing seriously, I had a loose grasp of many mathematical and technical concepts; and I was not sure how to tackle open-ended problems. Maintaining this research blog has clarified my thoughts and improved how I approach research problems. The goal of this post is to explain why I have found…
Imagine we want to compute the square root of a number n n n . The basic idea of Heron’s method , named after the mathematician and engineer, Heron of Alexandria, is to find a number g g g that is close to n \sqrt{n} n and to then average that with the number n / g n/g n / g , which corrects for the fact that g g g…
Large language models (LLMs) still feel a bit like magic to me. Of course, I understand the general machinery enough to know that they aren’t, but the gap between my outdated knowledge of the field and the state-of-the-art feels especially large right now. Things are moving fast. So six months ago, I decided to close…
The Black–Scholes formula is the crown jewel of quantitative finance. The formula gives the fair price of a European-style option, and its success can ultimately be measured by its impact on option markets. Before the formula’s publication in 1973 (Black & Scholes, 1973; Merton, 1973) , option markets were relatively…
Money. The villagers are tired of bartering. The dairy farmer wants to buy corn, even when he does not have milk to trade, and the corn farmer wants to buy meat, even when the butcher does not want corn. So they decide that special gray stones that they can collect from a nearby riverbed will represent an abstract…
A dimension is a physical quantity that can be measured, while a unit is a specific amount of a physical quantity. For example, time is a dimension, which can be measured in temporal units such as hours or seconds.
The existence claim for the singular value decomposition (SVD) is quite strong: “Every matrix is diagonal, provided one uses the proper bases for the domain and range spaces” (Trefethen & Bau III, 1997) . MIT professor Gilbert Strang has a wonderful lecture on the SVD, and he includes an existence proof for the SVD…