The ultimate guide to hiring qualified AI engineers
Introduction The field of artificial intelligence (AI) engineering is a rapidly emerging and evolving domain—and it represents the cutting edge of technological innovation today. As businesses and industries increasingly integrate AI into their operations, the demand for skilled AI engineers is surging. The US Bureau of Labor Statistics expects demand
Read moreNumber of groups of squarefree order
This post is a sort of footnote to the previous post, Estimating the number of groups of a given order. The following is taken from an answer to a question on Stack Exchange. In general there is no formula f(n) for the number of groups of order up to isomorphism. However,
Read moreEstimating number of groups of a given order
John Conway et al [1] give the name gnu(n) to the number of groups of order n, where “gnu” stands for group number. This function has been studied since the 19th century, but I don’t know whether there has ever been a standard notation for it. Mathematica calls it FiniteGroupCount.
Read moreChris’ Corner: Monaspace
I’m a sucker for a new coding font. I generally don’t think what coding font you use affects productivity in any significant way (unless it’s distracting) so farting around and switching it up is just a fun little thing to do. Like pushing around the furniture in your room or
Read morePeriod of a nonlinear pendulum
The term “nonlinear pendulum” is analogous to a retronym, a new name for an old thing to distinguish it from a new variation. For example, once upon a time a guitar was just a guitar. Now such a guitar is called an acoustic guitar to distinguish it from an electric
Read moreKepler triangle
A Kepler triangle is a right triangle whose sides are in geometric progression. That is, if the sides have length a < b < c, then b/a = c/b = k. All Kepler triangles are similar because the proportionality constant k can only take on one value. To see this,
Read moreDecoupling formal theorem proving effort
Terence Tao has been experimenting with formal theorem proving using Lean and writing about his experience. Here’s something Tao said on Mathstodon that I thought was interesting. It is remarkable how much “decoupling” is achieved by the Lean+Blueprint combo. Contributors can work locally on proving a lemma, without necessarily fully
Read morePartitioning dots and dashes
Given a set of dots and dashes, how many ways can they be partitioned into a set of Morse code letters? There is at least one way, since you could take each dot to be an E and each dash to be a T. If you have a sequence of n
Read moreSchwarz lemma, Schwarz-Pick theorem, and Poincare metric
Let D be the open unit disk in the complex plane. The Schwarz lemma says that if f is an analytic function from D to D with f(0) = 0, then for all z in D. (The lemma also says more, but this post will focus on just this portion of
Read moreFactored random numbers
A couple days ago Michael Nielsen posted an image of a one-page paper that gives an algorithm for generating factored random numbers, uniformly distributed from 1 to some designated N. The algorithm does not generate random numbers then factor them. It’s more efficient than that, generating the factorization along with
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