Justin Lanier

@jlanier.bsky.social

203 Followers 95 Following

A 4x4 puzzle grid, indicating an example of an alternating sign matrix; an example of a configuration of 21 points that maximized the number of pairs that are a unit distance apart. These are the two mathematical themes of the 2026 program.
4 by 4, 5 by 5, and 6 by 6 grids of the counting numbers from 1 to n squared.
A tiling of the hyperbolic plane in the disk model with 10 regular pentagons at every vertex; this time the image is centered on one of the pentagons.
A tiling of the hyperbolic plane in the disk model with 10 regular pentagons at every vertex.
from “Does one have to be a genius to do maths?” by Terry Tao: "The answer is an emphatic NO. In order to make good and useful contributions to mathematics, one does need to work hard, learn one’s field well, learn other fields and tools, ask questions, talk to other mathematicians, and think about the “big picture”. ... The number of interesting mathematical research areas and problems to work on is vast – far more than can be covered in detail just by the “best” mathematicians, and sometimes the set of tools or ideas that you have will find something that other good mathematicians have overlooked, especially given that even the greatest mathematicians still have weaknesses in some aspects of mathematical research."
Stevin made a number of other important advances in the study of the real numbers. He argued strongly in L'Arithmetique (1585) that all numbers such as square roots, irrational numbers, surds, negative numbers etc should all be treated as numbers and not distinguished as being different in nature. He wrote:- "Thesis 1: That unity is a number. Thesis 2: That any given numbers can be square, cubes, fourth powers etc. Thesis 3: That any given root is a number. Thesis 4: That there are no absurd, irrational, irregular, inexplicable or surd numbers. It is a very common thing amongst authors of arithmetics to treat numbers like √8 and similar ones, which they call absurd, irrational, irregular, inexplicable or surds etc and which we deny to be the case for number which turns up." His first thesis was to argue against the Greek idea that 1 is not a number but a unit and the numbers 2, 3, 4, ... were composed of units. The other three theses were encouraging people to treat different types of numbers, which were at that time treated separately, as a single entity - namely a number.
Two years after the publication of Hankel's monograph, Méray published "Remarques sur la nature des quantités" in which he considered Cauchy sequences of rational numbers which, if they did not converge to a rational limit, had what he called a "fictitious limit". He then considered the real numbers to consist of the rational numbers and his fictitious limits.
Photographs of eight mathematicians: Dr. Frank Morgan, Eve Parrott, Dr. Maia Karpovich, Dr. Emanuel Milman, Dr. Joe Neeman, Dr. Parker Duncan, Rory O'Dwyer, Dr. Eviatar Procaccia, Harun Khan, and Dr. Bernadette Faye.
A picture of a double bubble. A picture of the first 18 Fibonacci numbers, with the ones that are perfect powers highlighted.
Google suggested search results for "democra": democracy democracy sausage democracy sausage map
Ten squares arranged in two different ways: a 2x3 rectangle with a 2x2 square stuck to its side, and one that goes like this: 00X00 0XXX0 XX0XX X000X where the X's are the squares and the 0'x are empty space.