Justin Lanier

Yesterday I spent a fascinating morning talking maths with a group of GPs. All professions require some level of numeracy, but doctors face particular challenges when communicating mathematical ideas.
I've written up a short blog: robeastaway.com/blog/gp-maths

....and nickel...

You are almost—but not quite—off the grid. 😄 Hope you are having a nice getaway!

aluminum

Make more yourself at this link: demonstrations.wolfram.com/TilingTheHyp...

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."

Independent of thinking about AI, Terry Tao himself has an interesting and encouraging perspective regarding that first question:

Excited to say, "looking forward to it!" 🙌

Misread that as "origami".

It's okay, you can rate my response a 0%. 😆 Thanks for putting up with it.

Kind of joking, but just using a discrete metric: how far is this rectangle from being a square? Well, if it's not a square, it is 100% far from being a square; and if it *is* a square, then it is 0% far from being a square. It's like a graph theory metric: you are either at the spot, or not.

Probably 100% most of the time, but every once in a while 0%.

😅 Welcome! At least the weather ought to be relatively nice during your visit. Looking forward to your Sydney Ideas event on Thursday!

International Visitor Program - Sydney Mathematical Research Institute IVP August 2023 applications are due 8 August 2023, for July 2024–June 2025 visits (general applicants) & March 2024–June 2025 for Australian citizens/PR & NZ citizens.

Applications are now open for our International Visitor Program, open to #mathematicians to visit Aus 🐨 between July '26-'June 27, or March '26-June -27 (Aus/NZ citizens)
📅 Apply by Aug 1, info:
mathematical-research-institute.sydney.edu.au/internationa...
Please share with your networks 🔁 #MathSky

Please mail me my earned Certificate 0 with Honors at your earliest convenience. 👨‍🎓

“21st century mathematics”: a free month-long online enrichment program for math teachers.

Info + register: bit.ly/21math2025

Video part 1:

😄

What's Wrong with This Picture? Amazon.com: What's Wrong with This Picture?: 9781559535847: Michael Serra: Books

"What's Wrong with This Picture?" by Michael Serra pops to mind.

www.amazon.com/Whats-Wrong-...

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.

Simon Stevin, what a hero.

mathshistory.st-andrews.ac.uk/HistTopics/R...

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.

TIL that we narrowly missing lugging around not only the monikers "imaginary", "negative", "complex", and "irrational" for numbers, but also "fictitious limits". Real glad for that. 😅

from MacTutor's "The real numbers: Stevin to Hilbert"

Thanks for sharing!

+but some of the lead up smaller questions you ask on a given problem might be known and/or standardly tractable/checkable? That's my guess of your meaning. Glad to hear more!

This is wonderful, Peter, both the collection and the news from your student. Can you say more about the phrase "mathematicians might not know the answers to"? I'm curious about the wording, the "might not" in particular. Is this because you know the main problem in each of your Problems is open,+

Received! Glad to have you aboard, looking forward to it.

We must hang around different crowds, because I've heard literally no one say that this will not be terrible! 😆

Thanks for sharing!

YouTube video by TED The magic of Fibonacci numbers | Arthur Benjamin | TED

As a math appetizer for the program, here is a six-minute TED talk by mathematician Arthur Benjamin. The talk features the Fibonacci numbers, one of the two math topics for this year's program. (The other is bubbles!)

www.youtube.com/watch?v=SjSH...

21st century mathematics – 2025 An online learning experience for math teachers Registration for the 2025 program is now open! Here is the registration form. Registration will continue through the start of the program in July. If…

All the info and the registration form can be found here:

justinlanier.org/21st-century...

Please pass this along. And if it's a good fit for you, I hope you'll join in!

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.

There are lots of chances for teachers to work on problems collaboratively, encounter new math ideas, and grow as teachers and mathematicians in community. We also have a great lineup of guest mathematicians who will visit us and share about their work.

A picture of a double bubble. A picture of the first 18 Fibonacci numbers, with the ones that are perfect powers highlighted.

We are two weeks out from the start of "21st century mathematics", a program I run for K-12 math teachers. (Register now!) The program helps teachers connect the math they teach with some math that has been discovered in the 21st century. The program is flexible, free, & online.