John C. Baez's Blog, page 44

Bigness (Part 2)

In the 1980s, the mathematician Ronald Graham asked if its possible to color each positive integer either red or blue, so that no triple of integers obeying Pythagoras famous equation:

all have the same color. He offered a prize of $100.

Its was solved in 2016! The answer is no. You can do it for numbers up to 7824, and a solution is shown here:

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(White squares can go either way.)

But you cant do it for numbers up to 7825. To prove this, you could try all the ways of coloring these...

Bigness (Part 1)

The French mathematicians who went under the pseudonym Nicolas Bourbaki did a lot of good thingsbut not so much in the foundations of mathematics. In this paper, Adrian Mathias showed that their formalism was incredibly inefficient:

Adrian R. D. Mathias, A term of length 4,523,659,424,929, Synthese 133 (2002), 7586.

He proved that the definition of the number 1 in Bourbakis 1954 text on set theory requires 4,523,659,424,929 symbols and also 1,179,618,517,981 links connecting symbols, without...

Mathematics Seminars List

The coronavirus pandemic is pushing us to take seriously a revolutionary new technology called the internet. Heres a nice list of online math talks, organized by Jaume de Dios:

Mathematics Seminars List.

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The Best Work on Sustainability?

Some people want to give a prize for a discovery of high scientific value that has significant repercussions in the field of environmental sustainability in order to improve the quality of life, in harmony with the production system and the transition to new development models.

So, theyre looking for the very best recent work in these area:

energy transition towards renewable sources

sustainable mobility

clean energy and renewable resources

energy efficiency

clean technologies for the...

Category Theory Calendar

There are now enough online events in category theory that a calendar is needed. And here it is!

CT seminars, conferences & community events.

It should show the times in your time zone, at least if you dont prevent it from getting that information.

Structured Cospans and Petri Nets

 

This talk on structured cospans and Petri nets is the second part of a two-part series, but it should be understandable on its own. The first part was on structured cospans and double categories.

Im giving this second talk at the MIT Categories Seminar. Itll be on Thursday April 9th, 12 noon Eastern Time.

You can see my talk live on YouTube here, with simultaneous discussion on the Category Theory Community Server. (To join this, click here.) The talk will be recorded and remain...

A Categorical View of Conditional Expectation

 

Prakash Panangaden is giving the second talk at the ACT@UCR seminar. Itll happen on Wednesday April 8th at 5 pm UTC, which is 10 am in California, 1 pm on the east coast of the United States, or 6 pm in England. It will be held online via Zoom, here:

https://ucr.zoom.us/j/607160601

We will have discussions online hereI suggest going here 20 minutes before the talk, so you can meet people and chat:

https://categorytheory.zulipchat.com/

People will also discuss the talk afterwards.

Prakash...

How Scientists Can Fight COVID-19

A friend listed some calls for help:

The UK urgently needs help from modellers. You must be willing to work on specified tasks and meet deadlines. Previous experience in epidemic modelling is not required.

https://epcced.github.io/ramp/

MIT is having a Beat the Pandemic hackathon online April 3-5. You can help them develop solutions that address the most pressing technical, social, and financial issues caused by the COVID-19 outbreak:

https://covid19challenge.mit.edu/

The COVID-19 National...

Structured Cospans and Double Categories

 

Im giving the first talk at the ACT@UCR seminar. Itll happen on Wednesday April 1stIm not kidding!at 5 pm UTC, which is 10 am in California, 1 pm on the east coast of the United States, or 6 pm in England. It will be held online via Zoom, here:

https://ucr.zoom.us/j/607160601

We will have discussions online hereI suggest going here 20 minutes before the talk, so you can meet people and chat:

https://categorytheory.zulipchat.com/

Ill also chat with people afterwards at that location. With...

Online Worldwide Seminar on Logic and Semantics

Someone should make a grand calendar, readable by everyone, of all the new math seminars that are springing into existence. Heres another! Its a bit outside the core concerns of Azimuth, but itll have a lot of category theory, and it features some good practices that I hope more seminars adopt, or tweak.

Online Worldwide Seminar on Logic and Semantics, organized by Alexandra Silva, Pawel Sobocinski and Jamie Vicary.

There will be talks fortnightly at 1 pm UTC, which is currently 2 pm British...