Paul Taylor

I have been using email for 40 years. It used to work.

As an (independent) academic researcher, I need to contact new people, primarily in universities, to ask questions.

I refuse to use Google, Microsoft or the other American IT giants.

But they are increasingly preventing refuseniks from sending email at all.

I know what RFC, DNS, MX, SPF and DMARC mean. My email goes through small British companies with intelligent, friendly and helpful staff.

mxtoolbox.com says that I must have DMARC to send email to M$. So I set it up. I now get a dozen copies of the same report from G or M$ for each email that I send out.

They show that my email gets to G and M$ sites, but then it is marked as spam.

The stupid senior management of numerous universities has surrendered their staff email to M$.

Web searches and AIs preach about spam. I don't send spam - I want to contact my colleagues.

Rumour has it that previously unknown senders are treated with suspicion and their emails are sent to spam. In other words, it is impossible to **initiate** communication with someone.

Let's be blunt about this. They are a mafia that is enforcing an **oligopoly**. It's got nothing to do with reducing spam --- I have no doubt that they let through emails from "trusted partners", ie companies that bribe them enough to send their spam.

The result of this is that it will only be possible to send emails by paying M$ to do it, and then it will only be allowed to express "approved" opinions.

What can we do about this?

At the very least, those of you with senior positions in universities can tell your management to revert to competent standards-based email systems hosted on Linux systems.

www.paultaylor.eu/trans/

"Old and New Proofs of the Order-Theoretic Fixed Point Theorem"

I have just posted a new version of this paper (which was advertised here on 30 December by Toucanlan).

It was motivated primarily by my irritation with so-called proofs that recite stuff about successor and limit ordinals and conclude fixed points. Missing are what ordinal to use and the derivation of recursion from induction.

It gives the complete proof of this using transfinite recursion, quoting the original papers by Cantor, Hartogs and von Neumann. I have never found this in the literature.

It also gives the proof of the so-called Bourbaki-Witt theorem, actually due to Zermelo and Kuratowski.

("Zorn's Lemma" and "Tarski's Theorem" are also claerly stated in Kuratowski's 1922 paper.)

But as well there is the shorter, simpler constructive proof by Pataraia and me.

Plus a lot of history, which is a rabbit-hole!

I welcome comments from people who know the actual mathematical history (1904--23), not the post-war mythology.

Looking up to Archimedes. Siracusa, Sicily. He is holding a concave mirror to focus the Sun's rays on to the sails of Roman ships to set fire to them, holding back their invasion.

I found a great online resource in Ukraine: https://ouci.dntb.gov.ua/en/ There are lots of places where you can find where recent papers have been cited, but they're not much use before about 1980. This one told me about citations of the early 20th century papers on set theory that are part of my current historical study of the order-theoretic fixed point theorem. Слава Україні!