You’re absolutely right. Now, if you’ll excuse me, I must return to my work disproving the Poincare conjecture…

]]>At the *very* least. :)

As someone who enjoys toying with math problems from time to time, I appreciate this response. Yes, it’s good to have math amateurs; at the very least, we help dispel the notion that math is inaccessible or uninteresting. In addition, digging into a problem helps you understand its difficulties. I only recommend that amateurs clearly identify themselves as such, so as not to cause confusion. And that they take the time to work through problems in a good textbook, so as to become familiar with a base of knowledge.

]]>uhm,

Slutsky’s theorem?

]]>Precisely my point. The publishing costs are so low that I’m totally fine with an arxiv style open access but not where they journal asks me $1500 to publish a paper!

]]>Rahul:

I’d feel awkward criticizing pay-for-publish given that I do most of my publishing on this blog, and nobody’s paying me to do this, indeed I have to pay the hosting fees. OK, my university pays, but they’re paying from my discretionary research funds so it’s basically me paying. I’m not saying that pay-for-publish is perfect: as Liebling wrote, freedom of the press is guaranteed only to those who own one. But, now that publication costs are so low—running a blog costs a lot less than printing out a newsletter and mailing it to 10,000 people each month—it makes sense that lots of people, myself included, will go that route.

]]>And there likes the irony of open access.

I am all for open access but it seems a short path to pay-to-phblish.

The incentives are perverse. Did open access try to solve one problem and create another.

]]>he tries to claim that if in the limit the number of ones in x equals the number of zeroes in x then x is normal in base 2.

What does it mean that sqrt(2) is not “normal”? That means there is information to be gained by computing it to enough decimal points? Obviously I am thinking Carl Sagan’s Contact book, and where the burden of proof should be.

]]>What a good response!

I’ve learned a lot of math from trying (and failing) to prove soemthing I thought the real pro’s had missed. Even if my conjectures were just fantasy, they gave me a motivation to learn the definitions, etc. carefully that I would never have had solving end-of-chapter problems or just reading without an objective.

]]>Yes, I read about the RS publication on Moldoveanu’s blog.

]]>On the other I’m happy to see people trying to understand and explore mathematical problems and we all start somewhere. This is very much the kind of mistake a student could make in an introduction to proofs course (most ppl find the shift to thinking rigorously about math quite hard) and (as you note) it poses no danger to legitimate mathematics. Any mathematician or math adjacent PhD should be able to tell in a couple minutes it’s not worth their time.

The more I think about it the more I want to encourage the author to keep trying but suggest he spend a bit more time working through problems in a real math textbook first. If he is reading this I can’t promise I’ll have the time to respond but if he wants to email me at my last name at invariant.org I’d be happy to take a few minutes to explain in more detail where he goes wrong and suggest a book or two for him to work through.

]]>Groan to both Dzhaughn and Keith.

]]>That would just be normal envy ;-)

]]>Mathematicians it seems want to use the word “normal” as much as possible. Are they trying to compensate?

]]>This is interesting:

DISHONESTY IN ACADEMIA: THE DEAFENING SILENCE OF THE ROYAL SOCIETY OPEN SCIENCE JOURNAL ON AN ACCEPTED PAPER THAT FAILED THE PEER REVIEW PROCESS

“QUI TACET CONSENTIT”: AN ANSWER TO THE ROYAL SOCIETY OPEN SCIENCE JOURNAL ON AN PAPER ACCEPTED WITH A MATHEMATICAL ERROR

]]>Ah– of course. The distribution has to have bounded support, and be discrete, unless maybe we do something fancy with limits to base-infinity.

But I still object to the word “normal” being applied to the uniform distribution.

]]>“In mathematics, a real number is said to be simply normal in an integer base b[1] if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long have density b−n.”

https://en.wikipedia.org/wiki/Normal_number

But that raises an obvious question: Why not use the following definition instead?

“In mathematics, a real number is said to be simply normal in an integer base b[1] if its infinite sequence of digits is distributed *according to the Gaussian distribution*.”

They also appear on Arxiv.

Sure, but there’s little surprise or fun in that. Unlike e.g. this.

]]>