# Happy Birthday to me!

Well, today is my birthday. A gentleman never reveals his age, but it’s a perfect square[1]

fn1. And not the subject of a Beatles song

## 29 thoughts on “Happy Birthday to me!”

1. Many, many, square returns ;-D

2. Vee says:

Happy Birthday Professor

3. Hey, you’re no square, man, you’re a finger-poppin’, hip, happenin’ daddyo!
Happy birthday!

4. Hey, you’re no square, man, you’re a finger-poppin’, hip, happenin’ daddyo!
Happy birthday!

5. John, please delete the duplicated message, sorry.

6. Jason Soon says:

A happy 36th birthday it is, then ðŸ™‚

7. Paul Norton says:

Or maybe a well-seasoned 25, Jason!

8. Happy Birthday to you too, Jason, ya pagan.

9. Happy birthday John. May you grow old enough such that your beard is at least thrice as long and swarthy as it appears today. ðŸ˜‰

10. Dave Ricardo says:

81 years young. You should update the picture, though.

11. Happy Birthday. Not 64? Can’t think of another square.

12. cs says:

At least you don’t look 64. Happy birthday Prof Q.

13. wpc says:

Happy Birthday

14. 81, of course. But for JQ, any age would be a perfect square, by derivation from himself.

And, in months, all he needs is to be 3 times some other perfect square in years.

BTW, did you know the elegant proof that a pytahogorean triple with no common factors has the hypotenuse plus or minus the even side a perfect square, and plus or minus the odd side double a perfect square? It makes a standard formula for generating pythagorean triples work.

15. 49?

Happy Birthday ðŸ™‚

16. Homer Paxton says:

49 is a good age to achieve this year!

17. Rob says:

Happy birthday, Quiggers! For myself, I’ve recently arrived at your nearest prime number.

18. Katz says:

A leftie blogger was Quiggin.
Gave the Right a deserved wiggin’.
“From triumphalist braggin’,
You’re forever zaggin’,
When, for pity’s sake, you should’ve been ziggin’.”

Happy B’day JQ.

19. Razor says:

Happy Bithday, John.

1 is a good age.

20. A former film star was asked how he felt about hitting 80. He said he liked it, considering the alternative.

21. Inspired by Katz:

There was a busy blogger called Quiggin (John)
Who urged the social democrats to keep on and on
Till the non-left hit back
With dextrous Biff and Thwak
And set fire to the beard of Prof Quiggin (John).

Happy birthday John! Keep a jug of ale nearby, it could be handy for all manner of eventualities.

22. Jim Birch says:

Cheers John I seem to have been running a a little under 6 months behind you for about that long.

23. There was a busy blogger called Quiggin (John)

Which I misread as “a *busty* blogger called Quiggin”. Wondered for a moment what Rafe knew that the rest of us didn’t…

And happy birthday.

24. Perhaps this mystery number is a prime power? In which case there’s a finite field of that size.

And happy birthday.

25. One of the easiest mystery numbers is 153. Working in base ten (I clearly can’t put “10”), if you start with any positive integer divisible by 3, then keep forming new numbers by summing the cubes of their digits, you will eventually stop on 153.

The proof is left as an exercise for the reader (I like saying that – that’s Schadenfreude for you).

26. John Quiggin says:

I’ll take the 30-second challenge on this one

1. It’s trivial that 153 is a stopping point of the process
2. You can easily get an upper bound from the fact that 9^3<1000
3. Brute force enumeration of cases (left as an exercise for my computer) does the rest.

27. You left out two important things, the difference between mathematics and number crunching.

You should have done the computer stuff yourself, not just for the glory of it but because having your nose down in the dirt means you will spot oddities, things you would miss otherwise. Therefore it’s a good habit.

And, sheer brute calculation will make you miss any patterns etc. that would reduce or remove the brute force. You completely missed the relevance of divisibility by three; that is invariant under the iteration (which you should prove), and eliminates 2/3 of the brute force cases needing checking.

Mathematics works best when you can apply thought to cut back on work, which is to say work at a higher level.

In the “real world”, whatever that is, you can be tricked by the elegance of the mathematics. But the right way to use mathematical models etc. is to get you most of the way there, both reducing the work (see above) and highlighting exceptions that don’t fit. That’s how these things advance best.

I once did a brief essay on the distinctions between art, craft, and science, mostly to clarify it all in my own mind – its first version wasn’t very readable, even for me. But I think it’s useful to remain aware of the distinctions, since they can turn out very important. (Mathematics is not a science, by the way.)

28. James Farrell says:

Belated Happy Birthday, by the way. I haven’t read the blog for a fortnight.