# Hilbert's Hopes

You are a mathematician in the early 20th century and you receive a mysterious letter from your colleague David Hilbert.

I was playing around the other day and I think I've come up with an interesting ciphering technique (I had to use underscores to fill space though, so it's not the best). See if you can't figure out what this says!

EHT_SC_ECICSGROTFOSITIFONEISANEHNUIOAHTRURHTCITYDATNMEAMTEOFUNI_LAF__OATANNISIFOLEO_EFNUHEHES_MAAXNOGDART_TRCAMTCTKWLELPNINEITEHPMOAMTEHERANUSNDLECYTINOTS_DO_AEETULA_AMSAAMLATNLYFFHTNEDMNYZEHUIHTIYTNEEIGTITSSSH_LAHEWTFGICDAIGISSM_ECRYNISILEHMIIONNTU_BRCIPS

Take acre care,
D. Hilbert

What could he possibly be trying to tell you?

## 1 Answer

There are 256 characters in the message.

They can be arranged in a 16 by 16 square:
EHT_SC_ECICSGROT
FOSITIFONEISANEH
NUIOAHTRURHTCITY
DATNMEAMTEOFUNI_
LAF__OATANNISIFO
LEO_EFNUHEHES_MA
AXNOGDART_TRCAMT
CTKWLELPNINEITEH
PMOAMTEHERANUSND
LECYTINOTS_DO_AE
ETULA_AMSAAMLATN
LYFFHTNEDMNYZEHU
IHTIYTNEEIGTITSS
SH_LAHEWTFGICDAI
GISSM_ECRYNISILE
HMIIONNTU_BRCIPS

Now the fact that it's from Hilbert suggests using

a Hilbert curve:

Taking the letters in this order produces the message, from Hilbert's 1900 address to the International Congress of Mathematicians:

"The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!"

• In addition, the acre/care "typo" tells you which orientation of the curve to use. – 2012rcampion Apr 30 '16 at 4:58
• Man, that was quick! Also, "fill space" was supposed to be a clue to use his space-filling curve. – Volatility Apr 30 '16 at 5:20