There's a valid psychological reason why most of us are more likely to remember a 10 digit phone number rather than the first 10 digits of the value of Pi. It has to do with how we commit information to our short term memory. We are much better at memorizing lists or numbers in chunks. In UI design it's called chunking and it's the technique of breaking many units of information into smaller, limited units or chunks, so that the information is easier to process and remember.
A chunk can be thought of as any small unit of information - this could be a list of words, numbers or letters. Modern day research shows that the typical person is able to efficiently commit 4 chunks of information to memory, plus or minus one; meaning somewhere in the range of 3, 4, or 5. Some research has demonstrated that breaking a list of 10 words into chunks of 3, 3, and 4 is as easily memorized (short term) as a single list of 5 words.
We can see this in action very apparently with social security numbers and phone numbers, for instance sake. For example, I think we all would agree that memorizing this number:
Is more difficult than memorizing this:
And it's clearly more difficult to commit this number to short term memory:
The same can be said for birth dates, driver's license numbers, and even credit card numbers.
Chunking can also be applied more generally in UI design when you are required to present information to users that they need to commit to their memory (either long or short term). Breaking up long pieces of information into smaller digestible chunks will always be preferred in UI design. However, one has to be careful to not misapply this technique; when working with information that needs to be searched or scanned quickly, chunking is actually detrimental to the user's goal. Imagine how absurd it would be to google a keyword and the results be displayed to you only 3 or 4 items at a time!
Use chunking in a UI design where committing information to memory is the goal or is beneficial to the user. Do not use chunking in a UI design when a user needs to quickly scan a list to find the information they are searching for.