Many people celebrate March 14th as “Pi Day” because 3/14 matches the
first three digits of Pi.
Similarly, some people celebrate February 7th as “E Day” because 2/7
matches the first two digits of E.
[I suppose you could celebrate "Gamma Day" on May 8th (since gamma =
0.577, and the first two rounded non-leading-zero digits are 5 and 8),
but I don't think anyone does.]
However, these celebrations are based on an antiquated non-decimal
calendar, and it seems paradoxical to celebrate mathematical constants
in such a non-mathematical way.
Instead, we could create a time-linear function, f, that maps the instant
of the winter solstice (an observable physical phenomena) to 1, and
the instant immediately previous to the next solstice as 9.9999…
We would then celebrate constants yearly at an interval around time t,
when f(t) equalled the constant’s absolute value’s mantissa
Of course, we could compensate for Benford’s Law, but that might be overkill.