Τετάρτη, 14 Φεβρουαρίου 2018

constructive mathematics

Theorem 1: Given a \( C^{\infty }\) compact manifold \( M\) furnished with a smooth volume form \( \mu \), there exists an \( F_{\sigma} \)-set containing all diffeomorphisms which are Cohomology Free in \( C^{\infty}_{\mu} ( M ) \).

The actual statement of this theorem is in fact way more constructive than the one that we just gave. For lack of space we do not give the alternative statement, which would reflect more accurately the content of its proof. The proof actually provides a good description of the \( F_{\sigma} \)-set in terms of the solvability of the cohomological equation, and the condition which is necessary for solvability is obtained in a constructive way (admitting the underlying non-constructivity of the problem and the notions involved).

Therefore, the term constructive is used in the following, quite loose, sense. When one has to prove the existence of a solution to such a difficult equation, the only reasonable way to do it is by constructing one. Thus, they take their screwdriver, go down to the street and, when they have gathered enough cash to live on for some months, come back to their desk and construct a solution using step-by-step approximation.

Τρίτη, 6 Φεβρουαρίου 2018


- ναι, κοιτάξτε, κ. Αλαφούζο, εγώ με το κόμμα της απλής λογικής είμαι και ενάντια στη διαφθορά, και γι αυτό ήρθα να σας τα πω. γι αυτό και γιατί έχετε απίστευτες γάμπες. και ο αδερφός μου εμένα έκανε διδακτορικό στη σχιζοφρένεια, τώρα κάνει έρευνα στο τραλαλαλαλά, οπότε η λύση είναι στο ίντερνετ.

Δευτέρα, 22 Ιανουαρίου 2018

board diversity

- would you rather give your seminar on projector or blackboard?
- i think it's better if i write things while i talk so no projector, but in fact i would prefer a to give it on a whiteboard.
- you don't say...
- not that there's anything wrong with blackboards... i mean... you know... i have friends who are blackboards.

Τετάρτη, 10 Ιανουαρίου 2018

Κυριακή, 7 Ιανουαρίου 2018


- our only hope for a real single payer social security system was Bernie, but now even what we had with Obama is down the drain.
- well, in greece we have that jingle payer social security system thing and it's not really working.
- why's that?
- i mean, as a child you go door to door on christmas eve singing jingle bells and people give you pocket money. if that's all you have for social security it's kind of insufficient.