How much unfinished work and unexplored ideas should one share in a presentation?
tl;dr: Light is the best disinfection.

If you work in a relatively small sub-area, and know all your potential colleagues and collaborators, you can decide for yourself how likely is that some of them can "borrow" an idea from you and publish it as your own. Your personal intuition about your the situation in your particular case is much more relevant than a general discussion.

However, you can also consider the following facts to help you make your decision:


Publishing process in Maths usually takes much longer than in Physics, Chemistry, Engineering, or related "hard" areas. It is not uncommon for an article to be in first review for 6-9 months, and it is not uncommon to have 2 or more review cycles. Are you really ready to keep your findings secret until the paper is published?
If some ideas were shared among a small circle of colleagues, and two of them claim that they "own" the result, it is actually more difficult to find out, who was the original author, and who pretends to be one. On the contrary, if the pre-print is made public, and the ideas are presented on a large international conference (in a room with more than 10 people), than there are more witnesses who connect the idea with your name, and it is less likely that someone will dare to stole the authorship (but still possible, of course).
An important task of your supervisor (as any supervisor) is to ensure that the work will be eventually published; and as you know publishing is time- and effort-demanding. By expressing their concern, your adviser in some form encourages you to publish these ideas as soon as possible, which is a completely legitimate request. In fact, if one shares a good idea on a conference, but then never publishes it, someone else definitely will, sooner or later.