There are two kinds of mistakes: One is fatal and can destroy a theory, but the other is small and won't completely ruin your work.
Building in a safety margin, such as more time or funding, can turn fatal mistakes into contingent ones.

Don’t worry about small mistakes

If we have a conversation, read a book, or listen to a talk, we are very unlikely to remember much of it. Even if we enjoyed and valued it, only a small part will stay with us.
When you are communicating with people, try to give them something to take home. Choose a memorable line or idea, a visual image, or use humour.

Give people something to take home

Mathematician Frederic Riesz published the same ideas multiple times, each time improving until he was ready to publish a final paper.
In our work, we don't need to have fresh ideas all of the time. We can build on an initial idea. Sometimes, we can do our best work through an iterative process. For example, a writer could start by sharing an idea as a tweet. If it gets a good response, the replies help them expand it into a blog post, then a talk, and eventually, a book.

Share the same work multiple times

Presentation matters. The way our work looks influences how people perceive it.
Take the time to clean your equivalent of a blackboard to signal that you care about what you're doing.

Make sure the blackboard is spotless

Your one main point should be repeated over and over, like a theme with variations.
If we make one point well enough, people will understand and remember it. If we try to fit too much in, the audience will lose interest and go back to their thoughts before they were interrupted.

Every lecture should make only one point

One minute overtime can destroy the best of lectures.
It's essential to respect the time and attention of others. Attention spans are limited. After a certain point, people stop taking in new information. Don't expect them to still hang on your lips after the required time. Instead, put in the extra work for brevity and clarity.

Never run over time

Mathematician and philosopher Gian-Carlo Rota specialized in functional analysis, probability theory, phenomenology, and combinatorics.
In 1996, he gave a talk, "Ten Lessons I Wish I Had Been Taught," which contains valuable practical advice for making people pay attention to your ideas.

Making people pay attention to your ideas

Gian-Carlo Rota noted that many of the mathematicians he admired were known more for their work explaining and building upon existing ideas. Their extensive knowledge of their domain meant that they could expand further.
Never be afraid to stand on the shoulders of giants.

Remembered for your expository work

What we present should correspond to what we want an attentive listener to take down in his notebook.
We should make it simple for people to understand our ideas on the spot. We shouldn't expect them to revisit it later. Even if they do, we won't be there to answer questions or clear up any misunderstandings.

Make it easy for people to take notes

Try to spot someone in the audience whose work you have some familiarity with. Then rearrange your presentation so as to mention some of that person's work. Everyone in the audience has come to listen to your lecture hoping of hearing their work mentioned.
Reciprocity is very persuasive. If you want people to pay attention to your work, always pay attention to theirs first. Show that you see them and appreciate them.

Relate to your audience

They use a few tricks over and over again. The smartest and most successful people are often only good at a few things - or just one thing. However, they maximize those strengths without getting distracted.
If you've hit diminishing returns with improvements, then experiment with things you already have an aptitude for but haven't made them your focus.

Every mathematician has only a few tricks

Introductions are providing prospective readers with a strong motivation to read your work.
Introductions are about:
<ul>
<li>explaining what a piece of work will be about, </li>
<li>what the purpose is, </li>
<li>and why someone should be interested in it.</li>
</ul>

Every lecture should make only one point

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