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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...
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.
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 ...
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 ...
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 iter...
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.
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 interr...
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 ...
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 questio...
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.
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 experime...
Deep thinker. Like talking about the world, religion and politics.
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Writing can be a lonely, thankless job, filled with rejection. But it can also be very rewarding when your text resonates with people.
Ask yourself why you want to write and what do you want out of it. There’s no problem in doing it just because but a strong reason ...
You can’t predict what people will want to read. So don't worry about pleasing others.
Don’t try to visualize your audience; every reader is a different person. Don’t try to guess what sort of thing editors want to publish or what you think the country is in a mood to read...
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