Title missing a (2008).
and here say May 2007 https://terrytao.wordpress.com/?s=Discovering+a+solution
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Title missing a (2008).
and here say May 2007 https://terrytao.wordpress.com/?s=Discovering+a+solution
You shouldn’t always prototype first, before mapping what kind of problem you have, at the risk of reinventing the (square) wheel.
Rapid prototyping is the holy grail software is known for. But prototypes are not always cheap, and almost always go to prod and turn into technical debt. In other disciplines the instinct to just try something first would sound ridiculous (e.g. let’s always figure out open heart surgery from scratch, it’s just a quick experiment, if the patient dies we figure out later).
I’m a fan of the Cynefin framework [1] as a higher level tool to figure out if I should prototype at all - even if not very precise, because at least it forces me to think about it.
The way I structure my prototypes, I have to have a sense of the existing state of the art, which I then leverage to propose my hypothesis. I do a version of this for programming as well, I try and identify state of the art methods in the field, and use that to guide my implementation.
I find it very surprising that he suggests writing the introduction at the end of the paper. He doesn't explicitly mention the abstract, so I'm assuming the introduction includes the abstract of the paper. If that's true, I find it impossible to write any paper without first working out a fairly fleshed out abstract. It usually takes about 50% of my time to just write my abstract. The way I structure my prototypes, I…
This "stub" or aide-mémoire doesn't define the idea, just evokes it. So you better come back while that memory is still fresh, or you will not be able to work out what it was!
If it's daunting enough to be discouraging, consider doing tasks that quickly give you some sense of progress towards what like about it. To sustain your interest - your most precious resource.
This mightn't be most efficient, or give the best structure, but if it motivates you to do it, it will be far more efficient and better strucured than nothing!
The tips on how to prototype are very good. Let me give another perspective though: You shouldn’t always prototype first, before mapping what kind of problem you have, at the risk of reinventing the (square) wheel. Rapid prototyping is the holy grail software is known for. But prototypes are not always cheap, and almost always go to prod and turn into technical debt. In other disciplines the instinct to just try some…
In the case of surgery, where someone’s life is on the line, it’s not going to be worth the cost.
He talks about how to begin a daunting task: linear order, easiest/most straightforward first, or a top-down "skeleton" first. If it's daunting enough to be discouraging, consider doing tasks that quickly give you some sense of progress towards what like about it. To sustain your interest - your most precious resource. This mightn't be most efficient, or give the best structure, but if it motivates you to do it, it w…
Not sure how this applies to proof, which has to be perfect to work at all. Pehaps Tao's skeleton, then filling in the most crucial parts first, is exactly this.
I am a big fan of this approach. I have seen that if I stop and think about the problem too much in the beginning, it takes a whole lot longer to arrive at a good solution. Prototype -> Think -> Engineer. If you are lucky, you get to reuse some code from the prototype, if not that was hopefully a good lesson for the future.