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Every mathematician has only a few tricks (2020)

mathoverflow.net

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Re: Every mathematician has only a few tricks (2020)

#61

Post by sema4hacker »

forinti wrote: post #34
seanhunter wrote: post #19

My dad (an engineer not a mathematician) would use Newton-Raphson[1] to solve basically any problem that wasn’t very obviously linear. When I was a kid, some of my first programming memories were my dad getting me and my brother to implement Newton-Raphson in basic on an HP85a, getting me to implement Newton-Raphson in rpn on an HP calculator, debugging my dad’s (genuinely revolting) basic program[2] which wouldn’t r…

My dad was also an Engineer. He was also a Fortran fan. Once he asked me to explain OOP. After I explained the basics he said it was useless and never looked back.

Where OOP shines is implementing user interfaces. Most engineers doing math can ignore objects. But when a programmer has to implement a partitionable window with scroll bars and menus, constructing complicated objects built of simpler objects is a mess without OOP.

Re: Every mathematician has only a few tricks (2020)

#62

Post by cultofmetatron »

seanhunter wrote: post #19

My dad (an engineer not a mathematician) would use Newton-Raphson[1] to solve basically any problem that wasn’t very obviously linear. When I was a kid, some of my first programming memories were my dad getting me and my brother to implement Newton-Raphson in basic on an HP85a, getting me to implement Newton-Raphson in rpn on an HP calculator, debugging my dad’s (genuinely revolting) basic program[2] which wouldn’t r…

I fear not the man who practiced 1000 kicks but I fear the man who practiced one kick 1000 times

Re: Every mathematician has only a few tricks (2020)

#63

Post by jcmorrow »

tibbar wrote: post #11
philipov wrote: post #9

Earlier quoted context omitted.

For me, it's tracing code/pipelines to figure out how a result was produced, typically in the context of that result being wrong somehow. Go To Definition is the most useful function in any editor. I'm always surprised by how frequently colleagues don't think to do this and are left helpless.

This reminds me of my further theory that everyone needs one 'heavy' and one 'light' technique. The 'light' technique is something that often works well as a heuristic and can be an effective unit of iteration. The 'heavy' technique is something that you can fall back on in difficult cases, something that can reliably solve hard problems, even if it's slow. Sometimes the heavy technique is: just ask someone else. ;)

I have both felt and seen this at work and I would add to this the meta-technique of binary search. Once it is added to your light and heavy technique you can solve what seems intractable at first glance faster than many people can even orient to the problem.

Re: Every mathematician has only a few tricks (2020)

#64

Post by philipov »

jcmorrow wrote: post #63
tibbar wrote: post #11

Earlier quoted context omitted.

This reminds me of my further theory that everyone needs one 'heavy' and one 'light' technique. The 'light' technique is something that often works well as a heuristic and can be an effective unit of iteration. The 'heavy' technique is something that you can fall back on in difficult cases, something that can reliably solve hard problems, even if it's slow. Sometimes the heavy technique is: just ask someone else. ;)

I have both felt and seen this at work and I would add to this the meta-technique of binary search. Once it is added to your light and heavy technique you can solve what seems intractable at first glance faster than many people can even orient to the problem.

A related meta-technique is "starting at both ends and meeting in the middle". It's kind of like the inverse of binary search in some sense, isn't it?

Re: Every mathematician has only a few tricks (2020)

#65

Post by titzer »

cultofmetatron wrote: post #62
seanhunter wrote: post #19

My dad (an engineer not a mathematician) would use Newton-Raphson[1] to solve basically any problem that wasn’t very obviously linear. When I was a kid, some of my first programming memories were my dad getting me and my brother to implement Newton-Raphson in basic on an HP85a, getting me to implement Newton-Raphson in rpn on an HP calculator, debugging my dad’s (genuinely revolting) basic program[2] which wouldn’t r…

I fear not the man who practiced 1000 kicks but I fear the man who practiced one kick 1000 times

This applies to musicians. E.g. early blues guitarists only had a few licks but they played them so many times they honed them into perfection.

Re: Every mathematician has only a few tricks (2020)

#66

Post by nathanmcrae »

seanhunter wrote: post #19

My dad (an engineer not a mathematician) would use Newton-Raphson[1] to solve basically any problem that wasn’t very obviously linear. When I was a kid, some of my first programming memories were my dad getting me and my brother to implement Newton-Raphson in basic on an HP85a, getting me to implement Newton-Raphson in rpn on an HP calculator, debugging my dad’s (genuinely revolting) basic program[2] which wouldn’t r…

I would also toss differential evolution in the ring as a widely applicable and easy to implement technique.

https://en.wikipedia.org/wiki/Differential_evolution

Re: Every mathematician has only a few tricks (2020)

#68

Post by thr0waway001 »

forinti wrote: post #34
seanhunter wrote: post #19

My dad (an engineer not a mathematician) would use Newton-Raphson[1] to solve basically any problem that wasn’t very obviously linear. When I was a kid, some of my first programming memories were my dad getting me and my brother to implement Newton-Raphson in basic on an HP85a, getting me to implement Newton-Raphson in rpn on an HP calculator, debugging my dad’s (genuinely revolting) basic program[2] which wouldn’t r…

My dad was also an Engineer. He was also a Fortran fan. Once he asked me to explain OOP. After I explained the basics he said it was useless and never looked back.

Seems like a common theme of every veteran to dress the way used to in their prime for the rest of their lives, listen to the same music, watch the same movies, etc. and to use the same belief systems as well. On the one hand, if it worked for them, why not? There's no incentive to change. Heck, it is very much the definition of conservatism. Old men who don't change is so common that it borders on proverbial.

Very rarely, however, do you see a brilliant mind like Richard Feynman, a man who was so open to new ideas and out of the box thinking. Even in old age. Seeing someone, in good faith, question what they believe in light of new knowledge is very rare. Now that is a special thing.

Re: Every mathematician has only a few tricks (2020)

#69

Post by malux85 »

psychoslave wrote: post #45
malux85 wrote: post #7

Earlier quoted context omitted.

“The most successful people have failed more times than you have tried”

Success is relative. If the goal is to never fail, never try is the best strategy. Also the most sure path to finish in the 1% wealthiest is to start in its network. When the game is set to make 99% of players considered as losers in its own terms, the best strategy to have fun at scale is to not care about the highlighted goal. Keep awareness of how rules actually apply, take shortcuts if it feels safe and preferabl…

>Success is relative. If the goal is to never fail, never try is the best strategy.

This is dangerously not true, if you never try, then you are guaranteed to fail to live up to your potential, which is one of the greatest failures of all.

Re: Every mathematician has only a few tricks (2020)

#70

Post by tibbar »

psychoslave wrote: post #45
malux85 wrote: post #7

Earlier quoted context omitted.

“The most successful people have failed more times than you have tried”

Success is relative. If the goal is to never fail, never try is the best strategy. Also the most sure path to finish in the 1% wealthiest is to start in its network. When the game is set to make 99% of players considered as losers in its own terms, the best strategy to have fun at scale is to not care about the highlighted goal. Keep awareness of how rules actually apply, take shortcuts if it feels safe and preferabl…

I am having trouble thinking of situations where the only good outcome is being the top 1%. There are, to be sure, often power-law benefits to being exceptionally good, but to use your own example, being in the top 5% or 10% of wealth is nothing to sneeze at. It's all a spectrum.

With that said, I think you make some good points about the perspective people should have about competitive goals. Most contests are not strict meritocracies, and you are in for a lot of frustration if you assume that only effort matters when other slide by on their structural advantages. I would prefer to reframe the goal as 'work hard on what you have control over, as long as it provides some amount of benefit, and as long as you still care about the outcome.'

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