I recall a university lecturer telling us that mathematicians were still working to try and *rigourously* verify the validity of the techniques involved in the finite element method, long after engineers had started actually using it on real world problems. Very different mindset, in that respect!
I only know about perfect numbers because my wife once told me our wedding anniversary was perfect, which I incorrectly took as a compliment. We shan't live long enough for the next one...
I’ve always liked maths for its demand that you don’t just solve for the particular, you solve for the general case (my father did a maths degree and he liked encouraging to think in that way).
I’m interested by two elements of “professional maths”:
- how the little or big breakthroughs come about (it feels like they’re indescribably intellectual leaps, not slogging away like someone learning times tables) and
- how what seem like abstract concepts are applied to the real world - logs being obviously the one we are most familiar with lately, but one wonders how often knot theory or similar gets applied in factories. I’d find that interesting to read about.
Roger Penrose has some wonderful anecdotes of mathematicians talking to mathematicans about maths, often apparently incomprehensibly, and of maths emerging as it were from background and prior thought. Increasingly I think we do not know science or intellectual endeavour unless we know more of the history: logic, philosophy, demonstration (e.g. counting?) and coherence ('proof'?). Interesting indeed.
I love your dedication to things I would have a clue how to go about starting. You’ve reminded me of “Wondrous Numbers” that I read about probably about 40 years ago. So simple, and yet never proved. So far, all numbers have turned out to be wondrous, but there still might be be one that isn’t:
Interesting, thanks.
I recall a university lecturer telling us that mathematicians were still working to try and *rigourously* verify the validity of the techniques involved in the finite element method, long after engineers had started actually using it on real world problems. Very different mindset, in that respect!
I only know about perfect numbers because my wife once told me our wedding anniversary was perfect, which I incorrectly took as a compliment. We shan't live long enough for the next one...
I’ve always liked maths for its demand that you don’t just solve for the particular, you solve for the general case (my father did a maths degree and he liked encouraging to think in that way).
I’m interested by two elements of “professional maths”:
- how the little or big breakthroughs come about (it feels like they’re indescribably intellectual leaps, not slogging away like someone learning times tables) and
- how what seem like abstract concepts are applied to the real world - logs being obviously the one we are most familiar with lately, but one wonders how often knot theory or similar gets applied in factories. I’d find that interesting to read about.
Roger Penrose has some wonderful anecdotes of mathematicians talking to mathematicans about maths, often apparently incomprehensibly, and of maths emerging as it were from background and prior thought. Increasingly I think we do not know science or intellectual endeavour unless we know more of the history: logic, philosophy, demonstration (e.g. counting?) and coherence ('proof'?). Interesting indeed.
ok, definitely a Paul Simon fan :)
I love your dedication to things I would have a clue how to go about starting. You’ve reminded me of “Wondrous Numbers” that I read about probably about 40 years ago. So simple, and yet never proved. So far, all numbers have turned out to be wondrous, but there still might be be one that isn’t:
https://en.wikipedia.org/wiki/Collatz_conjecture
And do you also solve or offer statistical advice services to other scientific disciplines?