71–80 of 111 posts
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Maybe today's emphasis on "well rounded" education is a distraction from specialized talents.
Euler did his master’s dissertation on the philosophies of Descartes and Newton. He then joined the faculty at University of Basel in theology. I think this is ample evidence that he received a well-rounded education.
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Euler is in a class of one. Judging by the volume of work and the pleasure he takes in collaborations, Terence Tao seems to be having a positive impact. I am not a mathematician but I hear good things about the quality of his work.
> I am not a mathematician but I hear good things about the quality of his work. Not to be rude, but saying this about a Fields medallist is somehow very funny.
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Education is a cog/mandarin factory in most countries. Whizzkids will educate themselves, what's needed is giving people idle time in order to pursue things. Most influential thinkers found themselves with this in some fashion. How much talent is wasted making people jump through hoops in academia/finance/ad-tech? A lot of pre-industrial thinkers were associated with the clergy because they received tax money from pe…
The issue I see these days is that every industry is getting more and more competitive, and leaves less and less time to think more broadly or creatively. Can't go off reading about differential geometry when you need a guaranteed perfect SAT, a great entrance essay (i.e. a strong personal story), and easy-to-gauge extracurriculars ("placed X in Y", not "read some smart books and had some interesting thoughts that do…
I have read a few of these and enjoyed them greatly. Reading them you realise that Euler really did invent a huge swathe of mathematics in use today. In particular I read this one: http://eulerarchive.maa.org/hedi/HEDI-2009-02.pdf And I realised that Euler had found two formulae for Pi which can be used to calculate any hex digit of Pi. I wrote this up in a paper: "In 1779 Euler discovered two formulas for π which ca…
One other cool thing about Euler and BBP-type pi series: Euler seems to have derived his results in a manner similar to how the famous BBP formula
{\displaystyle \pi =\sum _{k=0}^{\infty }\left[{\frac {1}{16^{k}}}\left({\frac {4}{8k+1}}-{\frac {2}{8k+4}}-{\frac {1}{8k+5}}-{\frac {1}{8k+6}}\right)\right]}
is actually proven. A friend of mine gave the proof of the famous series result as an exercise in his honors calc 2 class one year. They had some fun with it.
https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%9...
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I always stress how our public education is broken since it can't handle extreme talent very good. Important breakthroughs that advance one or more fields extremely or shifting paradigms completely, were done or prepared by whizzkids. In these times, we need every whizzkid we can get.
Education is a cog/mandarin factory in most countries. Whizzkids will educate themselves, what's needed is giving people idle time in order to pursue things. Most influential thinkers found themselves with this in some fashion. How much talent is wasted making people jump through hoops in academia/finance/ad-tech? A lot of pre-industrial thinkers were associated with the clergy because they received tax money from pe…
Only those you see becoming one.
You never hear of all the "Einsteins" who never leave the patents office because they never got inspired for some passion or various other stupid reasons.
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I always stress how our public education is broken since it can't handle extreme talent very good. Important breakthroughs that advance one or more fields extremely or shifting paradigms completely, were done or prepared by whizzkids. In these times, we need every whizzkid we can get.
No system will handle an Euler well. It’s best to recognize them and move them out of the system.
I wouldn't be so pessimistic.
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The low hanging fruit argument only takes you so far. How many other mathematicians in his epoch or before were able to pick as many low hanging fruits as him?
By all means he was a crazy outlier generational genius. A few others in history, like Archimedes and Newton, have been accused of "not leaving anything for anyone else to discover" as well. The question was: why do we not seem to see these crazy outliers anymore? The answer is certainly not that truly exceptional people simply stopped being born after the year 1800. The nature of what it could mean to "know everythi…
Newton and Leibniz discovered calculus simultaneously. If calculus were a hot new idea now, dozens or hundreds of people would be discovering it simultaneously.
Look at NN/LLM AI for an example.
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Part of the problem is he wrote so much it has taken a while to go through it all. I believe the "Opera Omnia" project to publish all his works has been going for over a hundred years and is just about getting to the end now. So I would expect there's a huge amount that just hasn't been fully appreciated/digested.
How is this humanly possible? Was Euler even an order of magnitude faster at producing new math than, say, Gauss or von Neumann?
Euler's wikipedia page has one of the most casually jawdropping sentences I've ever read about a human being: "Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century." A quarter of a…
I own a copy of his "Elements of Algebra" and it's interesting to read because he actually talks and uses the notion of infinitesimals in this basic algebra book. And it makes sense! He essentially just says "think of the biggest number, make it even bigger!!! Now, put it under 1, and just like that we 'get almost zero'"
You would never see something like that now, or even then really, and yet the idea is so simple a kid understands. His writing just has such an optimistic and playful sense to it.