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There’s more to mathematics than rigour and proofs (2007)

terrytao.wordpress.com

11–20 of 95 posts

Re: There’s more to mathematics than rigour and proofs (2007)

#11
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

Aim for financial independence on that SDE and you can retire a few decades ahead of schedule. And you’ll have plenty of time for that sweet math learning.

Re: There’s more to mathematics than rigour and proofs (2007)

#12
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

keep the salary. if the goal it to change the world, to understand reality, to have an impactful life, have a good standard of living, etc. math is one of the hardest ways of achieving that. It's such a saturated field. Almost everything you can imagine has been done to the highest possible degree of abstraction. Every stone overturned except for things which may take a lifetime to even try to understand. Writing a b…

I'm not going to gainsay your experience, but it doesn't match mine. Much of what you do in graduate school is to discover where the accessible areas of research are--where do we have a foothold, and are making progress, and what are some achievable results?

There are big and hairy problems that are bad investments for a young mathematician. I would steer students clear of the Collatz conjecture. But once you get up to speed in your research area, you usually find interesting problems thick on the ground.

Tenure-track positions are competitive, but I don't think there are a lack of interesting things to work on.

Re: There’s more to mathematics than rigour and proofs (2007)

#13
post #8
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

One of my biggest regrets is not having studied (more) math. But would I regret not studying CS had I studied math? You really can't win :/

CS is math...

Re: There’s more to mathematics than rigour and proofs (2007)

#14
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

I'm still grumpy that I accepted I knew what real numbers were just because I could recite back the definition given by the teacher. There is so much depth there if you go looking...

The way I explain this super simply to people is absolute value.

To most people, it just means that when you take the absolute value of a negative number it becomes positive, and the absolute value of a positive number stays positive.

Now there is more to it, but how you might think of absolute value instead is as a distance function, particularly how far away from zero you are on a number line.

This is way over simplified, but an example of how there can be a little more buried beneath the surface.

Re: There’s more to mathematics than rigour and proofs (2007)

#15
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

I'm actually looking into this. Just an hour ago I mailed the local university that I won't be doing any courses there. My initial plan was to do a bachelor at around 50% speed. But working and having to girls (1,5 years and 3 weeks) makes that quite impossible. And looking at photos of myself at 17 makes me feel rather out of place at a university at age 42.

The Open University has an AI master that I'm thinking about right now. It has about 25% of the math that I want to learn, so that would be a good start. I did some prep work (an official high school math certificate) last few months and I noticed that I need a schedule to keep me going.

One thing that I'm quite certain about, is that doing math is the most important thing. And doing math leads to more doing math.

Re: There’s more to mathematics than rigour and proofs (2007)

#16
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

keep the salary. if the goal it to change the world, to understand reality, to have an impactful life, have a good standard of living, etc. math is one of the hardest ways of achieving that. It's such a saturated field. Almost everything you can imagine has been done to the highest possible degree of abstraction. Every stone overturned except for things which may take a lifetime to even try to understand. Writing a b…

About the simulation hypothesia, how is that different from Descartes evil demon?

https://en.m.wikipedia.org/wiki/Evil_demon

(apart from saying that the evil demon is a future type computer)

Re: There’s more to mathematics than rigour and proofs (2007)

#17
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

In the same boat. One of my dreams is to go back to school, learn vector analysis, differential equation, differential geometry, classic mechanics, electromagnetic, special relativity and finally general relativity.

Actually quite doable as long as one can grit through the Math, some of which do not need a back to back read.

Re: There’s more to mathematics than rigour and proofs (2007)

#18
post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

keep the salary. if the goal it to change the world, to understand reality, to have an impactful life, have a good standard of living, etc. math is one of the hardest ways of achieving that. It's such a saturated field. Almost everything you can imagine has been done to the highest possible degree of abstraction. Every stone overturned except for things which may take a lifetime to even try to understand. Writing a b…

What was this utter gibberish I just read? I’m absolutely positive you have the least idea of what modern mathematical research entails or is even about. Please refrain from sharing your opinions on subject matters which you clearly lack any understanding of.

Re: There’s more to mathematics than rigour and proofs (2007)

#19
I love Terry Tao’s writing on math. One thing that strikes me about him is that, despite being an absolute technical powerhouse, he writes in a very down to earth style that connects disparate areas of math - e.g. his article on “what is a gauge” https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/am... where he explains how dimensional analysis might be viewed as a change of coordinates. Too often exposition in math is myopic and fails to impart a unique perspective on the subject, but Tao imbues his writing with a wisdom that I consider the sign of a true genius.
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