# A Mathematician's Knowledge

J77
Then there is zero chance of said kids being the best mathematicians to attend the local primary school (elementary for the Americans), no matter what I do, since they have to cope with Ben Green and Paul Dirac as alumni.
Nah - with the new government places-from-lottery incentives they've an equal chance to end up in Hartcliffe, then they're likely to be the best if they get a GCSE :tongue:

Gib Z
Homework Helper
Tell me what $$e^{i\pi +2ki\pi}$$ is equal to then :)

Edit: Holy whack theres been alot of posts today, I was replying to people the page before, about ln -1...

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Ok, this may sound like a stupid question, but I really, really need to know.

How much more mathematical knowledge does a typical mathematician have than a math specialist student who has just finished fourth year university math courses?

Before you criticize my question, let me explain why I ask. I want to become a mathematician, so I need to get a feel of how much knowledge I need to acquire before I can become one. Now, I know that knowledge is not everything. Indeed, it is problem solving skills and generation of ideas that makes a true mathematician. I agree! Nevertheless, one must have immense prerequisite knowledge before they can come up with original ideas and solve open problems.

If the answer is, say, 3 times as much. Then I can focus on my problem solving skills, read thoroughly the proofs of theorems, etc..., and build my knowledge at the pace of a regular student. If, however, the answer is, say, 100 times as much, then I will know that I have to step up on my reading. So this question, I think, is important in order for me to get a sense of how much and in what manner I should self-study.

My guess is that a typical mathematician has 50 times as much knowledge as a math student who has just graduated from university. Any other ideas? A mathematician's honest answer would be greatly appreciated (and I won't think you are being arrogant).
Psychologists estimate 10,000 hrs before you can match the "masters" in a field and begin producing novel work. I think university math needs to be distinguished from pre-university math as the two are entirely different animals.

How many hrs did we spend in university studying Math independently?

3 years (UK system) x 30 weeks x 6 days x 4 hrs/day = 2160 hrs.

That's 21.6% of the way to becoming a first class professional mathematician.

Of course, if you're one of those hardworking kids who did 8 hrs a day, day in, day out, then it'll have been 4320 hrs, and you'll be considerably closer to your goal. (43.2%).

Add in a masters and postgraduate degree and you'll probably have clocked in 10,000 hrs, which is what you need to do to become a first-rate mathematician.

<My guess is that a typical mathematician has 50 times as much knowledge as a math student who has just graduated from university. Any other ideas?>

It's impossible to quantify but if you want numbers, my guess is that a working mathematician has many times more knowledge in their specialty than a new graduate, but probably less in adjacent areas due to forgetfulness. It's like that old saying, an expert has forgotten more than a non-expert ever knew.

But I don't think that's the right measure. A better measure is the hard to define quality of mathematical maturity. A working mathematician typically has much higher level of maturity than a new student, allowing him or her to gain insight and assimilate new material more rapdidly, and to quickly extract the essence of a theorem or proof. This is a mental activity that only comes with experience.