Translate

Thursday, January 11, 2018

Some math perspective and pep talk

The math sustains me like to say, and getting going into a new year is useful to reflect on just a bit, some of how that works.

Like one of those results will use for comfort:

P(x,n) = [x] - 1 - sum for j=1 to n of {P([x/p_j],j-1) - (j-1)}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

My way to count primes in its sieve form.

That is SO compact! The math has a succinct efficiency I appreciate. One of my favorite posts talking is actually on my blog Beyond Mundane: Simple and fast prime counter

One of the last results where I got lots of criticism over a decade ago, where what I saw as specious comparison to known methods ignored the new. Yes, basic concepts were same, so?

The innovation involved is how is simply displayed and compact, which is also obvious in comparison.

Love considering as the time passes. As over 15 years now and yeah, look over what math people still teach, as if a world of students cannot also find easier on the web.

And something that so floored me only a few years ago, realizing can easily find all integer solutions for:

x2 + (m-1)y2 = mn+1

From: Squares and nth powers

Not surprisingly to me, using this result, which follows from my BQD Iterator could make for popular shares. Like:

12 + 32 = 10

82 + 62 = 102

262 + 182 = 103

282 + 962 = 104

3162 + 122 = 105

From: Sum two squares to power of 10

Simplicity has HUGE benefits as if people get curious can check you on EVERY math detail. Web enables a lot as well, as folks can know. They can just check you on the facts.

Can also check what they thought they knew, about others in a high profile area. For me was lots of surprise for years.

Now these results are comforting, while less exciting, for me.

There is that thing about the math where when you discover you get a different emotional connection to your discoveries, which I know from how I look at my math discoveries versus math from others.

The math does not care. That actually IS a comfort. Because the knowledge is more important to me.

So yeah, this pep talk is working for me like usual. And what discoveries to pick? Is just about my mood. Could talk my better than Gauss's way to reduce binary quadratic Diophantine equations. Could go on again about my modular inverse method, but am on pause there. Still relishing it though.

Or lots of other things.

Pep talk complete! Well I feel better now. Who knows why humans who come and go might fight against mathematical discovery, and do we really care?

The math feels like a friend to me. And I know the math does not care. Convincing myself, I should not either. We humans have choice.

Knowledge should be about reinforcing choice. The math has given me more choice. Am thankful.


James Harris

No comments: