Math is better for comfort

Really escaped celebrity I now realize. Will put 'celebrity' label on this post as am talking it. The labels I think are helpful for others but great for me as well.

This blog goes back to 2005 and is useful to have help navigating it.

Had a global event I now know with that bizarre publication story I talked so much! But made no sense to me that I got published and nothing went right. 

Hostile people just ripped on me still and talked like publication didn't matter.

Thankfully here could refine and simplify argument and realized that people can just lie. My research success clearly caused so much hatred but I escaped most of it. Could just blog here and continue to advance.

Has been over 18 years now and just able to talk joy of lack of celebrity and staying free of social obligations because of my math. But yeah did get attention I know. Is just with public is quietly respectful.

Studied celebrities worried needed to understand but knowledge areas are so different. But I did safely interact with many celebrities online! And that ended when Google failed at social media as was mostly through now dead Google+ and I feel so lucky.

Gave a post earlier this year just to show a result again of my modular inverse method. Am like Euler in giving one. It still rattles me though. Took 5 years to give such a simple example. That's ok.

Math is my comfort and is how I get reassurance. Is perfectly reliable. Is really my best friend that will never leave me.

Reassurance with my math

Finally found myself just playing around with my method for finding a modular inverse and was reassuring. Math is that way. Doing a post to let know am still active and to show it again.

So will calculate modular inverse of 19 mod 1001 which is 7(11)(13).

Let 2m = 1 mod 1001, then F₀ = 19(19 + y₀) mod 1001. Can pick y₀ = 34. Then F₀ = 6 mod 1001. That was lucky! Can pick whatever I like. 

Picking so that F₀ is as small as possible without 19 as a factor but coprime to 1001, and usually regardless have found need to recurse with coefficient of d as new modulus.

6d = (6n - 7)(53) mod 1001

6d = 318n - 371 mod 1001 

And 6(167) = 1002 = 1 mod 1001 which is very convenient.

So: d = 53n - 896 mod 1001, so can use n = 1 and then d = -843. So 19^-1 = 843 mod 1001.

Those values worked better than I expected, as of course really like easy. But yeah is very reassuring to just do some math and get the correct answer. 

My way makes calculating the modular inverse so straightforward.

Am still active on this blog but often just reviewing. Have a lot of research results! Can play around endlessly with them.

Definitions drive innovation

Finally got around to defining mathematics and thought would emphasize how much a definition can help guide to new things never before considered.

Was back in 2005 when posted here my definition of mathematical proof which I discovered as got tired of screwing up so much.

Repeatedly my emotions got in the way and could take me MONTHS to find errors in mathematical arguments.

But with that definition could check even complex arguments in minutes.

Innovation has been at the forefront of what I do. And have over two decades now of discovery pushing past prior limits to ever greater knowledge. Better defining possibility is in definitions at the foundations.

Defining mathematics

Mathematics is a part of logic that is just about numbers and relationships between numbers.

Keys to analysis of numbers are conditional statements that are identities for a set of values for variables.

Identities are tautological statements with numbers. For example: 1 = 1

A conditional statement has variables for which is an identity. 

For example: x² + y² = z²

Is a valid statement for x = 3, y = 4, and z = 5.

Then reduces to 25 = 25.

The sets of values for which a conditional statement is an identity are solution sets.