mathoverflow.net/questions/20112/interesting-results-in-algebraic-geometry-accessible-to-3rd-year-undergraduates Interesting results in algebraic geometry accessible to 3rd year undergraduates
An elliptic curve is defined by numbers and . The curve is the set of all points of the real plane that satisfy the Equation 1. "Definition of the elliptic curves"
Equation 1. "Definition of the elliptic curves" definies elliptic curves over any field, it doesn't have to the real numbers. Notably, the definition also works for finite fields, leading to elliptic curve over a finite fields, which are the ones used in Elliptic-curve Diffie-Hellman cyprotgraphy.
Deterministic perfect information board game by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli is a collector at heart. But a collector of knowledge.
His uncle, which Ciro rassembles in many ways, was like that. But he collected physical objects such as wines and stamps. Or even worse, objects that were meant to be collected such Panini soccer sticker Albums! This Ciro looks down on.
With computers, knowledge takes no physical space and can be immediately shared with the hole world, and there is great beauty to that, as you can just keep collecting forever without filling up your house.
But of course, physical or not, all attachments futile.
Like other types collecting, once Ciro decides that "he must know everything about a given subject", he will keep coming back to that subject over and over. Not in a systematic way of course, since Ciro is a lazy bastard, but he will keep coming back for a very long time, and eventually become an expert at it.
This compulsive hoarding, together with Ciro Santilli's bad old event memory, are the fundamental reasons for OurBigBook.com.
If you are a pussy and work a soul crushing job, this is one way to lie to yourself that your life is still worth living: do one cool thing every day.
Find a time in which your mind hasn't yet been destroyed by useless work, usually in the morning before work, and do one thing you actually like in life.
Work a little less well for you boss, and a little better for yourself. Ross Ulbricht:Selling drugs online is not advisable however.
I hated working for someone else and trading my time for money with no investment in myself
Even better, try to reach an official agreement with your employer to work 20% less than the standard work week. For example, you could work one day less every week, and do whatever you want on that day. It is not possible to push your passion to weekends, because your brain is too tired. "You keep all non-company-related IP you develop on that time" is a key clause obviously.
On a related note, good employers must allow employees to do whichever the fuck "crazy projects", "needed refactorings or other efficiency gains" and "learn things deeply" at least 20% of their time if employees want that: en.wikipedia.org/wiki/20%25_Project. Employees must choose if they want to do it one day a week or two hours per day. One day per month initiatives are bullshit. Another related name: genius hour.
Highly relevant on this topic: Video "What Predicts Academic Ability? by Jordan B Peterson (2017)".
Maybe you will be fired, but long term, having tried, or even succeeded your dream, or a one of its side effects, will be infinitely more satisfying.
The same goes for school, and maybe even more so because your parents can still support you there. Some Gods who actually followed this advice and didn't end up living under a bridge:
- George M. Church "[We] hope that whatever problems... contributed to your lack of success... at Duke will not keep you from a successful pursuit of a productive career." Lol, as of 2019 the dude is the most famous biotechnologist in the world, those "problems" certainly didn't keep him back.
- Freeman Dyson proved the equivalence of the three existing versions of quantum electrodynamics theories that were around at his time, and he has always been proud of not having a PhD!
- Ramanujan, from Wikipedia:
He received a scholarship to study at Government Arts College, Kumbakonam, but was so intent on mathematics that he could not focus on any other subjects and failed most of them, losing his scholarship in the process.
- Person that Ciro met personally and shall remain anonymous for now for his privacy: once Ciro was at a bar with work colleagues casually, it was cramped, and an older dude sat next to his group.The dude then started a conversation with Ciro, and soon he explained that he was a mathematician and software engineer.As a Mathematician, he had contributed to the classification of finite simple groups, and had a short Wiki page because of that.He never did a PhD, and said that academia was a waste of time, and that you can get as much done by working part time a decent job and doing your research part time, since you skip all the bullshit of academia like this.Yet, he was still invited by collaborating professors to give classes on his research subject in one of the most prestigious universities in the world. Students would call him Doctor X., and he would correct them: Mister X.As a software engineer, he had done a lot of hardcore assembly level optimizations for x86 for some mathematical libraries related to his mathematics interests. He started talking microarchitecture with Ciro's colleagues.And he currently worked on an awesome open source project backed by a company.At last but not least, he said he also fathered 17 children by donating his sperm to lesbian mothers found on a local gay magazine, and that he had met most/all of those children after they were born.A God. Possibly the most remarkable person Ciro ever met, and his jaw was truly dropped.
Gandhi TODO source:
You can chain me, you can torture me, you can even destroy this body, but you will never imprison my mind
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