its sad how he isn't talked about as much as Einstein was



Alexandre Grothendieck

He was no dick.

There are/were a lot of true mathematical geniuses after him, but he's definitely the best of the 20th century, arguably ever although he clearly worked under more favorable conditions than mathematicians of previous centuries. It's just sick to think of all the theory he developed singlehandedly. Dude had true vision.

100 percent agree

for the 20th century, their are only 2 candidates

Grothendieck and Hilbert

There are plenty more candidates. Atiyah, Serre, Weil, Weyl. There was just too much diverse and influential math done in the 20th century to narrow it down to 2 names.

It's the New Year. Time to look forward. What is the likelihood that it will go the way of chess and the greatest mathematician of the 21st century will be a computer program?

would Alan Turing be considered a mathematician?

Definitely. Though I wouldn't put him in the conversation with the people mentioned here.

Zero imo. I'm sure they will continue to be useful to mathematicians, but doing great math requires not just memorization and effort, but synthesis, intuition, and vision. The way great mathematicans solve a hard problem is typically by developing a theory around it, and that problem as well as others fall out of the theory. The developing is a largely creative exercise I don't see computers duplicating any time soon.

The last mathematical genius is yet to be born. Whether of hominid decedents or a direct creation of hominid decedents. Not that any of that matters. Last is a rather silly term. It never lasts for long. Like the last good beer.

well im no expert of course but i like Ramanujan. iirc he discovered like 17-19? formulas for calculating 1/pi. seems a bit supernatural to me.

Is there some reason you didn't include von Neumann?

Happy new year everybody. May you have great health, happiness, creative thoughts and actions in 2017 and beyond.

PS: There is something very disturbing about this;
" dessin d'enfant
Guest

Posts: n/a "

A person with long posting history of contributions to the site doesn't deserve such treatment in my opinion unless something very terrible took place that i missed and i doubt. I don't know what caused it but can't there be a better choice of interactions so that people that invested so much time in the community feel more welcomed and appreciated even when they differ on some things from typical behavior? Does the world get better because of typical behavior by the way usually? What do we learn with conformity? An account with positive long term history deserves a continuity and an open future.

Happy new year buddy.

So whats up, did dessin get his acc deleted or something

Yeah, for not putting DS in that list.

Happy New Year, Masque.

Dessin d'enfant/Max Raker is awesome, obviously.

Not always the most in"genius" way to do it though. If I ask what are the chances of flipping nine coins and getting five or more heads, it would be silly to use your knowledge of combinatorics to do that specific problem. Or take the slightly harder problem of calculating the total number of ways of giving your girlfriend zero to ten different gifts if you have ten to choose from. Pascal's triangle, the coeficients of (x+y) to the tenth power, adding combinations, or seeing an analogy to binary numbers, are all general techniques where the answer "falls out". And using any of those techniques is dumb.

That's how I would do it. The coins one is C(9, 5)(1/2)^9, for example. What is the smart method?

Edit: Sorry, I misread. Yeah, you have to use tables.

Because 9 is odd it is always true that one wins.

p(5 or more out of 9)=p(opponent 4 or less out of 9) one forces the other.

but p(5 or more for you)+p(4 or less for you)=1

since p(4 or less for you)=p(4 or less for opponent) due to symmetry this means

p(5 or more for you out of 9)=1/2

That will work for all odd cases of a fair coin.

pwin=ploss, ptie=0


On the other hand in even number of flips

pwin+ploss+C(2n,n)*(1/2)^2n=1 so

pwin=ploss=1/2*(1-C(2n,n)*1/2^2n)

In other news today while playing with youtube challenges
https://www.youtube.com/watch?v=xgBGibfLD-U

i found this;

√9*log((10^4+5)*8^2+e^(-7!))/√163

gives Pi with 16 digits accuracy lol

3.1415926535897930...vs real thing 3.1415926535897932...

Now what is good about this?

Because it uses all digits/numbers from 1 to 10 only once to do so.

This comes by the way from https://en.wikipedia.org/wiki/Heegner_number


Also definitely computers/AI will solve more mathematical and harder problems than humans in this century.

This is why doing very abstract math and not helping with such vast human intelligence/IQ to get to AI faster is likely stupid/naive/funny or beyond your control likely . Which shows that the very smart (as in abnormally smart not talking about more "reasonable" behaving people like say Hilbert, Gauss, Hardy, Poincare etc type of brains) at least today (and likely all history) are actually a lucky accident of nature, special types of brains bordering on pathology often at the same time as they appear to emit brilliance constantly, unable to control their desires to go after what they do in the most rational manner. Their life choices also reveal that (very eccentric and unreasonable at times). They are not your usual standard understanding of what a very intelligent scientist that is methodical about their work is like ie people like Feynman, Einstein, Dirac, Heisenberg etc that i tend to view actually as the true "heroes" that delivered the impossible with exceptional life long effort not just brilliance. These physicists are in fact the true reason very hard math problems will be solved one day a lot faster than they would have been without technology, relying only on rare accidental brilliance brains being born.

So the very out of this world super-intelligent abstract mathematicians in my opinion cannot do whatever in math or science they want and they choose their topics anyway, no they don't work like that in full "control" of their path! Because if they did they would realize that the best way to solve problems in their top field is to develop the AI that will deliver them and even prolong their own life and brain state as long as they are alive! In a way that makes them eccentric or very selfish too, victims of their own brilliance. It makes them people highly amused by what they are doing but more likely than not not the kind of great brain problem fighters people may think they are. For this reason i see mathematicians like Gauss, Laplace, Lagrange even way back Archimedes etc as more "human" and less alien or in a subtle way pathological. I know i will be criticized for that position but i do view many top math brains in modern history as bordering/flirting with pathology at the same time and this is why all the weird biography details are so frequent with them.

They are bordering/flirting with the study of disease in general?

https://en.wikipedia.org/wiki/Pathology

What's up with Math mind? Why some great mathematicians such as Newton, Einstein, Gödel, Post, and the spirit of solitude Grothendieck become "too eccentric" at the end of their lives?

Gauss said about Galois: " He was the greatest among the youngest, the youngest among the greatest" or something like that. Did Galois have to die so young?

Sometimes I think the Math mind is out of this world. I could be wrong but I doubt it.

http://medical-dictionary.thefreedic....com/pathology

The original term is Greek and works both ways actually there too depending on whether you are very formal and proper or speaking in a less serious manner (same confusing usage there too ie pathologia vs pathologikos but understood by context), the medical study and sometimes the description of the condition ie what properly is best described as pathological instead. Why not focus on what is obvious i am talking about? Why be a bit pathological about this approach lol haha.

Or why do i perceive it that way too as mocking (maybe i am pathological too, but am i?)

(contrast this with a simple note on the jargonistic nature of the expression that should be avoided rather than the flirting with the study of disease mocking - i would not view this as pathological behavior ie behavior intending to insult a little bit the other side - sarcasm or whatever. LOL at grammar police in math thread too but then again it is exactly that grammar police that the abstract math has become about with endless definitions of things and gl to whoever lasts this linguistic game now! In a way Charlie hits the core of the issue here brilliantly metaphorically with this correction and focus on linguistics/grammar. It is after all a chess game of depths, same with the definitions and their endless labyrinth. This obviously now takes a very strange kind of brain like the brain of someone that plays in the blind 20 opponents.)

Anyway i should have used pathological but it was obvious what i was talking about. After all i have no evidence that we are talking about a disease here in the human brain that leads to mathematical skills (but you have the idiot savant cases too). But we are indeed talking about behavior that is abnormal and irrational often inside its own brilliance disconnected from the rest of the world and for that reason appears to be a medical type condition rather than the result of a very long term effort to get there to the capacity to deliver so important results in a very well coordinated life long plan way.

1. the branch of medicine treating of the essential nature of disease, especially of the changes in body tissues and organs that cause or are caused by disease.
2. the structural and functional manifestations of a disease. adj., adj patholog´ic, patholog´ical.
clinical pathology pathology applied to the solution of clinical problems, especially the use of laboratory methods in clinical diagnosis.
comparative pathology that which considers human disease processes in comparison with those of other animals.
experimental pathology the study of artificially induced pathologic processes.
oral pathology that which treats of conditions causing or resulting from morbid anatomic or functional changes in the structures of the mouth.
speech pathology (speech-language pathology) a field of the health sciences dealing with the evaluation of speech, language, and voice disorders and the rehabilitation of patients with such disorders not amenable to medical or surgical treatment. See also speech-language pathologist.
surgical pathology the pathology of disease processes that are surgically accessible for diagnosis or treatment.
Miller-Keane Encyclopedia and Dictionary of Medicine, Nursing, and Allied Health, Seventh Edition. © 2003 by Saunders, an imprint of Elsevier, Inc. All rights reserved.
pa·thol·o·gy (pa-thol'ŏ-jē), Avoid the jargonistic use of this word in the sense of 'disease' or 'abnormality.'
The form of medical science and specialty practice concerned with all aspects of disease, but with special reference to the essential nature, causes, and development of abnormal conditions, as well as the structural and functional changes that result from the disease processes.
[patho- + G. logos, study, treatise]

As long as mental affections do not affect the capability to work, they may not be "normal" but they are not considered pathological either.

well i think there have been some studies on some superb brains in mri scanning (or something like that) and i think they found that they distinguished themselves by having parts of both sides of the brain light up when they were thinking about some puzzles (or whatever it was). the brain is sort of divided into left and right and in normal people it lights up in one part at the time (for the most part and in this context). but these ppl seemed to utilize both parts at once. that may be one of the clues to how they do smart things that other people cant. i dont remember all the details or how everything went down.

when it comes to pathology the very intelligent is disproportionally represented having heavy mental diseases. i dont think thats news.