What are the Millennium Prize problems?

Jennifer Alonso García · 14-01-2021 10:00 · CEBE answers

It will not come to you as a surprise if I tell you that mathematicians love problems. Our lives revolve around finding and trying to solve problems. Often, we observe natural phenomena and wonder whether mathematics could help us to formally model their dynamics to further advance our understanding of the world. Sometimes, we discover problems and study theories that might not have a direct practical application. Luckily, more often than not, these theories, formerly viewed as “useless” have led to breakthroughs in science and technology. For example, number theory was seen as “useless” until Ron Rivest, Adi Shamir and Leonard Adleman created the RSA algorithm that since 1977 allows for secure data transmission.

Some of these mathematical challenges are what the Clay Mathematics Institute, based in New Hampshire (United States), calls the "Millennium Prize Problems". This institute selected seven important classic questions that had resisted solution by 2000. These problems were the “Poincaré conjecture”; the “P vs NP”; the “Hodge conjecture”; the “Riemann hypothesis”; the “Yang-Mills and mass gap”; the “Navier-Stokes equation”, and the “Birch and Swinnerton-Dyer conjecture”. To date, only the “Poincaré conjecture” has been solved, in this case by Russian mathematician Grigori Perelman in 2003. His result proves that 3-dimensional spaces without holes (a donut is an example of a space with a hole) can be deformed to a 3-dimensional sphere.

Among the unsolved remainder, let us focus on the fascinating "P vs NP problem".  

This is considered by many experts the most important open problem in computer science. Why? Think of a Sudoku grid which is an example of a NP problem. But first, let´s explain what a P problem is: If I give you a potential solution of a Sudoku grid, then it is easy to verify the solution. The time to check the solution increases with the grid, but it does not explode. In the case of the NP problem we find the inverse problem: Finding a solution to a Sudoku grid is hard and the bigger the grid the slower it becomes to find a solution. NP problems are difficult to solve but easy to check once we have found the solution (see graph). On the other hand, I can find solutions quickly for P problems.

Most computer scientists think that P is not equal to NP, as nobody has been able to prove yet that P = NP in well-known NP problems. The solution to this “Millenium Prize” problem would have great implications in our daily life. For example, if P=NP is true then it would mean that cryptography, an NP problem which is the mathematical base of all our online security systems, should be fully rethought. Think of accessing your email account. It is super easy to access if you know the password, but it is extremely hard to find the password if you do not know it already. If P=NP then it will be possible to create an algorithm that finds the password easily. Not all is bad news if P = NP because we would be able to solve many important problems in, for instance, logistics. Think of a salesman problem. For a given list of cities and distances, what is the shortest possible route that goes from the origin city to each city exactly once and returns to the origin city? It sounds easy, but it is actually a very hard optimization problem. If it is proven that P is not equal to NP, it would have less practical computational benefits but would clarify once for all that it is just not possible to develop quick algorithms to solve all problems. That would shift the focus of researchers to finding partial solutions instead of exact ones. Either way, very cool right?

In case you find some free time and solve one of these problems (you can find more info about the other ones here), you will help advance humanity and feed your savings account with a US$1 million prize.

Comments

Мисс Марвел 1 сезон. смотреть онлайн <a href="http://bit.ly/ms-marvel-1-8-seriya">Мисс Марвел (2021) смотреть онлайн бесплатно</a> Мисс Марвел (2021) смотреть онлайн бесплатно

ms-marveleunyg , 26 May 2022

Фильмы и сериалы - смотреть эфир онлайн. <a href="http://bit.ly/3jcmOtY">Прощание смотреть онлайн</a> Смотреть фильм онлайн - список всех старых фильмов, фильмография.

33225013 69924963 32865949153 92641647347956268759

75976308 33762359 877651136795 3836901584219309266

43411298 83416038 473624277483 7222587124839408531

ms-marveljmypf , 03 Jun 2022

Смотреть, Скачать MP4 360p, MP4 720p. <a href="http://bit.ly/3aZMHs3">Создатель просмотр фильма онлайн</a> Смотрите фильмы для всей семьи в лучшем онлайн-сервисе

29801201 6309445 188664617943 79686842770719108419

87119170 92505058 60059885601 8238677214866334638

76586999 82241139 99508211614 3511631112891380196

ms-marvelnkpzs , 03 Jun 2022

Последние выпуски передач и новые серии любимых сериалов! <a href="http://bit.ly/2S1ZKSr">Поезд в Пусан 2 Полуостров просмотр фильма онлайн</a> Смотреть онлайн полный фильм в HD 1080 фильмы онлайн

7731468 45108874 48691656598 7253709886032194980

6758968 33275421 897446617047 1989158230991831972

4456420 93447349 26092486589 4338210465803256031

ms-marvelwscea , 04 Jun 2022

https://bit.ly/Shkala-tonov

86573638 99628602 641683123498 29211459687595687299

57657475 54483631 837544988729 90155011985956961329

61126033 26694756 397211614240 7506806312216649497

lwbvuklerfpo , 13 Jun 2022

https://bit.ly/Shkala-tonov

5298256 41047125 705345606573 94738244658137443965

47633929 13198227 806242224223 7142837483586069918

67859592 86485510 680376107628 27431726160117898117

lmfzidlzxyoq , 13 Jun 2022

Мир Юрского периода: Господство http://bit.ly/mir-yurskogo-perioda-2022

86885040 1660353 817513261468 4290301112525408871

93053610 70869062 800539855519 25425412112947239266

6752855 88472032 956935251313 13087524511388406596

ltolgqlgfniu , 13 Jun 2022

http://is.gd/a2aKt7

luddfqlrcccc , 16 Jun 2022

http://clck.ru/rD36i

ljzznllzzkpj , 16 Jun 2022

Ривердэйл 1,2,3,4,5,6 сезон <a href="http://bit.ly/riverdehjl-6-sezon">Ривердэйл 1,2,3,4,5,6 сезон</a> Riverdale: наконец-то новый качественный молодежный сериал. Ривердэйл - сериал, которого мы так ждали от CW.
Ривердэйл хранит немало секретов и мистических тайн. Нашим неуемным искателям развлечений будет вовсе не до улыбок.
«Ривердейл» (англ. Riverdale) — американская телевизионная подростковая драма, основанная на комиксах Арчи.
Все серии подряд доступны бесплатно, в хорошем качестве HD 720p и FullHD 1080p на русском языке.

ldnppzljojow , 16 Jun 2022

http://tinyurl.com/2ad46zml

lacsoalbgdoq , 17 Jun 2022

http://tinyurl.com/27xw5c8u

ljbcwolvbipw , 17 Jun 2022

http://tinyurl.com/28wmw2cz

lqzjdhlbmmfi , 17 Jun 2022

http://images.google.co.zw/url?q=http://netstate.ru/

lrdizilljqit , 18 Jun 2022

http://images.google.co.zw/url?q=http://netstate.ru/

lwpkrglcmzcs , 18 Jun 2022

http://netstate.ru/video-2/index.html

llljldlwsomn , 19 Jul 2022

gay lesbian chat
gay mature men chat group
<a href="https://free-gay-sex-chat.com/">anonymous gay chat </a>

DeeynKlmr , 15 Sep 2022

gay chat apps for pc
<a href=https://chatcongays.com>ladybug chat noir gay</a>
gay universe man chat

GennieKlmr , 16 Sep 2022

custom essay writing
<a href=https://au-bestessays.org>essay writing service scam</a>
buy cheap essay online

MarrisKlmr , 20 Sep 2022

cheap essay buy
<a href=https://bestcampusessays.com>custom essay online</a>
i need help writing a narrative essay

DorolisaKlmr , 21 Sep 2022

college application essay writers
<a href=https://besteasyessays.org>best essay review services</a>
original essay writing service

MartyKlmr , 22 Sep 2022

best online essay writing service
<a href=https://bestessayreviews.net>i need someone to write my essay</a>
college essay help service

MerolaKlmr , 22 Sep 2022

best college essay writing services
<a href=https://bestessaysden.com>admissions essay help</a>
the best essay writers

AshlenKlmr , 23 Sep 2022

helping others essay
<a href=https://buyacademicessay.com>essay help live chat</a>
custom essay meister

NaniceKlmr , 26 Sep 2022

write my college essay for me
<a href=https://buy-eessay-online.com>write my essay online</a>
essay paper help

ChelsaeKlmr , 26 Sep 2022

helping others essays
<a href=https://buytopessays.com>usa essay writing services</a>
service essay

PennyKlmr , 27 Sep 2022

cheap essay
<a href=https://cheapessaywritingservice1.com>college essay writing help</a>
help me write an essay

TammieKlmr , 28 Sep 2022

essay writing service review
<a href=https://customcollegeessays.net>buying essay</a>
essaywriting service

AntonieKlmr , 29 Sep 2022

help to write essay
<a href=https://customessays-writing.org>how to be a good essay writer</a>
write my essay affordable

RhiamonKlmr , 30 Sep 2022

custom essay writing service org
<a href=https://customessaywwriting.com>custom admission essay</a>
college admission essay service

CharoKlmr , 30 Sep 2022

services essay
<a href=https://customs-essays-writing.org>best online essay writing service</a>
best essay review services

DronaKlmr , 01 Oct 2022

buy essay online cheap
<a href=https://firstessayservice.net>help with my essay</a>
personal essay writing service

TwylaKlmr , 02 Oct 2022

help me write a compare and contrast essay
<a href=https://geniusessaywriters.net>best custom essay writing service</a>
help writing college essays

LeilahKlmr , 03 Oct 2022

i need help on writing an essay
<a href=https://howtobuyanessay.com>buy essay online cheap</a>
custom essay company

CthrineKlmr , 04 Oct 2022

<a href=http://buylasixon.com/>lasix for dogs</a> Crazyfrog BcYvAOJuXbcWsrI 6 26 2022

Estuawl , 09 Oct 2022

help me with my essay
<a href=https://lawessayhelpinlondon.com>write my essay for me cheap</a>
buy essay online

GinnieKlmr , 09 Oct 2022

admission essay services
<a href=https://writemyessaycheap24h.com>help writing a compare and contrast essay</a>
custom essay writing service reviews

EasterKlmr , 13 Oct 2022

custom essays
<a href=https://besteasyessays.org>custom essay station</a>
best paper writing site

MartyKlmr , 20 Nov 2022

buy custom essays
<a href=https://bestessayreviews.net>essay helpers</a>
best essay helper

MerolaKlmr , 22 Nov 2022

buy custom essay
<a href=https://buyacademicessay.com>help writing a argumentative essay</a>
custom essay meister

NaniceKlmr , 26 Nov 2022

Leave a comment


Collaborative partners

This blog is supported by the Arts and Culture section of the Spanish Embassy in Belgium and by the Brussels section of the “Instituto Cervantes”, under the SciComm initiative #SPreadScience.

Instituto Cervantes Arts and Culture section of the Spanish Embassy

Disclaimer: The content of each post in “A Spoonful Of Science” is the responsibility of the corresponding author(s). Therefore, the viewpoints expressed on the blog are those of the author(s) of each post, which do not necessarily reflect the viewpoints, thoughts and opinions of CEBE members and representatives.

Would you like to send us a question?

“Do you have a burning question that you would like a scientist to answer? Or a topic you would like to learn about? Send it to us!”

Categories

Science Chronicles (19 Blogs)
CEBE answers (13 Blogs)
Gender equality in science (7 Blogs)
Winners "Your research in one image or 1000 words" - 1st Edition (7 Blogs)
Webinars (5 Blogs)
CEBE's online events (1 Blogs)