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Peruvian Mathematician Claims Proof of 300-Year-Old Conjecture

Categories: Latin America, Western Europe, France, Peru, Citizen Media, Good News, Ideas, Science

Peruvian mathematician [1] Harald Andrés Helfgott [2] made headlines after news [3] broke that he had demonstrated the solution to a 271-year-old problem in number theory.

Back in 1742, Prussian mathematician Christian Goldbach [4]‘s theory [5], known as Goldbach's conjecture, stated that “every integer greater than 5 can be written as the sum of three prime [numbers]”.

This conjecture, one of the most difficult problems in mathematics, has been investigated by many number theorists and confirmed by computers for all even numbers smaller than 10^18. After working hard on the so called Goldbach's weak conjecture [6], Helfgott managed to fully demonstrate it.

Harald Andrés Helfgott, foto compartida en Facebook. [7]

Harald Andrés Helfgott, image shared on Facebook.

Helfgott has a position at the National Center for Scientific Research [8] (CNRS) in France, and has published two papers “claiming having improved the estimates of major and minor arcs, enough to prove unconditionally Goldbach's weak conjecture.”

The blog Cajón de sastre [9] [es] republished the news [10] [es] and included a link to the compete work [11] on Helfgott's demonstration.

Meanwhile, Twitter users also expressed their opinion about Harald Helfgott's work using the hashtags #Helfgott [12] and #Goldbach [13].

Alberto Anguiano (@Dr_LAAG [14]) summed up the news in one tweet:

@Dr_LAAG [15]: #Goldbach [13]: “Todo número impar mayor que 5 puede expresarse como suma de tres números primos”, conjetura resuelta por un peruano #Helfgott [16].

@Dr_LAAG [15]: #Goldbach [13]: “every odd number greater than 5 can be written as the sum of three prime [numbers]”, conjecture solved by a Peruvian #Helfgott [16].

Twitter user and physicist V H Satheeshkumar (@VHSatheeshkumar [17]) expressed himself in three tweets:

@VHSatheeshkumar [18]#Helfgott [16] proves of one of the oldest open problems in #mathematics [19], the ternary #Goldbach [13] #conjecture [20] http://arxiv.org/abs/1305.2897  [21]. #numbers [22]

@VHSatheeshkumar [18]: Strong #Goldbach [13] #conjecture [20]: “Every even #number [22] greater than 2 can be written as the sum of two #primes [23].”

@VHSatheeshkumar [24]: Ternary #Goldbach [13] #conjecture [20]: “Every odd number greater than 5 can be written as the sum of three prime numbers.”

And dmv.mathematik.de (@dmv_mathematik [25]) asked:

@dmv_mathematik [26]: progress made proving #Goldbach [13]‘s #theorem [27]? #Helfgott [16] says so, proof published at http://arxiv.org/abs/1305.2897 [28]#math [29] #prime [30] #conjecture [20]

Norwegian mathematician Torgunn Karoline Moe (@TorgunnKaroline [31]) shared Helfogtt's work enthusiastically in two tweets:

@TorgunnKaroline [32]: Goldbach-artikkelen ligger her http://arxiv.org/abs/1305.2897  [33]. Les med måte! #helfgott [34] #goldbach [35] #abel [36]

@TorgunnKaroline [32] [no]: Goldbach's article can be read here http://arxiv.org/abs/1305.2897 [33]. Read his work! #helfgott [34] #goldbach [35] #abel [36]

@TorgunnKaroline [37]: @alexarje [38] For en fantastisk nyhet!! S2 #goldbach [35] #helfgott [34]

@TorgunnKaroline [37] [no]: @alexarje [38] For a fantastic news!!! S2 #goldbach [35] #helfgott [34]

Mexico_Today (@Mexico_Today [39]) tweeted cheerfully:

@Mexico_Today [40]: ►PERÚ: ‘INCREÍBLE!! MATEMÁTICO PERUANO RESUELVE CONJETURA DEBIL DE GOLDBACH’ #peru [41] #matemáticas [42] #goldbach [35]

@Mexico_Today [40] [es]: ►PERU: ‘INCREDIBLE!! PERUVIAN MATHEMATICIAN SOLVES GOLDBACH'S WEAK CONJECTURE’ #peru [41] #matemáticas [42] [mathematics] #goldbach [35]

More ironically, Mario Daniel (@Desiderantes [43]) said:

@Desiderantes [44]: Ok señores, ya probaron la conjetura de #Goldbach [13], ya se pueden dormir http://arxiv.org/abs/1305.2897 [45]

@Desiderantes [44] [es]: Very well, you all out there, #Goldbach [13] has been demonstrated, you may go to sleep now http://arxiv.org/abs/1305.2897 [45]

As this is Peru we are talking about, a football reference could not be absent, as laslo rojas (@amnesico [46]) wrote:

@amnesico [47]: Confirmado: Harald Helfgott es la Foquita de las matematicas: http://ow.ly/ldsE0  [48] #Goldbach [13] #Math [49]

@amnesico [47] [es]: Confirmed: Harald Helfgott is the Foquita of mathematics: http://ow.ly/ldsE0  [48] #Goldbach [13] #Math [49]

Jefferson Farfán [50], known as Foquita (little seal), is a Peruvian football player who is currently part of Bundesliga's Schalke 04 team.

Futhermore, Luis Biedma (@LBiedma [51]) simply said:

@LBiedma [52]: Acaban de probar la conjetura debil de #Goldbach [13]!? Que leeeeendoooo!!! #OMG [53] [Oh, Díos mío]

@LBiedma [52]: #Goldbach [13]‘s weak conjecture has just been demonstrated!? So niiiiiiice!!! #OMG [53]

Lastly, Luis das Cragfeit (@Cragfeit [54]) played with words:

@Cragfeit [55]: ¿Entonces #Goldbach [13] decía que si dos primos se casaban, siempre tendrían hijos que se dividieran por la mitad? #Preguntica [56] #PrimeNumbers [57]

@Cragfeit [55] [es]: So, #Goldbach [13] said that if two cousins got married, they would always have children that might be divided in halfs? #Preguntica [56] [little question] #PrimeNumbers [57]

In Spanish, “cousin” and “prime” are the same word: “primo.”

As Helfgott shared on Facebook [58] [es]:

Me parece que lo importante es – mas alla de donde vivamos o trabajemos – mantener un compromiso con la educacion y la ciencias en el Peru y Sudamerica, y con la matematica local en particular. […] Quisiera que esto sirva para que el trabajo que muchas generaciones han hecho por la matematica peruana sea apreciado.

I think the important thing -regardless of where we came from or where we live or work- is to stay engaged with education and science in Peru and South America, and with local mathematics in particular. […] I'd like this to be useful so the work many generations have made for Peruvian mathematics might be appreciated.