Julia Robinson

Julia Robinson
Umumiy maʼlumotlar
Tavalludi	8-dekabr 1919 St. Louis
Vafoti	30-iyul 1985 Berkeley
Qardosh loyihalar
Vikipediyadagi maqola Vikimaʼlumotlar sahifasi Vikiombordagi tasvirlar

Julia Hall Bowman Robinson (1919-yil 8-dekabr — 1985-yil 30-iyul) — amerikalik matematik. Hisoblash nazariyasi sohasiga, ayniqsa qaror qabul qilish muammolariga qoʻshgan hissasi bilan mashhur boʻlgan. Uning Gilbertning oʻninchi masalasi (hozirgi kunda Matiyasevich teoremasi yoki MRDP teoremasi deb ataluvchi) ustida olib borgan tadqiqotlari bu masalaning yakuniy yechimida hal qiluvchi ahamiyatga ega boʻlgan. Robinson 1975-yilda Amerika Qoʻshma Shtatlari Milliy Fanlar Akademiyasiga aʼzo etib saylangan.

Iqtiboslar

	Ushbu maqolada biz George W. Brown tomonidan taklif etilgan iterativ jarayonning toʻgʻriligini koʻrsatib beramiz... Bu usul har bir oʻyinchining galma-gal oʻz raqibining shu vaqtgacha toʻplangan aralash strategiyasiga qarshi eng yaxshi sof strategiyani tanlashiga asoslanadi.
	In this paper, we shall show the validity of an iterative procedure suggested by George W. Brown ... This method corresponds to each player choosing in turn the best pure strategy against the accumulated mixed strategy of his opponent up to then.

Agar matematik nazariyaning har bir tasdigʻi toʻgʻriligini aniqlashning samarali usuli mavjud boʻlsa, bunday nazariyani „hal qilinuvchan“ (decidable) deymiz. Agar bunday usul mavjud boʻlmasa, nazariya „hal qilinmaydigan“ (undecidable) hisoblanadi. Shuni taʼkidlash joizki, agar hal qilinmaydigan nazariyaning har bir tasdigʻini boshqa nazariyaning ekvivalent tasdigʻiga oʻtkazishning mexanik usuli mavjud boʻlsa, ikkinchi nazariya ham hal qilinmaydigan boʻladi. Ushbu tamoyil, natural sonlar arifmetikasining hal qilinmasligi bilan birga, bizga ratsional sonlar ustidagi chekli darajali maydonlar uchun hal qilish muammosini yechish imkonini beradi.

We say a mathematical theory is decidable if there is an effective method of determining the validity of each statement of the theory. If there is no such method, the theory is undecidable. It is clear that if there is a mechanical way of transforming each statement of an undecidable theory into an equivalent statement of another theory, the second theory is also undecidable. This principle, together with the fact that the arithmetic of natural numbers is undecidable, enables us to solve the decision problem for fields of finite degree over the rationals.

Men Oʻninchi muammo bilan kurashishda davom etdim. 1961-yilda Martin Davis, Hilary Putnam va men „Eksponentsial Diofant tenglamalarining hal qilinmasligi“ nomli qoʻshma maqolani chop etdik... Maqolada ba’zan „Robinson gipotezasi“ (yoki Martin aytganidek, „J.R.“) deb ataladigan gʻoya mavjud edi: unga koʻra, agar eksponentadan tezroq oʻsadigan, lekin juda dahshatli darajada tez boʻlmagan biron-bir Diofant munosabati mavjud boʻlsa, biz darajaga koʻtarish (eksponentsiya) amalini aniqlash imkoniga ega boʻlar edik. Bu ta’rifdan eksponentsial Diofant tenglamalari oddiy Diofant tenglamalariga ekvivalent ekanligi va shuning uchun Hilbertning oʻninchi muammosiga javob inkor (manfiy) boʻlishi kelib chiqardi. Oʻsha paytda koʻpchilik Martinga bu yondashuv kamida notoʻgʻri ekanligini aytishgan. Menga nisbatan esa xushmuomalaroq boʻlishgan.

And I continued to struggle with the Tenth Problem. In 1961 Martin Davis, Hilary Putnam, and I published a joint paper, "The undecidability of exponential diophantine equations," which used ideas from the papers Martin and I had presented at the International Congress along with various new results. The paper contains what is sometimes referred to as the Robinson hypothesis (or, as Martin calls it, "J.R.") to the effect that if there were some diophantine relation that grew faster than an exponential but not too terribly fast—less than some function could be expressed in exponentials—then we would be able to define exponentiation. It would follow from the definition that exponential diophantine equations would be equivalent to diophantine equations and that, therefore, the solution to Hilbert's tenth problem would be negative. At the time many people told Martin that this approach was misguided, to say the least. They were more polite to me.

Julia Robinson haqida iqtiboslar

Notices: Julia Robinson haqidagi xotiralaringizni aytib bera olasizmi, u qanday inson edi? Davis: Juda yoqimli, juda samimiy edi. Matematik va boshqa sohalardagi qiziqishlari juda keng edi. Va ulkan salohiyat egasi edi — mening nazarimda, u mendan ancha kuchliroq matematik boʻlganiga hech qanday shubha yoʻq. Biz birgalikda hech qanday natijaga erisha olmagan bir muammo ustida ishlaganmiz. Biz soʻz tenglamalari (word equations) uchun hal qilish muammosining yechilmasligini isbotlashga harakat qilgan edik. Ma’lum boʻlishicha, biz buni isbotlay olmasdik, chunki bu muammo aslida yechiladigan ekan. Makanin uni ijobiy hal qildi.

Notices: Can you tell me your memories of Julia Robinson, what she was like as a person? Davis: Very nice, very straightforward. Broad in her interests, mathematical and otherwise. And great power—there is no question in my mind that she was a much more powerful mathematician than I. We worked together on a problem on which we didn’t get anywhere. We were trying to prove the unsolvability of the decision problem for word equations. It turned out that we wouldn’t have been able to do that because the problem is solvable. Makanin solved it positively.

	Julia Robinsonda biz oʻz zamonasining qahramoni va barcha davrlar uchun oʻrnak boʻla oladigan matematikni koʻramiz. Bu — bolalik, xastalik, muhabbat, nikoh, umidsizlik, matonat va gʻalaba haqidagi hikoyadir.
	In Julia Robinson we find a mathematician who was a heroine in her own time and a role model for all time. It is a story of childhood, illness, love, marriage, disappointment, obsession, and triumph.