Safha-e-Awwal› E-Magazine ›100 Bari Daryaftein aur Ijadat

Sifar aur ashari nizam: kuch na hone ka hisab

Mobile number ho, bijli ka bill ho ya dukan ki raseed, hum har roz sirf das hindson se kaam chalate hain: ek se nau tak, aur sifar. Inhi das alamaton se hum chhoti se chhoti aur badi se badi raqam…

Atemad E-Magazine 20 October 2026 · 7 minute ka mutalia

Sifar aur ashari nizam: kuch na hone ka hisab — Alamati tasveer

Mobile number ho, bijli ka bill ho ya dukan ki raseed, hum har roz sirf das hindson se kaam chalate hain: ek se nau tak, aur sifar. Inhi das alamaton se hum chhoti se chhoti aur badi se badi raqam likh lete hain, kyunke har hindse ki qeemat us ki jagah se tay hoti hai. 205 mein do ka matlab do sau hai aur sifar batata hai ke dahai ki jagah khali hai. Yeh sada si baat insan ne sadiyon mein seekhi.

Khali jagah ka nishan

St Andrews University ke MacTutor archive mein sifar ki tareekh par ek tafseeli mazmoon hai. Us ke mutabiq qadeem Babul ke log hazar saal se zyada arse tak jagah ki qeemat wala nizam istemal karte rahe, magar us mein sifar nahin tha. Taqriban 400 qabl masih mein unhon ne khali jagah dikhane ke liye do tirchhe nishan lagana shuru kiye. Yunani mahir-e-falakiyat Ptolemy ne taqriban 130 eesvi mein ek gol nishan istemal kiya, magar woh ise adad nahin balke ek tarah ke waqfe ka nishan samajhta tha.

MacTutor ke mutabiq duniya ke doosre khitton mein bhi is taraf qadam uthe. Wasti Amrika ki Maya tehzeeb 665 eesvi tak bees ki bunyad par jagah ki qeemat wala nizam istemal kar rahi thi jis mein sifar ki alamat maujood thi. Hindustan mein riyazi dan Aryabhata taqriban 500 eesvi mein jagah ki qeemat wala nizam istemal karte the, agarche us mein abhi sifar ki alamat nahin thi. MacTutor ke mutabiq taqriban 650 eesvi tak Hindustani riyazi mein sifar ek adad ke taur par istemal hone laga tha.

Brahmagupta ke usool

MacTutor ke mutabiq Brahmagupta 598 eesvi mein paida hue, ghaliban Ujjain mein. Taqriban tees baras ki umr mein, 628 eesvi mein, unhon ne Bhillamala (aaj ka Bhinmal) mein "Brahmasphutasiddhanta" likhi, jo pachchees abwab par mushtamil falakiyat aur riyazi ki kitab hai. Baad mein woh Ujjain ki rasadgah ke sarbarah bane, jo us zamane mein Hindustan mein riyazi ka sab se bada markaz tha.

Brahmagupta ki khas baat yeh hai ke unhon ne sifar ko mahaz khali jagah ka nishan nahin balke ek baqaida adad maan kar us ke sath hisab ke qaide likhe. Musbat aur manfi adad ko woh "daulat" aur "qarz" kehte the. MacTutor un ke kuch qaide yun naqal karta hai: sifar mein se qarz nikalo to daulat banti hai; do qarzon ka hasil-e-zarb ya hasil-e-taqseem daulat hota hai; sifar aur kisi manfi adad ka majmua manfi hota hai. Yeh wohi usool hain jo aaj school ka har talib-e-ilm parhta hai, masalan manfi zarb manfi barabar musbat.

Har qaida durust nahin tha. Brahmagupta ne likha ke sifar ko sifar se taqseem karein to jawab sifar hai, jise MacTutor ghalat qarar deta hai. Kisi adad ko sifar se taqseem karne par unhon ne koi wazeh jawab nahin diya. MacTutor ke mutabiq do sau saal baad, 830 eesvi mein, riyazi dan Mahavira ne bhi is sawal par ek ghalat jawab diya.

Bakhshali ka makhtuta

Is kahani ka ek bab aaj ke Pakistan se juda hai. MacTutor ke mutabiq 1881 ki garmiyon mein zila Mardan ke gaon Bakhshali ke qareeb ek muzare ko pathar ki ek purani chardiwari ki khudai ke dauran bhoj patar (birch ki chhaal) par likha hua ek riyazi ka makhtuta mila. Us ke taqriban sattar auraq bache hain jin mein hisab, algebra aur kuch geometry ke qaide aur misalein hain, aur us mein sifar ke liye ek mota nuqta istemal hua hai. Yeh 1902 se Oxford ki Bodleian library mein mahfooz hai. Us ki tareekh par mahireen muttafiq nahin: 2017 mein teen auraq ki radio carbon jaanch ne teesri se daswin sadi eesvi tak ki mukhtalif tareekhein dein, aur in nataij ki tashreeh par bhi ilmi ikhtilaf hai.

MacTutor ke mutabiq Hindustan mein sifar ka woh pehla record jis ki tareekh maloom hai aur jis ke asli hone par sab muttafiq hain, Gwalior ka 876 eesvi ka ek katba hai.

Baghdad se Europe tak

Yeh nizam aage kaise phaila? MacTutor ke mutabiq taqriban 770 eesvi mein Hindustan se aayi ek falakiyati kitab Baghdad ke darbar tak pahunchi, jo baad mein Muhammad bin Musa al-Khwarizmi ki falakiyati jadwalon ki bunyad bani. Al-Khwarizmi (taqriban 780 ta 850) Baghdad ke "Bait ul Hikmat" ke aalim the. Unhon ne Hindi hindson par ek kitab likhi jis ka Arabi matan gum ho chuka hai, magar us ka Latin tarjuma "Algoritmi de numero Indorum" ke naam se baqi hai. Computer science ka lafz "algorithm" isi Latin naam ke zariye al-Khwarizmi ke naam se nikla hai. MacTutor ke mutabiq un ki kitab mein sifar samet poora nizam bayan hua tha.

Europe tak yeh nizam Italy ke Leonardo Pisano, yaani Fibonacci, ke zariye bade paimane par pahuncha. MacTutor ke mutabiq woh taqriban 1170 mein Pisa mein paida hue. Un ke walid shimali Africa ke shehar Bujayah (aaj ka Algeria) mein customs ke daftar mein Pisa ke tajiron ke numainde the, aur wahin Fibonacci ne yeh hindse seekhe. 1202 mein unhon ne "Liber abaci" likhi jis mein nau hindson aur sifar ki alamat ke sath hisab ka yeh tareeqa bayan kiya.

Aaj ka sifar

Aaj bank ka khata, school ka nateeja, dukan ki raseed aur computer ka hisab, sab inhi das hindson aur jagah ki qeemat wale isi nizam mein likhe jate hain. Sifar ki kahani Babul se Bhillamala, Baghdad aur Pisa tak kai hathon se guzri, aur us ka ek qeemti waraq Mardan ki mitti se bhi nikla. Sabaq yeh hai ke "kuch nahin" ko bhi ek naam aur ek qaida de diya jaye to woh sab se taqatwar hindsa ban sakta hai.

Makhaz

J. J. O'Connor and E. F. Robertson, "Brahmagupta", MacTutor History of Mathematics Archive, University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Brahmagupta/ — born 598, possibly Ujjain, died 670; Brahmasphutasiddhanta written in 628 at Bhillamala (Bhinmal) at about 30, 25 chapters; head of the Ujjain observatory; rules for fortunes, debts and zero; 0/0 = 0 is wrong; division of a number by zero left unresolved.
J. J. O'Connor and E. F. Robertson, "A history of Zero", MacTutor. https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/ — Babylonian place value without zero, two wedges c. 400 BC; Ptolemy's symbol c. 130 AD; Aryabhata c. 500; zero as a number in India by about 650; sum of zero and a negative is negative; Mahavira 830; Gwalior 876 first agreed dated record; Maya base-20 with zero by 665; al-Khwarizmi; Fibonacci's Liber abaci and the sign 0.
J. J. O'Connor and E. F. Robertson, "The Bakhshali manuscript", MacTutor. https://mathshistory.st-andrews.ac.uk/HistTopics/Bakhshali_manuscript/ — found summer 1881 near Bakhshali, Mardan tahsil, Peshawar district; birch bark, about 70 leaves; arithmetic, algebra, some geometry; dot for zero; presented to the Bodleian in 1902; range of scholarly datings.
Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk, "The Bakhshali Manuscript: A Response to the Bodleian Library's Radiocarbon Dating", History of Science in South Asia 5.1 (2017) 134–150. https://journals.library.ualberta.ca/hssa/index.php/hssa/article/view/22 — disagreement with the Bodleian team's interpretation of the radiocarbon dates.
Walter Slaje, "Once again on the origin of zero: the date of the Bakhshali manuscript", INDOLOGY list (16 Sept 2017), quoting the Bodleian results. https://list.indology.info/pipermail/indology/2017-September/046605.html — radiocarbon dates of three folios: 224–383, 680–779 (or 790–868), 885–993 cal AD.
J. J. O'Connor and E. F. Robertson, "Abu Ja'far Muhammad ibn Musa Al-Khwarizmi", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Al-Khwarizmi/ — c. 780–850; House of Wisdom, Baghdad; Indian text brought to the Baghdad court c. 770, basis of his Sindhind zij; arithmetic survives only in Latin as Algoritmi de numero Indorum; origin of the word algorithm.
J. J. O'Connor and E. F. Robertson, "Leonardo Pisano Fibonacci", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Fibonacci/ — born Pisa c. 1170; father at the customs in Bugia; learned the Indian numerals there; Liber abaci 1202.

100 Bari Daryaftein aur Ijadat: tamam tehreerein →