브라질(Brazil), 러시아(Russia), 인도(India), 중국(China)은 넓은 영토와 풍부한 인적 자원 및 자연 자원을 바탕으로 경제가 급성장하고 있는 이른바 브릭스(BRICs) 국가들이다.
이 중 특히 IT 분야에서 주목받고 있는 인도에서는 구구단이 아닌 십구십구단까지 가르친다는 사실이 알려지면서 얼마 전 화제가 되었다. IT의 강국으로 떠오른 인도의 저력이 혹시 십구십구단에서 나온 것이 아닌가 싶어 우리나라의 어느 초등학교에서도 시범적으로 십구십구단을 도입하기로 했다고 한다.
인도는 전통적으로 수학 강국이다. 특히 수학사에 있어 암흑기라고 할 수 있는 중세에는 인도의 수학이 수학사의 공백을 메워 주었다. 예를 들어 현재 우리가 사용하고 있는 아라비아 숫자는 원래 인도에서 만들어져 아라비아로 전파되었는데, 앞의 인도를 생략한 채 아라비아 숫자라고만 부르니 인도로서는 억울할 것이다.
우리는 아라비아 숫자를 워낙 오래 동안 익숙하게 사용해왔기 때문에 그 편리함을 인식하지 못하지만, 사실 아라비아 숫자는 대단한 발명품이다.
예를 들어 234를 로마숫자로 적는다면 100을 나타내는 C를 두 번 적고, 10을 나타내는 X을 세 번 적고, 5에서 1을 뺀다는 의미로 IV를 배열한 CCXXXIV가 된다. 숫자를 적기도 불편하지만 계산을 할 때 번거롭기 그지없다. 그에 반해 아라비아 숫자는 100을 2번 적지 않아도 100의 자리에 2가 있으면 자연스럽게 200임을 나타내는 ‘위치적 기수법’을 따르는데, 여기에는 평범해 보이지만 기발한 아이디어가 들어있다.
뿐만 아니라 인도는 0을 본격적인 수로써 인정하였는데, 이는 인도가 불교의 발원지라는 점과 무관하지 않다.
불교에서 중요한 개념 중에 하나는 비어있다는 공(空)인데, 인도에서는 공(空)의 아이디어를 수로 표현한 0을 하나의 수로 자연스럽게 받아들일 수 있었다.
유사한 맥락에서 중국이 양수와 음수를 일찍이 받아들인 것도 중국의 전통적인 음양사상과 관련된다.
인도의 수학자들은 방정식의 풀이에 주력하여 이차방정식의 해법을 알아냈고, 특히 방정식을 거꾸로 계산하여 푸는 ‘역산법’을 개발했다.
인도 수학자 ‘바스카라’는 그의 저서 <릴라바티>에서 다음과 같이 아름다운 시구의 형식으로 수학 문제를 표현했다.
“반짝이는 눈을 가진 아가씨, 거꾸로 계산하는 방법을 알면 내 말을 들어봐요. 어떤 수에 3을 곱해서 그 곱의 3/4을 더하고 7로 나눈 다음, 그 나눈 것의 1/3을 빼서 그 자신을 곱한 뒤 52를 다시 빼고 그것에 제곱근을 취해서 8을 더하고 10으로 나누면 2가 된다오. 그 수는 얼마이겠소?”
이 문제는 복잡해 보이지만 마지막에 얻은 값 2에서 시작하여 거꾸로 역산법으로 풀면 구하고자 하는 값 28을 비교적 쉽게 계산할 수 있다.
신비주의적인 요소와 결합된 <릴라바티>는 수학책이지만 산스크리트 문학의 대표작으로 인정받을 만큼 문학적 가치도 높다.
그러다보니 엄밀한 논증을 바탕으로 한 순수수학적인 측면이 약해지게 되어, 인도 수학이 지속적인 우위를 지키지 못한 한계로 작용하기도 했다.
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)
중세에 꽃피웠던 인도 수학의 맥을 이은 사람은 20세기 초의 전설적인 수학자 라마누잔(Ramanujan, 1887~1920)이다. 영화 ‘굳 윌 헌팅’에 보면 윌의 천재성을 라마누잔에 비유하는 장면이 나오는데, 라마누잔은 특히 정수론 분야에 뛰어난 업적을 남겼다.
정규교육을 제대로 받지 못한 라마누잔을 발탁하여 영국 왕립회원이 되기까지 중요한 역할을 한 영국의 수학자 하디(Hardy)와 라마누잔 사이에 재미있는 일화가 전해온다.
라마누잔이 병석에 있을 때 하디는 문병을 갔는데, 자신이 타고 온 택시 번호 1729가 별 특징 없는 수라고 말했다.
사실 하디는 1729가 133×13이기 때문에 1729의 약수로 13이 포함되었다는 사실이 마음에 걸려서 그런 언급을 했다. 그런데 라마누잔은 몸져 누워서도 “아니, 1729는 특별한 수입니다. 1729는 9와 10을 각각 세제곱한 수의 합이자 (1729=729+1000=93+103), 1과 12를 각각 세제곱한 수의 합입니다 (1729=1+1728=13+123). 따라서 두 가지 다른 세제곱의 합으로 나눌 수 있는 최초의 수입니다.”라고 답했다고 한다.
수에 대한 뛰어난 직관력을 가진 두 수학자의 면모를 보여주는 일화이다.
![](data:image/png;base64,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)
라마누잔은 자신의 노트에 마방진을 하나 남겼다. 마방진이란 가로와 세로와 대각선에 있는 수의 합이 같도록 정사각형 모양으로 수를 배열한 것을 말한다. 라마누잔이 남긴 마방진의 첫 줄에 있는 22 12 18 87은 그의 출생 년도인 1887년 12월 22일을 뜻한다. 이 마방진을 보면 역시 수학의 귀재답다는 생각이 든다.
현재 미국의 실리콘 밸리를 지탱하고 있는 고급 두뇌의 상당수가 인도인이며, 인도의 델리대학교는 IT 분야에서 세계적인 메카로 자리매김하고 있다.
그 요인으로 인도가 여러 교과 중 수학을 유난히 중시한다는 점을 꼽을 수 있지만 이공대 우대 분위기도 중요한 요인으로 작용한다고 한다.
인도에서는 의사보다도 엔지니어를 선호하여 많은 엘리트들이 엔지니어를 지망한다니, 우리의 입장에서는 단지 부러울 따름이다.