Among the discoveries of Indian mathematicians of the Gupta Empire was the system of ten numerals. Other mathematical ideas that the Gupta mathematicians appeared to understand, though they did not necessarily discover them, included the decimal system, negative numbers, imaginary numbers, and algebra.
Ten numerals: It is possible to develop a mathematical system based on just four numerals, or seven, or any other amount; but by far the most practical method is a system based on ten numerals, from 0 to 9. Virtually all types of mathematics in use today involve a "base-10" system of numerals.
Decimal system: In a decimal number, each place after the decimal point can be thought of as a separate fraction, with the denominator (the number on the bottom) a multiple of 10. In the decimal number 0.534, for instance, the first number to the right of the decimal point is equal to 5/10; the second equals 3/100; and the third is the same as 4/1000. As one moves farther away from the decimal point, the denominator grows larger by a factor of 10—and thus the value of the fraction grows smaller. If a number is in the fifth position to the right, for instance, one can know that the denominator is 10 to the fifth power.
Negative numbers: A negative number is simply a number below 0. These numbers are "real," as anyone who has ever had an overdrawn checkbook knows. If a person has $100 in his account, and he writes a check for $120, that means he has -$20 in his account. To get back to $0, he will have to deposit $20.
Imaginary numbers: An imaginary number is the square root of a negative number. Any number can be squared, or multiplied by itself: thus 2 squared is 4. But what about the square root of -4? Obviously it cannot be 2; nor can it be -2, because multiplying a negative number by itself creates a positive number. Thus it is an imaginary number. As strange as such a concept sounds, it can be useful for solving complex equations.
Algebra: Algebra is a type of mathematics that makes it possible to find the value for a previously unknown number, which is called a variable. A simple algebraic equation would be "8 = 2x." The term 2x means 2 multiplied by the variable x. Obviously, if x can be multiplied by 2 to equal 8, then 8 can be divided by 2 to find x. Once this is done, the value of x (4) can be found easily.
Cult concepts such as negative numbers and imaginary numbers, and used basic concepts of algebra.
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