Mathematical Tricks by The Aadyanagha Foundation

Glories to Duranteshwar Mahadev and Aadyanagha Mahadevi 🙏!

Well! Many of you all must have had a phobia for mathematics (or some of you still have it). Right?

This blog aims at removing that phobia for mathematics. We have launched some shortcuts to simplify mathematical problems so that you all do not have to spend extra money in coaching classes! That too free of cost!

This post specifically aims to focus on addition, subtraction, multiplication and division.

1. Left to Right Addition and Subtraction 

Let's count the circles below:

Yes. There are 5 circles here.

Now we bring similar number of circles. What are we doing?

It is not possible to count each circle every time. So we add.

Addition is the process of bringing many things together to find a total. It is symbolized by a “+” sign. 

For example, there are 4 cookies in a plate. 2 more cookies are added. Hence, there are 6 cookies now.

If we understand with the context of number line, we realize that addition means moving forward in a number line.

Subtraction is the process of taking away something from a given set of things. It is symbolized by a “-” sign.

In a subtraction problem (Z - A = K), the minuend is the first number (Z), representing the total amount you start with, while the subtrahend is the second number (A), representing the quantity to be taken away. The result is called the difference (K).

For example, Jerry had 10 sweets. He gave 4 sweets to his best friend named Mickey. As a result, Jerry now has 4 less sweets. Hence, Jerry is left with 6 sweets.

If we understand with the context of number line, we realise that subtraction means moving backwards in a number line.

Let's read a sentence. "God is great". Did we read it from left to right or right to left?

Yes! We read the sentence from left to right. Now do you think we can add and subtract in the same way? Why not!

Sample Sum for Left to Right Addition

Sample Sum for Left to Right Subtraction

Let's take a sum!

1. 67 + 89

Since 6 & 9 are in the tens place and 7 & 9 are in the ones place, let's understand the breakdown logically!

67 = 6 Tens + 7 Ones = (6 * 10) + (7 * 1) = 60 + 7

89 = 8 Tens + 9 Ones = (8 * 10) + (9 * 1) = 80 + 9

Since we have got a simple breakdown of the numbers, let's solve the sum!

67 + 89 = (60 + 7) + (80 + 9) = 60 + 7 + 80 + 9 = (60 + 80) + (7 + 9) = 140 + 16 = 156 

Wasn't this easier than the traditional method? The traditional method is prone to errors related to carry forward because we are more used to operating from left to right, but the traditional methods use the right to left approach!

Now let's try another sum.

2. 78 - 42

First we break down the numbers using expanded form.

78 = 7 Tens + 8 Ones = (7 * 10) + (8 * 1) = 70 + 8

42 = 4 Tens + 2 Ones = (4 * 10) + (2 *1) = 40 + 2

Now we solve the sum.

78 - 42 = (70 + 8) - (40 + 2) = 70 + 8 - 40 - 2 = (70 - 40) + (8 - 2) = 30 + 6 = 36

In the same way, this too was simpler than the traditional method!

Now let's do some sums using the combination of both methods.

3. 942 + 786 - 351

First we break down the numbers using expanded form.

942 = 900 + 40 + 2

786 = 700 + 80 + 6

351 = 300 + 50 + 1

Now we solve the sum.

942 + 786 - 351 = (900 + 40 + 2) + (700 + 80 + 6) - (300 + 50 + 1) 

= 900 + 40 + 2 + 700 + 80 + 6 - 300 - 50 - 1 

= (900 + 700 - 300) + (40 + 80 - 50) + (2 + 6 - 1) 

= 1300 + 70 + 7 = 1377

Just imagine! If we use these methods, the risk of human error would be minimized.

2. Zigzag Approach

First we try solving the sum below using Left to Right Approach.

Let us solve the same sum using Zigzag Approach.

Let us solve some problems.

1. 74 + 68 - 92

First we break down the numbers using expanded form

74 = 70 + 4

68 = 60 + 8

92 = 90 + 2

Now we solve the sum.

74 + 68 - 92 = (70 + 4) + (60 + 8) - (90 + 2)

= 70 + 4 + 60 + 8 - 90 - 2

= 74 + 60 + 8 - 90 - 2

= 134 + 8 - 90 - 2

= 142 - 90 - 2

= 52 - 2

= 50

2. 942 + 786 - 351

First we break down the numbers using expanded form.

942 = 900 + 40 + 2

786 = 700 + 80 + 6

351 = 300 + 50 + 1

Now we solve the sum.

942 + 786 - 351 = (900 + 40 + 2) + (700 + 80 + 6) - (300 + 50 + 1) 

= 900 + 40 + 2 + 700 + 80 + 6 - 300 - 50 - 1

= 940 + 2 + 700 + 80 + 6 - 300 - 50 - 1

= 942 + 700 + 80 + 6 - 300 - 50 - 1

= 1642 + 80 + 6 - 300 - 50 - 1 

= 1722 + 6 - 300 - 50 - 1 

= 1728 - 300 - 50 - 1 

= 1428 - 50 - 1 

= 1378 - 1 

= 1377

3. Step Addition

Do you think we will be able to use methods like Left to Right Addition or Zigzag Addition method for larger numbers? No. That will be a time taking process. Hence, we have discovered a new method. But before that, let us understand the logic behind this method. 

Understanding the logic behind step operators

Over here, the first thing that we did was add the hundreds, tens, and ones separately.  Since we will be using the Step Operator, we can see the irrelevancy of zero here. And thus, separated them into 10 hundred, 21 tens, and 16 ones.  Finally, we used the Step Operator to get the final answer. 

The idea here is that we have : 

10 hundreds + 21 tens + 16 ones 

= (10 hundreds) + (2 hundreds + 1 ten) + (1 ten + 6 ones) 

= 12 hundreds + 2 tens + 6 ones 

= 1226 

In this sum, we see too many zeroes over here having minimal impact on the final addition. 

Step operator added to remove zeroes

The Step Operator is just a visual wall used to keep different place-values separated so you don't have to write out endless zeros.

​Think of the | bar as a divider between the Left-Hand Side and the Right-Hand Side.

Now if we see carefully. We see 9 Thousands + 12 Hundreds + 06 Tens + 21 Ones. 

Let us further understand this via a simpler sum.

What is close to the step?

As mentioned before, we add the step operator to remove the extra zeroes. So, from here we can understand that 14 step 28 means 140 + 28. So, the 4 in the 14 is actually in the Tens place and the 2 in the 28 is also in the Tens place. Hence, we add the numbers closest to the step.

When you want to remove the bar and get your final answer, you add the two digits that are touching the bar together.

Let us try an example.

1. 24 + 35

2 + 3 └┐ 4 + 5

= 05 └┐ 09 

= 59

Note : The right side of a step operator should always hold a two-digit number. If a calculation gives you a single digit, you must put a 0 in front of it (e.g., 8 becomes 08). Adding two one-digit numbers or multiplying two one-digit numbers lead to a two-digit number at the maximum. (For example : 9 + 9 = 18 and 9 * 9 = 81 - as 9 is the highest one-digit number)

2. 135 + 420

1 + 4 └┐ 3 + 2 └┐ 5 + 0

= 05 └┐ 05 └┐ 05

= 55 └┐ 05

= 555

3. 7624 + 9835

7 + 9 └┐ 6 + 8 └┐ 2 + 3 └┐ 4 + 5 

= 16  └┐ 14 └┐ 05 └┐ 09

= 174 └┐ 05 └┐ 09

= 1745 └┐ 09

= 17459

Another question arises. Suppose you add many 2 digit numbers and you get something like this while adding the tens place and ones place : 24 └┐ 135 - Then how will you solve?

Let us translate the meaning of it. It will mean 24 Tens + 135 Ones = (2 Hundreds + 4 Tens) + (1 Hundred + 3 Tens + 5 Ones) = 375. This means we will add the 24 and 13, maintaining the 5 intact in the ones place.

When you have 24 └┐ 135, look at the digits that are smashed right up against the step operator. In this case, it is the 4 on the left and the 13 on the right. Treat the numbers directly next to the line as your target. You are adding the 24 and the 13 together. Put your the sum (37) next to the untouched digit (5) giving you a final answer of 375.

4. Multiplication using Expanded Form

First let us understand that multiplication is nothing but repeated addition. For example,

3 × 1 = 3

3 × 2 = 3 + 3 = 6

3 × 3 = 3 + 3 + 3 = 9

3 × 4 = 3 + 3 + 3 + 3 = 12

Multiplication was introduced so that the time spent on repeated addition is minimized.

Let us take some illustrations.

1. 24 × 7 

(20 + 4) × 7 = 140 + 28 = 168

2. 946 × 8

(900 + 40 + 6) × 8 = 7200 + 320 + 48 = 7568

3. 1234 × 5

(1000 + 200 + 30 + 4) × 5 = 5000 + 1000 + 150 + 20 = 6170

5. Step Multiplication

Let us try the same examples using step operator.

1. 24 × 7 

2 × 7 └┐ 4 × 7

= 14 └┐ 28

= 168

2. 946 × 8

9 × 8 └┐ 4 × 8 └┐ 6 × 8

= 72 └┐ 32 └┐ 48

= 752 └┐ 48

= 7568

3. 1234 × 5

1 × 5 └┐ 2 × 5 └┐ 3 × 5 └┐ 4 × 5

= 05 └┐ 10 └┐ 15 └┐ 20

= 60 └┐ 15 └┐ 20

= 615 └┐ 20

= 6170

6. Speed Division

Division is the process of grouping things equally.

Just the way multiplication is repeated addition, in the same way division is repeated subtraction.

Let us take a situation. There are six friends - Gauri, Shriya, Vani, Siya, Radhika and Meenakshi. They see a box having 42 dolls. They decide to distribute the dolls among each other equally.

42 - 6 = 36

36 - 6 = 30

30 - 6 = 24

24 - 6 = 18

18 - 6 = 12

12 - 6 = 6

6 - 6 = 0

Since one friend picks one doll each in the each attempt, 6 dolls are reduced. So the number of times each friend picks a doll is 7 times. So each friend has 7 dolls. Here 42 is the dividend, 6 is the divisor and 7 is the quotient.

One day the friends see 15 shells. They want to distribute the shells equally.

15 - 6 = 9

9 - 6 = 3

Each friend could collect only 2 shells. The remaining 3 were left on the beach. Here 3 is the remainder.

I. Tabular Division

Here we solve the following sums.

1. 13240 / 5

13240 is the dividend ; 5 is the divisor ; 2648 is the quotient ; 0 is the remainder

2. 968 / 4

968 is the dividend ; 4 is the divisor ; 242 is the quotient ; 0 is the remainder

3. 143622936 / 6

143622936 is the dividend ; 6 is the divisor ; 23937156 is the quotient ; 0 is the remainder

II. Divisibility Test for numbers

1. All even numbers are divisible by 2. Numbers ending with 0, 2, 4, 6 and 8.

2. Any number whose digits sum up to a number that is a multiple of 3, is divisible by 3. For example : the sum of the digits of numbers 12, 24 and 63 is 3, 6 and 9 respectively.

Any even number divisible by 3 is a number divisible by 6.

Any number whose digits sum up to 9 is divisible by 9.

Any even number divisible by 9 is divisible by 18.

3. Any number whose last two digits is divisible by 4 is a number divisible by 4. For example, 124 is 100 + 24. We already know 100 is a multiple of 4. We also know that multiplication is repeated addition. So if you add two multiples of 4, it is automatically divisible by 4. 

In the same way, any number whose last three digits are divisible by 8 is a number divisible by 8. For example, 1024 is 1000 + 24. We already know 1000 is a multiple of 8. So if you add two multiples of 8, it is automatically divisible by 8. 

Any number divisible by 3 and 4 is divisible by 12 ; Simultaneously any number divisible by 3 and 8 is divisible by 24.

4. Any number which ends with 0 or 5 is divisible by 5. Any number ending with 0 is a multiple of 10. In the same way any number which ends with 00, 25, 50 or 75 is divisible by 25.

5. To check whether a number is divisible by 7, we double the last digit, subtract it from the rest of the number. If the result is divisible by 7, the original number is too.

For example, in 343 : 34 - (3 × 2) = 28 which is divisible by 7. 

Let's also see for 14 : 1 - (4 × 2) = -7 which again is divisible by 7.

6. To check whether a number is divisible by 11, we alternatively add and subtract the digits of the number from left to right. If the end result is 0 or a multiple of 11, it is a multiple of 11.

For example, in 1364 = 1 - 3 + 6 - 4 = 0, which proves it is divisible by 11.

III. Division Shortcuts

I. Divisibility by 5 - Dividing by 5 can also be written as multiplying by 1/5. 2/10 is an equivalent fraction of 1/5. So while dividing a number by 5, we can multiply the number by 2 and then divide it by 10.

For example, 165 ÷ 5 = (165 × 2) ÷ 10 = 330 ÷ 10 = 33

II. Divisibility by 4 and 8 - Dividing by 4 is considered as multiplying by a quarter (1/4). A quarter is half of half (1/2).

For example, 28 ÷ 4 = (28 ÷ 2) ÷ 2 = 14 ÷ 2 = 7

In the same way, dividing by 8 is considered as dividing by half of a quarter.

For example, 72 ÷ 8 = (72 ÷ 4) ÷ 2 = ((72 ÷ 2) ÷ 2) ÷ 2 = (36 ÷ 2) ÷ 2 = 18 ÷ 2 = 9

III. Divisibility by 25 - 4/100 is an equivalent fraction of 1/25. So while dividing a number by 25, we can multiply the number by 4 and then divide it by 100.

For example, 625 ÷ 25 = (625 × 4) ÷ 100 = 2500 ÷ 100 = 25

7. Double Step Multiplication

Do you think we can use a step operator while multiplying 2 two-digit numbers? Let us try.

1. 42 × 35

42 × 3 └┐└┐ 42 × 5

= 4 × 3 └┐ 2 × 3 └┐└┐ 4 × 5 └┐ 2 × 5

= 12 └┐ 06 └┐└┐ 20 └┐ 10

= 126 └┐└┐ 210 (we will add the 26 with the 21)

= 1470

2. 98 × 67

98 × 6 └┐└┐ 98 × 7

= 9 × 6 └┐ 8 × 6 └┐└┐ 9 × 7 └┐ 8 × 7

= 54 └┐ 48 └┐└┐ 63 └┐ 56

= 588 └┐└┐ 686

= 6566

8. Optimized Double Step Multiplication

Let us try an alternative method.

1. 42 × 35

42 × 3 └┐└┐ 42 × 5

= 4 × 3 └┐ 2 × 3 └┐└┐ 4 × 5 └┐ 2 × 5

= 12 └┐ 06 └┐└┐ 20 └┐ 10

= 126 └┐└┐ 20 └┐ 10 (Adding 26 and 20) (double step)

= 146 └┐ 10 (Adding 6 and 1) (single step)

= 1470

2. 98 × 67

98 × 6 └┐└┐ 98 × 7

= 9 × 6 └┐ 8 × 6 └┐└┐ 9 × 7 └┐ 8 × 7

= 54 └┐ 48 └┐└┐ 63 └┐ 56

= 588 └┐└┐ 63 └┐ 56 (Adding 88 and 63) (double step)

= 651 └┐ 56 (adding 1 and 5) (single step)

= 6566

9. Cross Multiplication

I. 2 Digit × 2 Digit

Steps :

i. First we calculate the value in the hundreds place by multiplying the digits in the tens place. Tens × Tens = Hundreds.

Targeting the Hundreds Place

ii. Then we put a step operator and calculate the cross products of the digits in tens place with the digits in ones place and sum them up to find the value in the tens place. Tens × Ones = Tens.

Targeting the Tens place

iii. Then we again put a step operator and calculate the value in the ones place by multiplying the digits in the ones place. Ones × Ones = Ones.

Targeting the Ones Place

iv. Conducting a step operation and solving the sum

Performing Step Operation

1. 42 × 35

(4 × 3) └┐ (2 × 3) + (4 × 5) └┐ (2 × 5)

= 12 └┐ 06 + 20 └┐ 10

= 12 └┐ 26 └┐ 10

= 146 └┐ 10

= 1470

2. 98 × 67

(9 × 6) └┐ (8 × 6) + (9 × 7) └┐ (8 × 7)

= 54 └┐ 48 + 63 └┐ 56

= 54 └┐ 111 └┐ 56

= 651 └┐ 56

= 6566 

II. 3 Digit × 3 Digit

Steps :

i. First we calculate the value in the ten thousands place by multiplying the digits in the hundreds place. Hundreds × Hundreds = Ten Thousands.

Targeting the Ten Thousands Place

ii. Then we put a step operator and calculate the cross products of the digits in hundreds place with the digits in tens place and sum them up. Hundreds × Tens = Thousands.

Targeting the Thousands Place

iii. Then we put a step operator and calculate the cross products of the digits in hundreds place with the digits in ones place, the product of the digits in the tens place and sum them up. Hundreds × Ones = Hundreds ; Tens × Tens = Hundreds.

Targeting the Hundreds Place

iv. Then we put a step operator and calculate the cross products of the digits in tens place with the digits in ones place and sum them up to find the value in the tens place. Tens × Ones = Tens.

Targeting the Tens Place

v. Then we again put a step operator and calculate the value in the ones place by multiplying the digits in the ones place. Ones × Ones = Ones.

Targeting the Ones Place

vi. We us the step operator and solve the sum.

Performing step operation and ensuring that there is a two-digit number on both sides

1. 126 × 457

(1 × 4) └┐ (1 × 5) + (2 × 4) └┐ (1 × 7) + (2 × 5) + (6 × 4) └┐ (2 × 7) + (6 × 5) └┐ (6 × 7)

= 04 └┐ 05 + 08 └┐ 07 + 10 + 24 └┐ 14 + 30 └┐ 42

= 04 └┐ 13 └┐ 41 └┐ 44 └┐ 42

= 53 └┐ 41 └┐ 44 └┐ 42

= 571 └┐ 44 └┐ 42

= 5754 └┐ 42

= 57582

III. 2 Digit × 2 Digit × 2 Digit

Steps :

i. First we calculate the value in the thousands place by multiplying the digits in the tens place. Tens × Tens × Tens = Thousands.

Targeting the Thousands Place by calculating the product of the circled numbers

ii. Then we add a step operator and calculate the value in the hundreds place by multiplying the two tens digits with one ones digit and adding all such combinations Tens × Tens × Ones = Hundreds.

Targeting the Hundreds Place by calculating the product of the circled numbers in each box and adding all such combinations

iii. Then we add a step operator and calculate the value in the tens place by multiplying the one tens digits with two ones digit and adding all such combinations Tens × Ones × Ones = Tens.

Targeting the Tens Place by calculating the product of the circled numbers in each box and adding all such combinations

iv. Then we add a step operator and calculate the value in the ones place by multiplying the digits in the ones place. Ones × Ones × Ones = Ones.

Targeting the Ones Place by calculating the product of the circled numbers

v. We use the step operator and solve the sum.

1. 24 × 15 × 31

(2 × 1 × 3) └┐ (2 × 1 × 1) + (2 × 5 × 3)  + (4 × 1 × 3) └┐ (4 × 5 × 3) + (4 × 1 × 1)  + (2 × 5 × 1) └┐ (4 × 5 × 1)

= 06 └┐ 2 + 30 + 12 └┐ 60 + 4 + 10 └┐ 20

= 06 └┐ 44 └┐ 74 └┐ 20

= 104 └┐ 74 └┐ 20

= 1114 └┐ 20

= 11160

IV. Shortcuts for calculating squares and cubes using step operators

1. (az)² = a² └┐ 2az └┐ z²

Example : 64 × 64 = (6)² └┐ 2 (6 × 4) └┐ (4)² = 36 └┐ 48 └┐ 16 = 4096

2. (ijk)² = i² | 2ij | 2ik + j² | 2jk | k²

Example : 124 × 124 = (1)² └┐ 2 (1 × 2) └┐ 2 (1 × 4) + (2)² └┐ 2 (2 × 4) └┐ (4)² = 01 └┐ 04 └┐ 12 └┐ 16 └┐ 16 = 15376

3. (az)³ = a³ └┐ 3a²z └┐ 3az² └┐ z³

Example : 15 × 15 × 15 = (1)³ └┐ 3 ((1)² × 5) └┐ 3 (1 × (5)²) └┐ (5)³ = 01 └┐ 15 └┐ 75 └┐ 125 = 3375

10. Squaring a number ending with 5

Example :

1. 65 × 65

i. Multiply the portion of the number before 5 (i.e. 6) with its subsequent number (i.e. 7) : 6 × 7 = 42

ii. Append it with 25.

65 × 65 = 4225

Let's cross verify using cross multiplication :

(6 × 6) └┐ (6 × 5) + (6 × 5) └┐ (5 × 5)

= 36 └┐ 30 + 30 └┐ 25 

= 36 └┐ 60 └┐ 25 

= 420 └┐ 25

= 4225

2. 35 × 35

i. Multiply the portion of the number before 5 (i.e. 3) with its subsequent number (i.e. 4) : 3 × 4 = 12

ii. Append it with 25.

35 × 35 = 1225

3. 125 × 125

i. Multiply the portion of the number before 12 (i.e. 12) with its subsequent number (i.e. 13) : 12 × 13 = 01 └┐ 02 + 03 └┐ 06 = 156

ii. Append it with 25.

125 × 125 = 15625

11. Multiplication Shortcuts

I. Multiplying a number with 11

Example :

1. 42 × 11

i. Write the first digit = 4

ii. Then write the sum of the digits 4 and 2 = 6

iii. Then write the last digit = 2

42 × 11 = 462 

For verification : (4 × 1) └┐ (2 × 1) + (4 × 1) └┐ (2 × 1) = 04 └┐ 06 └┐ 02 = 462

2. 98 × 11

i. Write the first digit = 9

ii. Then write the sum of the digits 9 and 8 = 17 (since it is a two-digit number, 1 will be added to the 9)

iii. Then write the last digit = 9

98 × 11 = 1078

3. 76 × 11

i. Write the first digit = 7

ii. Then write the sum of the digits 7 and 6 = 13 (since it is a two-digit number, 1 will be added to the 7)

iii. Then write the last digit = 6

76 × 11 = 836

II. Multiplying a number with 99

Example :

1. 99 × 73

First : 73 - 1 = 72

Then : 100 - 73 = 27

99 × 73 = 7227

2. 99 × 64

First : 64 -1 = 63

Then : 100 - 64 = 36

99 × 64 = 6336

II. Multiplying a number with 999

Example :

1. 999 × 357

First : 357 - 1 = 356

Then : 1000 - 357 = 643

999 × 357 = 356643

2. 999 × 421

First : 421 - 1 = 420

Then : 1000 - 421 = 579

999 × 421 = 420579

For verification : (1000 - 1) × 421 = 421000 - 421 = 420579

Conclusion 

Finally I just want to say that it is very important that Indians are familiarized with these concepts at an early age. These techniques should also be implemented in schools so that parents don't lose their money in fraudulent EdTech companies charging exorbitant fees and not refunding them when the parents are dissatisfied with the services.

Thanks and Regards,

The Aadyanagha Foundation.

Vocabulary Mastery by The Aadyanagha Foundation

Glories to Duranteshwar Mahadev and Aadyanagha Mahadevi 🙏!

In a world where words hold the power to inspire, persuade, and connect, a rich vocabulary is one of the greatest treasures you can possess. The ability to articulate your thoughts with precision and elegance not only boosts confidence but also opens doors to deeper understanding, better communication, and endless opportunities. Whether you're preparing for exams, crafting compelling stories, or simply expressing yourself with clarity and flair, expanding your word power is a joyful and rewarding journey.

Here’s a curated list of powerful words to elevate your language and sharpen your mind.

1. Decadent - To be luxuriously self-indulgent, often to the point of moral or cultural decline

2. Repertoire - A person's entire collection of learned skills and behaviors that are related to a specific task or setting

3. Ratiocinate - To think or argue logically and methodically

4. Ephemeral - Lasting for a very short time ; Transient or fleeting

5. Esoteric - Intended for or likely to be understood by only a small number of people with a specialized knowledge or interest

6. Inchoate - Just begun, so not fully formed or developed ; Rudimentary or disorganized

7. Cohort - A group of people with shared characteristics

8. Placidity / Tranquility / Serenity - A state of calmness

9. Nocuous / Pernicious - Harmful / Injurious

10. Celerity - Quickness

11. Forbearance / Fortitude / Longanimity - Tolerance / Patience

12. Lummox - A clumsy and stupid person

13. Inimical - Unfriendly

14. Ludic - Playful

15. Acrimonious - Bitter

16. Exigency - Urgent need

17. Intrepid / Dauntless - Fearless, bold, adventurous.

18. Aver - Assert as true

19. Irenic - Promoting peace

20. Placate / Mollify - To make someone less angry or anxious

21. Panacea - Solution / Remedy

22. Rectitude - Morally correct behavior or thinking

23. Nefarious - Wicked / Evil

24. Repudiate - To refuse to accept or support something

25. Duplicitous - Deceptive / Misleading

26. Myrmidon - A loyal follower who executes orders without questions

27. Nebulous - Hazy and vague

28. Epiphany - A life-changing realization

29. Altercation - A loud, heated or angry argument or disagreement between people

30. Pulchritude - Beauty

31. Penchant - Strong liking

32. Oblivion - A state of unawareness of what's going on

33. Oneirataxia - An inability to distinguish between fantasy and reality

34. Ubiquitous - Pervasive / Omnipresent

35. Trajectory - The path someone / something is on

36. Felicity - Happiness

37. Quintessential - The most perfect or purest form of an idea, object or a person

38. Recuperate - To regain health, strength or energy after a period of exhaustion, illness or injury ; To get anything back that you lost

39. Deviance - Departure from usual or accepted standards

40. Intercede - Intervene on behalf of another

41. Expound - Explain or present in detail

42. Volition - Power to make your own decisions

43. Succinct - Briefly explained

44. Pertinent / Germane - Relevant

45. Ignominy - Public shame or disgrace

46. Perturbed - Agitated

47. Infallible - Incapable of any error

48. Bemoaning - Expressing discontent or sorrow

49. Err - To make a mistake ; Non-adherence to standards

50. Cogent - Clear, logical, and convincingly written or spoken

51. Wondrous - Extremely and surprisingly good

52. Activize - To activate

53. Flummery / Codswallop - Nonsense / Rubbish

54. Petrified - Terrified

55. Copious / Profuse - Abundant

56. Deliberation - Pondering

57. Divulge - Disclose

58. Exuberant / Ebullient - Full of energy and enthusiasm

59. Flummox - To confuse

60. Avocations - Hobbies

61. Calumniation - A statement that is malicious, false and defamatory

62. Traduce / Vilify - To defame

63. Delinquent - Someone or something that fails to fulfill an obligation, duty or expected standard

64. Vicissitude - A change of circumstances or fortune, typically one that is unwelcome or unpleasant

65. Axiomatic - Self-evident or unquestionable

66. Salient - Most noticeable or important

67. Contrite - Feeling or expressing remorse or penitence

68. Fastidious - Very attentive to and concerned about accuracy and detail

69. Inscrutable - Impossible to understand

70. Obsequious / Subservient / Servile - Obedient or attentive to an excessive degree

71. Pusillanimous - Timid / Coward

72. Quixotic - Excessively idealistic, unrealistic and impractical

73. Imbroglio - An extremely confused, complicated or embarrassing situation

74. Chimerical - Hopeful for something illusory or impossible to achieve

75. Banal - Not original to a point that it is obvious and boring

76. Partisan - A strong supporter of a party, cause or a person

77. Internecine - Destructive to both sides in a conflict

78. Lackadaisical / Indolent - Lazy

79. Brazen - Shameless

80. Plethora - In large quantities

81. Puissant - Powerful

82. Surmise - To infer with little evidence 

83. Rescind - To take back and repeal

84. Omnilegent - To be able to read all languages 

85. Forte - Something someone is very good at

86. Pathos - An emotion of sympathy 

87. Exultant - Very happy and joyful 

88. Biciptical - Having two points of origin 

89. Nugator - A person who trifles and makes light of things

90. Intramural - Happening inside a particular institution or community 

91. Collocate - To place things next to each other

92. Linchpin - Something that holds separate parts together 

93. Schadenfreude - Enjoyment obtained from the troubles of others

94. Transfigure - To change something to make it look more beautiful or spiritual 

95. Flibbertigibbet - A frivolous or flighty person who is easily distracted

96. Proletarian - Relating to the working class

97. Particularization - A detailed description of something specific

98. Presage - An omen

99. Xenial - Hospitable (Especially to visiting strangers or foreigners)

100. Ardor - Extreme vigor, energy, enthusiasm

101. Affiliation - The state of being connected or associated

102. Gossamer - Very light, thin and delicate

103. Otiose - Serving no practical purpose

104. Manumit - To release someone being a slave

105. Sod - To irritate or disturb someone

106. Diminuendo - A gradual decrease in volume

107. Introversion - Focusing on thoughts and energy inside oneself

108. Vincible - Can be defeated or overcome

109. Ingratiate - To try to get someone's approval by doing or saying things that will please them

110. Facundity - The quality eloquent or fluent

111. Unperson - A person stripped of their identity or existence

112. Largesse - Generosity in giving gifts or money

113. Purveyor - Someone who supplies provision (especially food)

114. Grapple - To firmly grab or struggle with something

The Superiority of Vegan Leather Over Traditional Leather: An Environmental Economic Chemistry Perspective

Glories to Aadyanagha Mahadevi and Duranteshwar Mahadev 🙏!

In an era of climate urgency and ethical consumerism, the fashion industry is undergoing a material revolution. But how do we objectively measure 'better'? Enters Environmental Economic Chemistry — an interdisciplinary lens that merges the 12 Principles of Green Chemistry (waste prevention, atom economy, safer chemical design, renewable feedstocks, and energy efficiency) with economic valuation tools like life-cycle costing and externality pricing. It quantifies not just direct production costs but the hidden societal burdens of pollution, resource depletion, and lost ecosystem services.

Vegan Leather - In alignment with Environmental Economic Chemistry 

Applying this framework reveals a clear winner : vegan leather (especially plant-based alternatives) outperforms traditional animal leather across chemical sustainability, environmental metrics, and economic viability. Here's why — backed by life-cycle assessments (LCAs), chemical process analysis, and market economics.

Here's a comprehensive list of vegan leather alternatives, expanding on the ones you mentioned (Mushroom Leather, Corn Leather, Coconut Leather, Apple Leather, Banana Leather, Papaya Leather, Mango Leather, Watermelon Leather, Pineapple Leather). I've included as many established, emerging, and innovative options as possible, grouped by primary source for easier reading.

Most of these are plant-based, fungi-based or bio-based materials that repurpose agricultural waste, by-products, or fast-growing resources. Many are blended with bio-resins or minimal coatings for durability (not all are 100% plastic-free). They offer varying degrees of breathability, biodegradability, and scalability.

1. Vegan Leathers Based on Fruits, Vegetables, Fungi and Other Plants

i. Pineapple Leather (Piñatex) : Made from pineapple leaf fibers (agricultural waste). One of the most established and widely used options.

ii. Apple Leather : From apple peels, cores, and pomace waste from juicing/cider production.

iii. Banana Leather : From banana plant stems or fibers (often waste after fruit harvest).

iv. Orange, Lime and Lemon Leather : Made from the waste of these citrus fruits.

v. Mango Leather : From leftover mangoes or peels (e.g., Fruitleather Rotterdam).

vi. Papaya Leather : From papaya waste or fibers.

vii. Watermelon Leather : From watermelon rind or pulp waste.

viii. Grape Leather (Vegea) : From grape skins, seeds, and stems leftover from wine production.

ix. Olive Leather (Oleatex or similar) : From olive pits or processing waste.

x. Coconut Leather : From coconut husk fibers or coir.

xi. Corn Leather : From non-food-grade corn stalks or husks (agricultural by-products).

xii. Cactus Leather : From nopal/prickly pear cactus. Harvested from mature pads without harming the plant; very water-efficient.

xiii. Agave Leather : From agave fibers or waste.

xiv. Bamboo Leather : From bamboo fibers or pulp.

xv. Cork Leather : From the bark of cork oak trees (harvested regeneratively every 9–12 years without cutting the tree).

xvi. Leaf Leathers (general category) : Includes teak leaves, betel nut palm leaves (Palm leather), or elephant ear plant leaves.

xvii. Mushroom Leather (Mycelium Leather) : Grown from mycelium (the root-like structure of fungi). Brands include Reishi (MycoWorks), Mylo (Bolt Threads, though production has faced challenges), Forager (Ecovative), and MuSkin (from specific mushroom caps like Phellinus ellipsoideus). Often highly customizable and scalable in vertical farming.

2. Other Innovative/Bio-Based Vegan Leathers

i. Coffee Leather : From coffee grounds or cherry waste.

ii. Tea Leather or Kombucha Leather : From fermented tea cultures or kombucha by-products (sometimes called 'teather').

iii. Seaweed/Algae Leather : From marine algae or seaweed biomass.

iv. Hemp Leather : From hemp fibers (strong and durable plant-based option).

v. Linseed Oil Leather (Lino Leather) : Based on flax/linseed derivatives.

vi. Mirum : A 100% plastic-free, bio-based material often using plant oils, rubber, and minerals (not tied to one single plant).

vii. Celium (by Polybion) : Bacterial nanocellulose grown on fruit/agro-industrial waste (kombucha-like process).

viii. PHLYDE : Circular materials from upcycled fruits, vegetables, and algae.

ix. Rubber Leather : From plant-derived natural rubber alternatives).

x. Grain/Protein-Based (emerging) : Such as Uncaged, using proteins from agricultural grains.

Traditional Leather vs Vegan Leather

1. Chemical Processes: From Toxic Tanning to Cleaner Synthesis

Traditional leather starts with animal hides and relies on chrome tanning—the dominant method for ~ 90% of global production. Raw hides undergo beamhouse operations (soaking, liming, deliming) followed by chromium sulfate treatment to cross-link collagen proteins. This 'efficient' process uses up to 2.5 kg of chemicals per kg of leather, generates 6.1 kg of solid waste, and releases hazardous effluents containing chromium, formaldehyde, arsenic, and sulfides. These violate green chemistry principles: they create persistent pollution, use hazardous reagents, and produce non-biodegradable waste.

Vegan leather sidesteps hides entirely. Production involves:

i. Bio-polymer composites (e.g., cellulose from pineapple leaves in Piñatex or mycelium in mushroom leather) or plant fibers bound with bio-based resins.

ii. Milder polymerization or fermentation processes using renewable feedstocks, enzymes, or phyto-tannins — no heavy metals required.

These align with green chemistry by prioritizing renewable raw materials, reducing hazardous synthesis, and minimizing waste. Even PU-based vegan options avoid the chromium-heavy tanning step, though next-gen plant-based variants (cactus, apple, grape) are fully bio-derived and often biodegradable.

2. Environmental Impacts: LCA Metrics Tell the Story

LCAs under Environmental Economic Chemistry reveal stark differences in global warming potential (GWP), water footprint, land use, and ecotoxicity.

i. Carbon Footprint: Traditional leather clocks in at 110 kg CO₂e/m² (including livestock farming, which dominates ~ 85% of emissions via methane and deforestation). Synthetic vegan leather: just 15.8 kg CO₂e/m². Plant-based options like cactus leather drop even lower (~ 5 kg CO₂e/m²), with some LCAs showing 0.8–8.8 kg. Vegan alternatives are 7times less climate-intensive.

ii. Water & Land Use: One cow / bull / buffalo hide tote bag requires ~ 17,128 liters of water. Tanning alone uses 250 L/kg. Livestock grazing drives deforestation (80% linked to cattle ranching). Vegan options use dramatically less land and water — cactus leather, for example, needs ~200 L/m² and sequesters carbon during growth.

iii. Pollution & Biodiversity: Chrome effluents pollute rivers (e.g., 40 million liters of untreated wastewater daily into India's Ganges). Vegan materials avoid this entirely, reducing ecotoxicity and supporting circular economies via agricultural by-products. Plant-based vegan leather even biodegrades faster, closing the loop — unlike chemically laden traditional leather.

iv. Trophic Level Waste: To get a cow / bull / buffalo hide, you must first grow the biomass to feed the animal. This involves massive inputs of nitrogen-based fertilizers (N₂ + 3H₂ → 2NH₃ via the Haber-Bosch process), which is energy-intensive and carbon-heavy. By using microbial fermentation or plant-waste upcycling, we bypass the thermodynamic losses associated with animal metabolism (respiration, heat, and non-usable biomass).

3. Economic Analysis: Direct Costs + Externalities = Vegan Wins

Traditional leather hides massive externalities—costs society pays via health impacts, water cleanup, and climate adaptation. Livestock subsidies and pollution remediation inflate the true price.

Vegan leather flips the script:

i. Production Costs: Scalable from agricultural waste (no animal rearing). Plant-based options are often cheaper at volume.

ii. Market Growth: The global vegan leather market is exploding—from ~USD 80 billion in 2024 to USD 219 billion by 2035 (CAGR ~ 9.55%). Demand from fashion, automotive, and furnishings drives innovation and price drops.546d1c

iii. Long-Term Economics: Lower regulatory risks (stricter chemical bans), brand value from ethics/sustainability, and circular revenue (biodegradable or recyclable). Externalities like carbon pricing make traditional leather increasingly uncompetitive.

In short: Vegan leather internalizes fewer costs while delivering superior performance in a growing ethical market.

Conclusion: Vegan Leather Is the Chemically, Environmentally, and Economically Superior Choice

Through the rigorous lens of Environmental Economic Chemistry, vegan leather—particularly plant-based innovations — excels by preventing waste at the source, minimizing hazardous chemicals, slashing emissions and resource use, and avoiding billions in unpriced externalities. Traditional leather's 'by-product' narrative crumbles under LCA scrutiny. As mentioned in one of the previous blogs, biogas-blackwater systems will make cattle so useful that nobody will sell them to beef and leather industries.

The future? Invest in bio-based vegan alternatives, support green chemistry R&D, and choose products that align with a sustainable economy. Your next bag, jacket, or shoes can be kinder to the planet — without compromise.

Thanks,

The Aadyanagha Foundation.

Dream Education System

Glories to Aadyanagha Mahadevi and Duranteshwar Mahadev 🙏!

I have spent considerable time reflecting on our childhood education system and wanted to share my vision for a more holistic and structured 'Dream Education System.'.

Nursery Classes should focus on improving the following:

1. Basics of Alphabets and Words

2. Basics of Numbers and Counting 

3. Reading, Writing and Speaking 

4. Drawing & Colouring, Playing, Dance & Music (Basics and Age-Friendly)

For Class I - V, there should be the following structure in a simplified manner :

1. English (50% British English and 50% American English)

2. Vernacular Language - Hindi for better national connectivity

3. Third Language (Regional Language or Urdu or Sanskrit)

4. Mathematical Aptitude (Simplified methodology to ensure all basic concepts are absorbed early)

5. Digital Literacy (Basics) - Practical only

6. General Knowledge (Basics of Science & Business, History & Geography, Sports & Entertainment and Art & Culture) - Oral only 

All basics of Maths and Digital Literacy should be completed by Class V ...... So that pressure is minimized.

Maths syllabus - Basic Arithmetic (from counting, addition, subtraction, multiplication, division, factors and multiples to ratios, proportions, percentages and averages), Basic knowledge of Lines, Angles and Shapes (mensuration portions can be taught later), Introduction to Algebra - all should be taught in a fun way

Digital Literacy - Basic knowledge of parts of computers and laptops, Basic knowledge of Microsoft Word & Google Docs, Microsoft Powerpoint & Google Slides and Microsoft Excel & Google Sheets, Microsoft One Note & Google Keep, Microsoft Access, Paint, Excalidraw, etc (Advanced knowledge shouldn't be touched at this stage)

Promotions should not be kept on hold at this period.

From Class VI - X, there should be the following in a simple manner :

1. English (A balanced curriculum covering both British and American English standards)

2. Vernacular Language (Tadbhav Hindi with little combinations of Sanskritized Tatsam Hindi and Urdu Hindi) and Third Language (Regional / Urdu / Sanskrit - Project Based) - By making Third Language Project-Based, student pressure is also reduced and simultaneously, knowledge of regional languages is preserved.

3. Mathematical Aptitude and Logical Reasoning - Should be simplified to a level where students are not afraid of the subject, but concepts should be clear.

4. Digital Literacy - It is non-negotiable in today's time! Should include simplified concepts of modern day computers, phones, laptops, applications, etc.

5. Science Fundamentals (Physics, Chemistry, Biology and Environment) - Should be concise, inter-connected and age-friendly! 

6. Business Fundamentals (Industry & Commerce, Economics and Accounts) - Should be taught early! Frankly we were taught tougher science in our early years (like classes VI - VIII) but the commerce taught during the later years (like IX - X, when students leave science) was too basic! Basics of management should be known at an early stage.

7. Civilizational Studies (Geography, History, Civics & Politics) - Should be concise and age-friendly!

8. Social Studies (Philosophy, Sociology, Psychology and Anthropology) - You will not be able to understand civilizational studies without understanding these aspects! Should also include authentic quotations from scriptures like Quran, Purans, Vedas, Gita, Upanishads, etc ....... To avoid misrepresentations that may cause social divide!

9. Arts, Music, Dance and Sports (General Knowledge based - Full paper would be in multiple choice questions format)

Note : For Science Fundamentals, Business Fundamentals, Civilizational Studies and Social Studies, there should be sectional division (for the subsections in brackets given earlier to maintain distinction) with separate textbooks (thin and concise that sufficiently clear the concepts), projects and examinations. But the marks should be clubbed into one. For example : Science Fundamentals = Physics + Chemistry + Biology + Environment ; Business Fundamentals = Industry & Commerce + Economics + Accounts ; Civilizational Studies = Geography + History + Civics & Politics ; Social Studies = Philosophy + Sociology + Psychology + Anthropology.

Note : Aspects of Physical Geography like Geology, Hydrology, Oceanography, Pedology, Astronomy, etc are a part of Environment in Fundamental Science. The Geography in Civilizational Studies includes human geography and regional geography.

From Classes XI - XII. there should be the following :

1. Science Stream should be further divided into the following - i. Science & Research (Pure - Science) ; ii. Engineering ; iii. Healthcare (Medicine, Pharmacy, Nutrition, etc) ; iv. Sustainability ; v. Agriculture ; vi. Infotech (Artificial Intelligence + Information Technology + Data Science). 

Customized subjects and syllabus for each. For example, no extra physics for a Healthcare student and no extra biology for a engineering student. Research & Auditing should also be included in each of the six streams.

I. Subjects in Science & Research Stream :

i. Physical Science (Sub-Sections : Physics, Chemistry and Astronomy)

ii. Life Science (Sub-Sections : Botany, Zoology and Microbiology)

iii. Environmental Science (Amalgamation of Geology, Hydrology, Oceanography, Pedology, Meteorology, Climatology)

iv. Social and Business Studies (Concise information on Sociology & Psychology, Economics & Accounting, Finance & Marketing, Industries)

v. Maths

vi. Digital Literacy 

vii. Research & Auditing Methodologies

This stream is mainly for those who cannot decide among other streams.

II. Subjects in Engineering Stream :

i. Physics for Engineering 

ii. Chemistry for Engineering 

iii. Environmental Studies for Engineers

iv. Biology, Anthropology, Sociology and Psychology for Engineering (all in one)

v. Industrial and Commercial Studies for Engineering (inclusive of Marketing, Finance, Economics and Accounting customized for Engineers)

vi. Maths for Engineers 

vii. Digital Literacy 

viii. Research & Auditing Methodologies 

III. Subjects in Healthcare Stream :

i. Physics for Healthcare (inclusive of Biophysics and Biotechnology)

ii. Chemistry for Healthcare (inclusive of Biochemistry and Pharmacology)

iii. Biology 

iv. Environmental Studies for Healthcare 

v. Anthropology, Sociology & Psychology for Healthcare (all in one)

vi. Industrial and Commercial Studies for Healthcare (inclusive of Biomarketing, Bioeconomics, Bioaccounting, Banking & Insurance for Healthcare, etc)

vii. Maths for Healthcare 

viii. Digital Literacy 

ix. Research & Auditing Methodologies 

IV. Subjects in Sustainability Stream :

i. Geology & Pedology 

ii. Hydrology & Oceanography 

iii. Meteorology & Climatology 

iv. Environmental Physics, Chemistry & Biology 

v. Environmental Marketing, Economics & Accounting 

vi. Environmental History, Geography, Sociology & Psychology 

vii. Environmental Law

vii. Maths for Sustainability 

ix. Digital Literacy 

x. Research & Auditing Methodologies 

V. Subjects in Agriculture Stream :

i. Geology & Pedology 

ii. Hydrology & Oceanography 

iii. Meteorology & Climatology 

iv. Agricultural Physics, Chemistry & Biology 

v. Agricultural Economics, Accounting, Finance & Marketing 

vi. Agricultural History & Geography 

vii. Agricultural Rights & Law

viii. Maths for Agriculture 

ix. Digital Literacy 

x. Research & Auditing Methodologies 

VI. Subjects in Infotech Stream :

i. Artificial Intelligence 

ii. Information Technology 

iii. Computer Science 

iv. Data Science & Data Analytics 

v. Digital Finance & Digital Marketing 

vii. Physics & Chemistry for Infotech 

viii. Sociology & Psychology for Infotech 

ix. Maths for Infotech 

x. Research & Auditing Methodologies 

These should be student friendly. Focus should be on understanding the concepts, rather than memorization.

2. Commerce Stream should be renamed to Business Stream or Commerce and Industry Stream because Business includes both Commerce and Industry. It should include the following subjects - 

i. Industrial and Commercial Studies for Business divided into two parts

Industrial Studies for Business - Little bit of basic level science to be included for better business strategies. For example : principles of food science for food processing industries ; knowledge of nutrition for restaurant businesses to develop creative strategies to survive in the competition ; basic knowledge of chemicals for beauty industries ; basic knowledge of machines for electronic goods ; knowledge of alchemy, geology, hydrology, oceanography for manufacturing ; knowledge of energy efficiency for curating unique marketing strategies, etc. Also includes a bit of history and geography of industries

Commercial Studies  for Business (Finance, Banking & Insurance, Marketing & Communication, Trade & Logistics, Sustainability, etc) - Includes history and geography of certain sectors. For example, knowledge of geography is important for trade, transport and warehousing ; knowledge of history of banking, insurance, marketing and trade, etc.

iii. People Management (Organisational Behaviour, Human Resource Management, Stakeholder Management)

iv. Advanced Business Accounting (Financial Accounting, Cost Accounting, Tax Accounting, Environmental Accounting)

v. Advanced Business Economics (Microeconomics & Macroeconomics for Class XI, Socioeconomics, Geoeconomics, Econochemistry & Environomics for Class XII) - Again it should be student-friendly, but should also ensure basic concepts are absorbed in a simplified way.

vii. Research and Auditing Methodologies 

vi. Business Maths (Customized)

viii. Digital Literacy and Business Intelligence (Customized Data Science, Information Technology and Artificial Intelligence)

ix. Business Law (Basic level).

Industrial Studies & Commercial Studies to be clubbed together into one subject named Fundamentals of Science and Business. 

3. Humanities Stream should have the following :

i. History, Geography, Civics & Politics (separate subjects but marked under one) - Mandatory 

ii. Anthropology, Sociology, Psychology & Philosophy (separate subjects but marked under one) - Mandatory 

iii. Archeology & Architecture - Mandatory 

iv. Sustainability & Lifestyle (Simplified knowledge of Technology, Finance, Marketing, Materials, Nutrition and Sustainability) - Mandatory 

v. Research & Auditing Methodologies - Mandatory 

vi. Quantitative Aptitude & Logical Reasoning - Mandatory 

vii. Digital Literacy & Mass Communication - Mandatory 

viii. Fashion Designing - Optional

ix. Interior Designing - Optional

x. Hospitality Management - Optional

4. Law & Security Stream should be added having the following subjects :

i. Sociology & Psychology 

ii. Sustainability & Lifestyle 

iii. Business & Environmental Law

iv. Constitutional Law

v. Civil & Family Law

vi. Human Rights & Criminal Law

vii. Digital Literacy & Cyber Law

viii. Quantitative Aptitude & Logical Reasoning

ix. Research & Auditing Methodologies 

x. General Knowledge (Basic Theories of Science Fundamentals (Physics, Chemistry, Biology and Environment), Business Fundamentals (Industry, Commerce, Economics and Accounting), Civilizational Studies (Geography, History, Civics and Poltics) and Social Studies (Anthropology, Sociology, Psychology and Philosophy)) 

xi. Forensic Investigation 

xii. Public Policy & Governance 

xiii. Crisis Management 

xiv. Indian Penal Code and Bharatiya Nyay Samhita (simplified)

xv. Ethical and Moral Responsibilities as a Social Citizen 

5. Maths Stream should also be added which should have subjects split into the following:

i. Arithmetic & Algebra 

ii. Geometry, Mensuration & Trigonometry 

iii. Sets, Combinatorics & Probability 

iv. Calculus, Vectors & Statistics 

v. Logical Reasoning 

vi. General Knowledge (Basic Theories of Fundamental Science (Physics, Chemistry, Biology and Environment), Business Studies (Industry, Commerce, Economics and Accounting), Civilizational Studies (Geography, History, Civics and Poltics) and Social Studies (Anthropology, Sociology, Psychology and Philosophy)) - Theory based - only Multiple Choice Questions 

vii. Quantitative Applications in Technology and Finance (Amalgamation of Physics, Chemistry, Economics and Accounting) (detailed numericals with fun examples) - beyond theory already covered in General Knowledge - It even includes how all four can be used together (for example, it even includes aspects like Econochemistry, Physicoaccounting, etc.)

viii. Methods to Remove Math Phobia

ix. Digital Literacy 

x. Shortcuts for Maths

xi. Vedic and Islamic Maths - Theory - Practicals merged with Shortcuts for Maths

This stream is mainly for curriculum developers, maths teachers, etc. They will get jobs as teachers across all streams and can develop customized syllabus for each stream. They can even get jobs in coaching centers for competitive exams.

6. There should also be a specialized Literature & Linguistics Stream for people passionate about Literature. It should have the following subjects :

i. English Literature 

ii. English Grammar & Vocabulary 

iii. Hindi Literature 

iv. Hindi Grammar & Vocabulary 

v. 1 Regional Language / Sanskrit / Urdu (Preference to be given to the language chosen as Third Language ; If some new language is being chosen, then 1 year training is needed to understand letters and words) - Simplified 

vi. 1 International Language - Simplified 

vii. Mass Communication 

viii. General Knowledge 

ix. Quantitative Aptitude and Logical Reasoning 

x. Digital Literacy 

This is an ultra-niche stream mainly for curriculum developers and language teachers. They will get jobs as teachers across all streams and can develop customized syllabus for each stream. They can even get jobs in coaching centers for competitive exams.

7. There should also be a Defence Stream having the following subjects :

i. Strategic Geography, Military History & International Relations

ii. Defence Technology & Healthcare 

iii. Defence Management (Resource Allocation, Supply Chains, etc)

iv. Military Psychology and Sociology 

v. Digital & Cyber Defence 

vi. Constitutional & Defence Law

vii. Disaster Management 

viii. Quantitative Aptitude and Logical Reasoning 

ix. Ethics & International Law of Conflict

This shall be a theory-based stream. Again there shall be no cut-offs. No rigorous physical training here as the children are too young for such hard training. But physical fitness and mental wellness are important here. Syllabus should be curated in an age-friendly manner with fun examples. Practicals can be done in game-format.

There should be dedicated online schools for the stream. Only those students should this stream who want to be a part of defence.

8. There should be a dedicated Theology Stream, the curriculum of which should be developed by honest, peaceful and religious experts. The work of these people would be to debunk people spreading misinformation in the name of religious philosophies and ensure that there are no toxic divisions based on sects, religions and caste. The students in this stream need to be serious. If they score well, they are assured a high position in society. This stream will have the following subjects :

i. Sanskrit and Arabic Literacy - Basic Level

ii. General Knowledge (same as Law Stream and Maths Stream)

iii. Bhagavad Gita and Ishwar Gita

iv. Summarised Quran and Vedas (should be curated by genuine experts who don't misguide in the name of Quran and Vedas) (there should be a separate Section for Vedas and Quran) (One paper for Quran and one paper for Vedas, taught by honest, secular and well-read Muslims and Hindus)

v. Sectarian Philosophies in Hinduism (Giving a Summary of all Sects)

vi. Puranic and Hadith Literature (stories and poems with references to ensure there is no social divide) - Hindi

vii. Summarised Ramayana and Mahabharata 

viii. Summarised Guru Granth Sahib 

ix. Jain and Buddhist Philosophies 

x. Christian, Jew and Zoroastrian Literature - English (stories and poems with references)

xi. Scientific, Business and Artistic Acumen across different religions (also includes contributions of different religions in these fields)

xii. Quantitative Aptitude and Logical Reasoning (also includes contributions of different religions in these fields) (should include methods like Vedic Maths, Al-Jabr Method, Rule of Three, Bede's System, etc)

xiii. Digital Literacy and Mass Communication 

xiv. Human Rights, Criminal and Cyber Law

xv. National Integrity and Civilizational Pride

For this stream, each religion would have a secular and unbiased expert. For example, for the Quran, an honest and well-read Muslim would be needed, while for Vedas, an honest and well-read Hindu would be needed. A background check would be done to ensure that they haven't indulged in anti-secular activities.

This stream will have a centralised syllabus all over to avoid clashes. Only serious students are to join this stream. These students will be in a high position. They will have the power to punish anti-social and anti-national elements who would create chaos in the name of caste, sects and religion. They will also work to punish any online abuse and cyber-bullying. They will play a big role in patriotism too. They will also have the power to ban movies and shows that hurt religious sentiments. They will also have the power of punishing criminals indulging in forced conversions and human trafficking.

No cut-offs for this stream. There should be dedicated online schools for this stream.

A person from any caste, religion or sect can join this stream.

Professional disciplinary action may be taken against certified theology practitioners found guilty by due legal process of hate crimes, incitement to violence, communal harassment, extremist mobilization, coercive religious activity, or deliberate dissemination of harmful misinformation.

Secular unity is nationalism itself ......... Any anti-secular activity from any religion should be considered as anti-national. This stream strictly rejects pseudo-secularism too.

9. There should be a Fashion Stream specifically for people into fashion designing and jewellery designing. It should be having the following subjects :

i. Sustainable Textiles, Jewellery & Materials Science

ii. Fashion History & Global Culture

iii. Fashion Economics, Accounting & Marketing 

iv. Quantitative Aptitude and Digital Literacy for Fashion

v. Fashion Designing & Jewellery Designing (with practicals)

vi. Fashion Sociology & Psychology 

10. There should be a Hospitality Stream for people interested in travel, tourism, hotel management and interior design. It should having the following subjects :

i. Culinary Arts & Food Science

ii. Travel & Tourism Geography 

iii. Cultural History & Heritage 

iv. Hospitality Services Marketing & Operations 

v. Hospitality Economics & Accounting 

vi. Quantitative Aptitude and Digital Literacy for Hospitality 

vii. Interior Decoration (with practicals)

11. There should be an Arts & Sports Stream too. Arts, Music, Dance & Sports are clubbed together as these are the most competitive and volatile careers. So a wide range of skill-sets will be helpful as a back-up in case they aren't able to make it in one category. No cut-offs needed here. It is actually for those who are very clear that they want to join Fine Arts, Performing Arts & Sports, Creative Design and Mass Communication! Following are the subjects :

i. Literature, Vocabulary & Diction (both English and Hindi) - Mandatory

ii. Classical and Folk Dance (1 dance form on a rotation basis ; a student can choose maximum 10 dance forms ; Basics would be completed ; Mastery would be achieved in Higher Level) - Elective (I said maximum 10, not minimum. Even taking just 1 dance form is enough. That too if this elective is chosen)

iii. Classical and Folk Music - Elective

iv. Swimming & Yoga (only practical assessment) - Mandatory (because they are life-saving skills)

v. Bollywood & International Dance and Music (only practical assessment) - mandatory (because basic dance should be known ........ Further basic vocal exercises too are important ; optional parts here - knowledge of various instruments)

vi. Acting, Photography & Filmmaking (only practical assessment) - Elective

vii. Sports (1 sport per day on a rotation basis ; a student can choose maximum 5 sports of their choice from a large range of choices ; Basics would be completed ; Mastery would be achieved on a higher level) (only practical assessment) - Elective (Again only 1 is enough, there is no compulsion to take 5. That too if this elective is chosen.)

viii. Martial Arts (only practical assessment) - Elective

ix. Fine Arts (only practical assessment) (includes aspects for Fashion Designing & Interior Designing) - Elective

x. General Knowledge (Basic Theories of Science Fundamentals (Physics, Chemistry, Biology and Environment), Business Fundamentals (Industry, Commerce, Economics and Accounting), Civilizational Studies (Geography, History, Civics and Poltics) and Social Studies (Anthropology, Sociology, Psychology and Philosophy)) - Mandatory

xi. Mathematical Aptitude & Logical Reasoning - Mandatory 

xii. Digital Literacy & Mass Communication - Mandatory 

xiii. Ethics, Patriotism and Spirituality - Mandatory 

xiv. Cookery - Mandatory (because it's a life-skill)

Every sport, dance, music and art will be on basic level where one can be sufficiently confident. Higher levels will be taught based on prior learning or speed of learning.

Minimum 3 electives to be chosen. More than 3 electives can be chosen.

This stream will have dedicated physical schools. Only serious students should join this stream. It will even have online classes for academic subjects. Like other streams, it will have dashboard courses.

12. So there are 16 streams in total. Each stream has its customized maths and Digital Literacy syllabus. English and Hindi are there for each stream except for Theology Stream and Arts & Sports Stream (because they have their own syllabus for English and Hindi).

13. For Classes XI - XII : Since Arts & Sports Stream is a practical stream, it should have dedicated physical schools for the same (academic portions can be taught online). Rest others can be taught online. For lab-related work, there should be dedicated buildings for labs for Science Streams (Science & Research, Engineering, Healthcare, Agriculture, Sustainability). The theory portion of these streams (Science & Research, Engineering, Healthcare, Agriculture, Sustainability) Business, Humanities, Law & Security, Maths, Literature & Linguistics, Defence, and Theology streams can be done 100% online as they do not have any lab-work. Infotech Stream too can be done 100% online with the software installed in the laptop itself. Some parts of Fashion and Hospitality should be practicals, rest theory portions to be taught online.

Online classes will be conducted live. In case, classes are missed, students can see class recordings.

Strong teacher-student and peer-to-peer interaction will be actively encouraged throughout the system. Students will interact regularly through moderated Google Chat and WhatsApp groups, which will serve as natural starting points for building friendships. The school website will host student profiles so that kids from different streams can find each other, share their skills, and work together on projects. Peers will be free to exchange numbers and plan informal meet-ups. In addition, the system will organize regular school trips for educational and recreational purposes. Students will also come together on physical campuses for extra-curricular activities, cultural events, and special gatherings, ensuring a healthy balance between online flexibility and meaningful real-life social connections. The laptop would be returned once Class XII is over, but the school email-ID and profile in school website would be retained.

For Nursery - Class X : Physical Schools

14. For Classes XI - XII : For uniformity and discipline, the school should provide laptops and should create school-emails for each child so that there is parity and discipline. The activities on the school-email should be scrutinized by the school. It shouldn't be mixed up with the personal email.

15. A student can choose a simplified course of their liking from the school dashboard. It can include any course from any stream. On completing the course, they receive a certificate. They can take courses even from streams different from the one they are studying. These courses will be simplified and pre-recorded. These indeed include a pool of vocational courses. These certifications can be used as a back-up.

16. Qualified people not getting the right jobs can be used in curriculum development tailored for each stream.

This will help students study a customized and career-oriented syllabus, which in turn will reduce study pressure on students.

Higher education should embrace interdisciplinary studies to bridge the gap between fields.

17. Exemption Cut-offs to be set for each stream so that there is minimized mental pressure :

Science & Research - 60%+ (as it has a huge subject load)

Law & Security and Maths - 55%+ (as a lot of memorization is involved)

Engineering, Healthcare and Infotech - 65%+

Business and Humanities - 70%+

Sustainability and Agriculture - 70%+

Defence, Theology and Arts & Sports - No cut-offs

If cut-offs are not met, selection tests can be used for entry.

Scholarship Cut-offs for those who scored high:

Science & Research - 70-80%+ (as it has a huge subject load)

Law & Security, Literature & Linguistics and Maths - 75%+ (as a lot of memorization is involved)

Engineering, Healthcare and Infotech - 80-90%+

Business and Humanities - 80-90%+

Sustainability and Agriculture - 80-90%+

Defence, Theology, Fashion, Hospitality and Arts & Sports - No cut-offs

16. Curriculum should be taught in an age-friendly and fun manner with realistic examples, to ensure education is not boring!

Colleges should have interdisciplinary studies like the ones given below within the curriculum for the relevant degrees - 

Geoeconomics, Geoaccounting, Econohistory, Accountohistory, Accountophysics / Physicoaccounting, Econophysics, Bioeconomics, Econochemistry, Environomics, Enviroaccounting, Chemoaccounting, Bioaccounting, Physfinance, Chemofinance, Biofinance, Physimarketing, Chemomarketing, Biomarketing, Enviromarketing, Envirofinance, Geomarketing, Geochemistry, Geophysics, Geobiology, Histophysics, Histochemistry, Histobiology, Socioeconomics, Socioaccounting, Socioecology, Sociomarketing, Neuroscience, etc

These subjects should be there for relevant fields.

Hehe many of the names are crafted by me. But impossible is nothing. Every subject has its linkages.

There can be scope for multiple specializations in graduation and post-graduation as many things that are being taught during graduation are already being taught in school, leaving scope for studying new things.

The marking system should be the following :

1. 10% Class Assessment ; 2. 10% Project Work ; 3. 80% Written Examination (50% Multiple Choice Questions, 25% Brief Answer Questions ; 15% Long Answer Questions, 10% Short Answer Questions within Written Examination) - Not applicable for subjects mentioned as 'only practical assessment' in Arts & Sports Stream 

Stream Switching 

The Dream Education System recognizes that self-discovery is a journey. Should a student realize that their chosen stream does not align with their true passion, they are provided the flexibility to switch to a new specialization. This transition is viewed not as a setback, but as a proactive 'Academic Pivot' — akin to pursuing a second graduation to align with one's evolving goals.

High performance during such a transition is celebrated as a mark of higher intelligence, adaptability, and self-awareness. While students in the Science & Research stream may transition into applied fields like Engineering, Healthcare, Sustainability, or Agriculture due to their foundational overlap, a formal switch is required for those moving into distinct domains such as Infotech, Law, Maths, Humanities, or Business to ensure they master the specific core competencies of those fields.

Stream Selection Conferences 

In order to avoid situations like stream switching, there should be conferences before Class XI begins. Here students will be given a detailed overview of all streams, so that they have mental clarity to choose the correct stream. They will also receive motivation to choose any stream they like, simultaneously counselling the parents to let their children choose the stream they like. These conferences will ensure every stream is treated with equal respect.

As mentioned before, dashboard courses would be helpful in giving knowledge beyond a the chosen stream. This will help in switching streams in college.

Co-Curricular Activities & Holistic Well-being

Obviously Ethics, Patriotism & Spirituality, Fitness, Sports, Acting, Music, Dance, Arts & Writing, etc would be for every field as an integral part of the curriculum. In every age, for every stream! These will be treated as essential refreshment and holistic development components, not optional extras, ensuring students maintain physical health, emotional balance, and creative expression alongside academic pursuits.

There should also be subconscious re-programming programmes for students so that they realise the strength of their subconscious mind! Specially in Ethics and Spirituality classes.

Ethics & Spirituality should also include sex education post adolescence. There should also be strong character-building lectures where people learn to look beyond caste and religion.

Final Note

I just shared a vision. I may be correct or wrong. But I know that revisions need to be made in the current education system, so that it is in alignment with the holistic development of children. I understand the implementation may be a time-taking process. It will also involve high amount of teacher training and many other challenges. But it's also good for tackling unemployment as many qualified students aren't getting the right jobs (some sadly being delivery people). We can at least try to take small steps towards this vision. Once implemented, it will be prolific in the long run.

Thanks and Regards,

The Aadyanagha Foundation.