This causes me to wonder why the text was dropped in the 1980s and what has replaced it? Is the spirit of Kiseloev still alive? I like that St Petersburg to Moscow example, that would have helped me as a kid understand why the hell I was learning about negative numbers. Personally I never really care about math until I got to predictive models and the math could be applied to something obviously very useful.
On the St. Petersburg to Moscow example — yes, that's the Kiselev move exactly. Take a situation that already has direction in it, name one direction positive and the other negative, and let the rules of signed arithmetic emerge naturally from the physics. Modern textbooks just decree "negative numbers exist; here are their rules." Kiselev makes negative numbers feel necessary. That's the difference between a textbook that teaches and a textbook that tests.
On the date — it's actually earlier than the 1980s. The removal of Kiselev started quietly in 1956 and was completed by the Kolmogorov reform of 1968-70. Andrey Kolmogorov — possibly the greatest Russian mathematician of the 20th century — chaired the committee. He was a brilliant mathematician and, by his own students' later admission, a poor pedagogue. The reform replaced Kiselev with new "rigorous, set-theoretic" textbooks by Kolmogorov himself (geometry) and Vilenkin, Makarychev, Atanasyan, Nikolsky and others (algebra and geometry) — and those are still the default Russian school textbooks today, under steady criticism. A. M. Abramov, who actually helped write Kolmogorov's geometry, admitted in 'Teachers' Newspaper' in 1994 that the books they had replaced were "national heritage" and that he hadn't understood at the time what was being destroyed. That confession is one of the most striking documents.
I only recently discovered that the USSR managed to wreck school mathematics education not once but twice in the 20th century alone.
The first collapse came after the Revolution of 1917.
Before the revolution, gymnasium students could study from Kiselev’s textbooks and reach serious mathematics, including elements of calculus, by their mid-teens. After the revolution, the old curriculum was dismantled.
For a period, traditional algebra and geometry were pushed aside or effectively banned from the school programme.
The country entered an educational darkness.
The Marxist pedagogues tasked with designing the new Soviet school — Albert Pinkevich, Pavel Blonsky, Stanislav Shatsky — built their system under the influence of Dewey’s “labour school” theory. Abstract mathematics was replaced by ideological and “practical” activity. The result was predictable: by the early 1930s, the Soviet state discovered that it was running out of engineers, and many school-leavers could barely handle arithmetic.
Then came the 180-degree reversal. The old seriousness had to be restored.
That first disaster at least happened in a period of revolution, civil war, and institutional chaos.
The second disaster is more revealing.
Later in the Soviet period, the USSR fell into the same trap as the West: the fashionable cult of “new math”. Once again, school mathematics was redesigned by people who confused mathematical sophistication with teachability. The result was a collapse in comprehension.
One of the most famous Russian mathematicians, Vladimir Arnold, later called the abandonment of Kiselev’s textbooks one of the greatest mistakes in mathematical education.
There is an uncomfortable lesson here. The second reform episode involved Kolmogorov himself. He later became an ardent supporter of the school mathematics reform project.
Kolmogorov was one of the greatest mathematicians of the 20th century.
But being a great mathematician does not automatically make one a great school mathematics educator.
I will be writing about both episodes. They matter, because the same pattern keeps repeating: ideological fashion arrives, classical pedagogy is dismissed as obsolete, children stop understanding mathematics, and decades of damage are then explained away as “modernisation.”
What you’ve surfaced with A. P. Kiselev is not just a historical curiosity—it’s a high-signal pedagogical archetype that quietly shows up in every domain where mastery scales across millions of people with uneven instruction quality.
Below is a Level-3 synthesis: extracting the invariant principles, mapping them across disciplines, and connecting them into a unified “learning system architecture.”
I. CORE TEACHING ESSENCE (ABSTRACTION LAYER)
Strip away math, Russia, and textbooks—you get this:
1. Truth-first, not rule-first
* Don’t state rules → derive necessity
* Knowledge is not given; it is forced by consistency
Example:
“− × − = +” is not memorized—it becomes inevitable under a coherent system.
2. Learner = participant, not consumer
* The student is treated as a co-reasoner
* Exposure to real proofs early (e.g., Euclid)
This is radical:
You are not teaching math facts → you are inducting into mathematical thinking
3. Concrete → Abstract → Generalization pipeline
* Start with physical intuition
* Transition to symbolic structure
* End with general law
This is a compression pipeline:
Reality → Model → Rule
4. Minimal axioms, maximal consequence
* Few assumptions
* Everything else unfolds logically
This mirrors:
* Euclidean geometry
* First principles thinking (popularized by Elon Musk)
5. Pedagogical density (compression efficiency)
* Each page does maximum cognitive work
* High signal-to-noise ratio
This is why it scaled to ~80M students:
* Works even with weak teachers
* The book itself encodes intelligence
6. Internal consistency over authority
* Rules are validated by coherence across scenarios
* Not by “teacher says so”
This is scientific thinking, not schooling.
7. Cognitive inevitability
* The learner feels:
“It couldn’t be otherwise.”
That’s the highest form of understanding.
II. META-PRINCIPLE (THE ENGINE)
All of the above collapse into one master principle:
A system teaches well when it makes knowledge feel inevitable rather than arbitrary.
This is the same principle behind:
* Good proofs
* Good physics models
* Good trading systems
* Good strategy
III. CROSS-DOMAIN ISOMORPHISMS (SIMILAR SYSTEMS)
Now the key: this pattern is NOT unique to math.
1. MATHEMATICS / LOGIC
Euclid’s Elements
* Axioms → propositions → proofs
* No memorization, only derivation
How to Solve It
* Teaches thinking process, not answers
2. PHYSICS
The Feynman Lectures on Physics
* Concepts derived from physical intuition
* Not formula memorization
Richard Feynman approach:
* If you can’t derive it → you don’t understand it
3. COMPUTER SCIENCE
Structure and Interpretation of Computer Programs
* Programs as mathematical processes
* Builds abstraction layers step-by-step
Direct parallel to Kiselev:
* From concrete computation → abstraction → systems
4. STRATEGY / THINKING
The Art of Strategy
* Behavior emerges from incentives
* Not rules, but structures
First Principles Thinking (Musk)
* Break assumptions → rebuild necessity
6. LANGUAGE / GRAMMAR
The Cambridge Grammar of the English Language
* Descriptive, not prescriptive
* Grammar emerges from usage patterns
7. MUSIC
Johann Sebastian Bach
* Harmony rules emerge from structure of sound
* Not arbitrary conventions
8. ENGINEERING
First Principles Thinking
* Reduce to fundamentals
* Reconstruct system
IV. WHY KISELEV DOMINATED (SYSTEMS VIEW)
This is critical.
Not ideology
Not authority
Not inertia
It survived because:
1. Robust to teacher quality
* System is self-explanatory
2. Aligned with human cognition
* Brain prefers causality over memorization
3. High transferability
* Students could apply knowledge, not recall it
4. Low entropy
* Minimal confusion, maximal clarity
VII. UNIVERSAL FRAMEWORK (REUSABLE)
You can apply this everywhere:
Step 1 — Identify the phenomenon
* What is actually happening?
Step 2 — Introduce directional structure
* Like positive/negative
Step 3 — Build scenarios
* Concrete cases
Step 4 — Extract invariants
* What must always hold?
Step 5 — Generalize rule
* Not imposed—discovered
⸻
VIII. FINAL SYNTHESIS
Kiselev represents a rare category:
A pedagogical system that encodes thinking itself.
And the deeper law behind it:
Systems that derive truth from necessity outcompete systems that impose rules from authority.
This causes me to wonder why the text was dropped in the 1980s and what has replaced it? Is the spirit of Kiseloev still alive? I like that St Petersburg to Moscow example, that would have helped me as a kid understand why the hell I was learning about negative numbers. Personally I never really care about math until I got to predictive models and the math could be applied to something obviously very useful.
Here is another bit of history https://valeman.medium.com/how-the-bolsheviks-destroyed-russian-mathematical-education-by-importing-american-progressive-e9c69f3c5568
Dewey did a lot of damage.
yes
On the St. Petersburg to Moscow example — yes, that's the Kiselev move exactly. Take a situation that already has direction in it, name one direction positive and the other negative, and let the rules of signed arithmetic emerge naturally from the physics. Modern textbooks just decree "negative numbers exist; here are their rules." Kiselev makes negative numbers feel necessary. That's the difference between a textbook that teaches and a textbook that tests.
On the date — it's actually earlier than the 1980s. The removal of Kiselev started quietly in 1956 and was completed by the Kolmogorov reform of 1968-70. Andrey Kolmogorov — possibly the greatest Russian mathematician of the 20th century — chaired the committee. He was a brilliant mathematician and, by his own students' later admission, a poor pedagogue. The reform replaced Kiselev with new "rigorous, set-theoretic" textbooks by Kolmogorov himself (geometry) and Vilenkin, Makarychev, Atanasyan, Nikolsky and others (algebra and geometry) — and those are still the default Russian school textbooks today, under steady criticism. A. M. Abramov, who actually helped write Kolmogorov's geometry, admitted in 'Teachers' Newspaper' in 1994 that the books they had replaced were "national heritage" and that he hadn't understood at the time what was being destroyed. That confession is one of the most striking documents.
I only recently discovered that the USSR managed to wreck school mathematics education not once but twice in the 20th century alone.
The first collapse came after the Revolution of 1917.
Before the revolution, gymnasium students could study from Kiselev’s textbooks and reach serious mathematics, including elements of calculus, by their mid-teens. After the revolution, the old curriculum was dismantled.
For a period, traditional algebra and geometry were pushed aside or effectively banned from the school programme.
The country entered an educational darkness.
The Marxist pedagogues tasked with designing the new Soviet school — Albert Pinkevich, Pavel Blonsky, Stanislav Shatsky — built their system under the influence of Dewey’s “labour school” theory. Abstract mathematics was replaced by ideological and “practical” activity. The result was predictable: by the early 1930s, the Soviet state discovered that it was running out of engineers, and many school-leavers could barely handle arithmetic.
Then came the 180-degree reversal. The old seriousness had to be restored.
That first disaster at least happened in a period of revolution, civil war, and institutional chaos.
The second disaster is more revealing.
Later in the Soviet period, the USSR fell into the same trap as the West: the fashionable cult of “new math”. Once again, school mathematics was redesigned by people who confused mathematical sophistication with teachability. The result was a collapse in comprehension.
https://www.youtube.com/watch?v=WyPSeyCXXqA
One of the most famous Russian mathematicians, Vladimir Arnold, later called the abandonment of Kiselev’s textbooks one of the greatest mistakes in mathematical education.
There is an uncomfortable lesson here. The second reform episode involved Kolmogorov himself. He later became an ardent supporter of the school mathematics reform project.
Kolmogorov was one of the greatest mathematicians of the 20th century.
But being a great mathematician does not automatically make one a great school mathematics educator.
I will be writing about both episodes. They matter, because the same pattern keeps repeating: ideological fashion arrives, classical pedagogy is dismissed as obsolete, children stop understanding mathematics, and decades of damage are then explained away as “modernisation.”
Very good piece, discussion outcome with AI:
What you’ve surfaced with A. P. Kiselev is not just a historical curiosity—it’s a high-signal pedagogical archetype that quietly shows up in every domain where mastery scales across millions of people with uneven instruction quality.
Below is a Level-3 synthesis: extracting the invariant principles, mapping them across disciplines, and connecting them into a unified “learning system architecture.”
I. CORE TEACHING ESSENCE (ABSTRACTION LAYER)
Strip away math, Russia, and textbooks—you get this:
1. Truth-first, not rule-first
* Don’t state rules → derive necessity
* Knowledge is not given; it is forced by consistency
Example:
“− × − = +” is not memorized—it becomes inevitable under a coherent system.
2. Learner = participant, not consumer
* The student is treated as a co-reasoner
* Exposure to real proofs early (e.g., Euclid)
This is radical:
You are not teaching math facts → you are inducting into mathematical thinking
3. Concrete → Abstract → Generalization pipeline
* Start with physical intuition
* Transition to symbolic structure
* End with general law
This is a compression pipeline:
Reality → Model → Rule
4. Minimal axioms, maximal consequence
* Few assumptions
* Everything else unfolds logically
This mirrors:
* Euclidean geometry
* First principles thinking (popularized by Elon Musk)
5. Pedagogical density (compression efficiency)
* Each page does maximum cognitive work
* High signal-to-noise ratio
This is why it scaled to ~80M students:
* Works even with weak teachers
* The book itself encodes intelligence
6. Internal consistency over authority
* Rules are validated by coherence across scenarios
* Not by “teacher says so”
This is scientific thinking, not schooling.
7. Cognitive inevitability
* The learner feels:
“It couldn’t be otherwise.”
That’s the highest form of understanding.
II. META-PRINCIPLE (THE ENGINE)
All of the above collapse into one master principle:
A system teaches well when it makes knowledge feel inevitable rather than arbitrary.
This is the same principle behind:
* Good proofs
* Good physics models
* Good trading systems
* Good strategy
III. CROSS-DOMAIN ISOMORPHISMS (SIMILAR SYSTEMS)
Now the key: this pattern is NOT unique to math.
1. MATHEMATICS / LOGIC
Euclid’s Elements
* Axioms → propositions → proofs
* No memorization, only derivation
How to Solve It
* Teaches thinking process, not answers
2. PHYSICS
The Feynman Lectures on Physics
* Concepts derived from physical intuition
* Not formula memorization
Richard Feynman approach:
* If you can’t derive it → you don’t understand it
3. COMPUTER SCIENCE
Structure and Interpretation of Computer Programs
* Programs as mathematical processes
* Builds abstraction layers step-by-step
Direct parallel to Kiselev:
* From concrete computation → abstraction → systems
4. STRATEGY / THINKING
The Art of Strategy
* Behavior emerges from incentives
* Not rules, but structures
First Principles Thinking (Musk)
* Break assumptions → rebuild necessity
6. LANGUAGE / GRAMMAR
The Cambridge Grammar of the English Language
* Descriptive, not prescriptive
* Grammar emerges from usage patterns
7. MUSIC
Johann Sebastian Bach
* Harmony rules emerge from structure of sound
* Not arbitrary conventions
8. ENGINEERING
First Principles Thinking
* Reduce to fundamentals
* Reconstruct system
IV. WHY KISELEV DOMINATED (SYSTEMS VIEW)
This is critical.
Not ideology
Not authority
Not inertia
It survived because:
1. Robust to teacher quality
* System is self-explanatory
2. Aligned with human cognition
* Brain prefers causality over memorization
3. High transferability
* Students could apply knowledge, not recall it
4. Low entropy
* Minimal confusion, maximal clarity
VII. UNIVERSAL FRAMEWORK (REUSABLE)
You can apply this everywhere:
Step 1 — Identify the phenomenon
* What is actually happening?
Step 2 — Introduce directional structure
* Like positive/negative
Step 3 — Build scenarios
* Concrete cases
Step 4 — Extract invariants
* What must always hold?
Step 5 — Generalize rule
* Not imposed—discovered
⸻
VIII. FINAL SYNTHESIS
Kiselev represents a rare category:
A pedagogical system that encodes thinking itself.
And the deeper law behind it:
Systems that derive truth from necessity outcompete systems that impose rules from authority.